Buchmann, N. A.; Atkinson, C.; Jeremy, M. C.; Soria, J.
2011-04-01
Hemodynamic forces within the human carotid artery are well known to play a key role in the initiation and progression of vascular diseases such as atherosclerosis. The degree and extent of the disease largely depends on the prevailing three-dimensional flow structure and wall shear stress (WSS) distribution. This work presents tomographic PIV (Tomo-PIV) measurements of the flow structure and WSS in a physiologically accurate model of the human carotid artery bifurcation. The vascular geometry is reconstructed from patient-specific data and reproduced in a transparent flow phantom to demonstrate the feasibility of Tomo-PIV in a complex three-dimensional geometry. Tomographic reconstruction is performed with the multiplicative line-of-sight (MLOS) estimation and simultaneous multiplicative algebraic reconstruction (SMART) technique. The implemented methodology is validated by comparing the results with Stereo-PIV measurements in the same facility. Using a steady flow assumption, the measurement error and RMS uncertainty are directly inferred from the measured velocity field. It is shown that the measurement uncertainty increases for increasing light sheet thickness and increasing velocity gradients, which are largest near the vessel walls. For a typical volume depth of 6 mm (or 256 pixel), the analysis indicates that the velocity derived from 3D cross-correlation can be measured within ±2% of the maximum velocity (or ±0.2 pixel) near the center of the vessel and within ±5% (±0.6 pixel) near the vessel wall. The technique is then applied to acquire 3D-3C velocity field data at multiple axial locations within the carotid artery model, which are combined to yield the flow field and WSS in a volume of approximately 26 mm × 27 mm × 60 mm. Shear stress is computed from the velocity gradient tensor and a method for inferring the WSS distribution on the vessel wall is presented. The results indicate the presence of a complex and three-dimensional flow structure, with
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K;
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation...
Oxygen transfer in human carotid artery bifurcation
Institute of Scientific and Technical Information of China (English)
Z.G.Zhang; Y.B.Fan; X.Y.Deng
2007-01-01
Arterial bifurcations are places where blood flow may be disturbed and slow recirculation flow may occur.To reveal the correlation between local oxygen transfer and atherogenesis, a finite element method was employed to simulate the blood flow and the oxygen transfer in the human carotid artery bifurcation. Under steady-state flow conditions, the numerical simulation demonstrated a variation in local oxygen transfer at the bifurcation, showing that the convective condition in the disturbed flow region may produce uneven local oxygen transfer at the blood/wall interface.The disturbed blood flow with formation of slow eddies in the carotid sinus resulted in a depression in oxygen supply to the arterial wall at the entry of the sinus, which in turn may lead to an atherogenic response of the arterial wall, and contribute to the development of atherosclerotic stenosis there.
Shape optimization of the carotid artery bifurcation
Bressloff, N. W.; Forrester, A.I.J.; Banks, J.; Bhaskar, K.V.
2004-01-01
A parametric CAD model of the human carotid artery bifurcation is employed in an initial exploration of the response of shear stress to the variation of the angle of the internal carotid artery and the width of the sinus bulb. Design of experiment and response surface technologies are harnessed for the first time in such an application with the aim of developing a better understanding of the relationship between geometry (anatomy) and sites of arterial disease.
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K;
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T....... The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Mathematical model for blood flow through a bifurcated artery using couple stress fluid.
Srinivasacharya, D; Madhava Rao, G
2016-08-01
In this article, the blood flow through a bifurcated artery with mild stenosis is investigated taking blood as couple stress fluid. The artery configuring bifurcation is assumed to be symmetric about the axis of the artery and straight cylinders of finite length. The governing equations are non-dimensionalized and coordinate transformation is used to convert the irregular boundary to a regular boundary. The resulting system of equations is solved numerically using the finite difference method. The variation of shear stress, flow rate and impedance near the apex with pertinent parameters are studied graphically. It has been noticed that shear stress, flow rate and impedance have been changing suddenly with all the parameters on both sides of the apex. This occurs because of the backflow of the streaming blood at the onset of the lateral junction and secondary flow near the apex in the daughter artery.
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Lee, Cheng-Hung [Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Linkou, Chang Gung University College of Medicine, Tao-Yuan, Taiwan (China); Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan (China); Jhong, Guan-Heng [Graduate Institute of Medical Mechatronics, Chang Gung University, Tao-Yuan, Taiwan (China); Hsu, Ming-Yi; Wang, Chao-Jan [Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital, Linkou, Tao-Yuan, Taiwan (China); Liu, Shih-Jung, E-mail: shihjung@mail.cgu.edu.tw [Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan (China); Hung, Kuo-Chun [Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Linkou, Chang Gung University College of Medicine, Tao-Yuan, Taiwan (China)
2014-05-28
The deployment of metallic stents during percutaneous coronary intervention has become common in the treatment of coronary bifurcation lesions. However, restenosis occurs mostly at the bifurcation area even in present era of drug-eluting stents. To achieve adequate deployment, physicians may unintentionally apply force to the strut of the stents through balloon, guiding catheters, or other devices. This force may deform the struts and impose excessive mechanical stresses on the arterial vessels, resulting in detrimental outcomes. This study investigated the relationship between the distribution of stress in a stent and bifurcation angle using finite element analysis. The unintentionally applied force following stent implantation was measured using a force sensor that was made in the laboratory. Geometrical information on the coronary arteries of 11 subjects was extracted from contrast-enhanced computed tomography scan data. The numerical results reveal that the application of force by physicians generated significantly higher mechanical stresses in the arterial bifurcation than in the proximal and distal parts of the stent (post hoc P < 0.01). The maximal stress on the vessels was significantly higher at bifurcation angle <70° than at angle ≧70° (P < 0.05). The maximal stress on the vessels was negatively correlated with bifurcation angle (P < 0.01). Stresses at the bifurcation ostium may cause arterial wall injury and restenosis, especially at small bifurcation angles. These finding highlight the effect of force-induced mechanical stress at coronary artery bifurcation stenting, and potential mechanisms of in-stent restenosis, along with their relationship with bifurcation angle.
Wall Shear Stress Distribution in Patient Specific Coronary Artery Bifurcation
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Vahab Dehlaghi
2010-01-01
Full Text Available Problem statement: Atherogenesis is affected by hemodynamic parameters, such as wall shear stress and wall shear stress spatial gradient. These parameters are largely dependent on the geometry of arterial tree. Arterial bifurcations contain significant flow disturbances. Approach: The effects of branch angle and vessel diameter ratio at the bifurcations on the wall shear stress distribution in the coronary arterial tree based on CT images were studied. CT images were digitally processed to extract geometrical contours representing the coronary vessel walls. The lumen of the coronary arteries of the patients was segmented using the open source software package (VMTK. The resulting lumens of coronary arteries were fed into a commercial mesh generator (GAMBIT, Fluent Inc. to generate a volume that was filled with tetrahedral elements. The FIDAP software (Fluent Corp. was used to carry out the simulation by solving Navier-Stokes equations. The FIELDVIEW software (Version 10.0, Intelligent Light, Lyndhurst, NJ was used for the visualization of flow patterns and the quantification of wall shear stress. Post processing was done with VMTK and MATLAB. A parabolic velocity profile was prescribed at the inlets and outlets, except for 1. Stress free outlet was assigned to the remaining outlet. Results: The results show that for angle lower than 90°, low shear stress regions are observed at the non-flow divider and the apex. For angle larger than 90°, low shear stress regions only at the non-flow divider. By increasing of diameter of side branch ratio, low shear stress regions in the side branch appear at the non-flow divider. Conclusion: It is concluded that not only angle and diameter are important, but also the overall 3D shape of the artery. More research is required to further quantify the effects angle and diameter on shear stress patterns in coronaries.
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Omid Arjmandi-Tash
2012-12-01
Full Text Available Introduction: Atherosclerosis is a focal disease that susceptibly forms near bifurcations, anastomotic joints, side branches, and curved vessels along the arterial tree. In this study, pulsatile blood flow in a bifurcation model with a non-planar branch is investigated. Methods: Wall shear stress (WSS distributions along generating lines on vessels for different bifurcation angles are calculated during the pulse cycle. Results: The WSS at the outer side of the bifurcation plane vanishes especially for higher bifurcation angles but by increasing the bifurcation angle low WSS region squeezes. At the systolic phase there is a high possibility of formation of a separation region at the outer side of bifurcation plane for all the cases. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these peaks drop as bifurcation angle is increased. Conclusion: It was found that non-planarity of the daughter vessel lowers the minimum WSS at the outer side of the bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky.
Sultanov, Renat A
2008-01-01
We report computational results of blood flow through a model of the human aortic arch and a vessel of actual diameter and length. On the top of the aortic arch the branching of the %%three arteries are included: the subclavian and jugular. A realistic pulsatile flow is used in all simulations. Calculations for bifurcation type vessels are also carried out and presented. Different mathematical methods for numerical solution of the fluid dynamics equations have been considered. The non-Newtonian behaviour of the human blood is investigated together with turbulence effects. A detailed time-dependent mathematical convergence test has been carried out. The results of computer simulations of the blood flow in vessels of three different geometries are presented: for pressure, strain rate and velocity component distributions we found significant disagreements between our results obtained with realistic non-Newtonian treatment of human blood and the widely used method in the literature: a simple Newtonian approximati...
Huang, Xu; Yin, Xiaoping; Xu, Yingjin; Jia, Xinwei; Li, Jianhui; Niu, Pei; Shen, Wenzeng; Kassab, Ghassan S; Tan, Wenchang; Huo, Yunlong
2016-03-01
Although atherosclerosis has been widely investigated at carotid artery bifurcation, there is a lack of morphometric and hemodynamic data at different stages of the disease. The purpose of this study was to determine the lesion difference in patients with carotid artery disease compared with healthy control subjects. The three-dimensional (3D) geometry of carotid artery bifurcation was reconstructed from computed tomography angiography (CTA) images of Chinese control subjects (n = 30) and patients with carotid artery disease (n = 30). We defined two novel vector angles (i.e., angles 1 and 2) that were tangential to the reconstructed contour of the 3D vessel. The best-fit diameter was computed along the internal carotid artery (ICA) center line. Hemodynamic analysis was performed at various bifurcations. Patients with stenotic vessels have larger angles 1 and 2 (151 ± 11° and 42 ± 20°) and smaller diameters of the external carotid artery (ECA) (4.6 ± 0.85 mm) compared with control subjects (144 ± 13° and 36 ± 16°, 5.2 ± 0.57 mm) although there is no significant difference in the common carotid artery (CCA) (7.1 ± 1.2 vs. 7.5 ± 1.0 mm, P = 0.18). In particular, all patients with carotid artery disease have a stenosis at the proximal ICA (including both sinus and carina regions), while 20% of patients have stenosis at the middle ICA and 20% have stenosis expansion to the entire cervical ICA. Morphometric and hemodynamic analyses suggest that atherosclerotic plaques initiate at both sinus and carina regions of ICA and progress downstream.
Lee, Cheng-Hung; Jhong, Guan-Heng; Hsu, Ming-Yi; Liu, Shih-Jung; Wang, Chao-Jan; Hung, Kuo-Chun
2014-05-01
The deployment of metallic stents during percutaneous coronary intervention has become common in the treatment of coronary bifurcation lesions. However, restenosis occurs mostly at the bifurcation area even in present era of drug-eluting stents. To achieve adequate deployment, physicians may unintentionally apply force to the strut of the stents through balloon, guiding catheters, or other devices. This force may deform the struts and impose excessive mechanical stresses on the arterial vessels, resulting in detrimental outcomes. This study investigated the relationship between the distribution of stress in a stent and bifurcation angle using finite element analysis. The unintentionally applied force following stent implantation was measured using a force sensor that was made in the laboratory. Geometrical information on the coronary arteries of 11 subjects was extracted from contrast-enhanced computed tomography scan data. The numerical results reveal that the application of force by physicians generated significantly higher mechanical stresses in the arterial bifurcation than in the proximal and distal parts of the stent (post hoc P stenting, and potential mechanisms of in-stent restenosis, along with their relationship with bifurcation angle.
Vourliotakis, Georgios; Mantas, Georgios; Katsargyris, Athanasios; Aivatidi, Christine; Kandounakis, Yannis
2013-10-01
A 71-year-old male patient with severe left buttock and lower-extremity claudication due to iliac artery bifurcation stenoses was referred to our institution for endovascular treatment. A 'kissing' technique was used in order to dilate the proximal parts of both internal and external iliac arteries and avoid compromization of the internal iliac artery during proximal external iliac artery stenting. A balloon expandable stent was inserted via a left ipsilateral retrograde access to the narrowed origin of the left external iliacartery and a balloon catheter via a right contralateral access inside the origin of the left internal iliac artery. Simultaneous balloons inflation restored full patency of both vessels. Twelve months later the patient is doing well, free of buttock or lower-extremity claudication symptoms. For iliac artery bifurcation atherosclerotic disease, endovascular repair with the 'kissing' technique can achieve a complete bifurcation reconstruction offering significant clinical benefit in selected patients. PMID:23493274
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Zhonghua Sun
2013-01-01
Full Text Available The aim of this study is to investigate the relationship between intraluminal appearances of coronary plaques and left coronary bifurcation angle and plaque components using coronary CT virtual intravascular endoscopy (VIE. Fifty patients suspected of coronary artery disease undergoing coronary CT angiography were included in the study. The left bifurcation angle in patients with diseased left coronary artery which was measured as 94.3° ± 16.5 is significantly larger than that in patients with normal left coronary artery, which was measured as 76.5° ± 15.9 (P<0.001. Irregular VIE appearances were found in 10 out of 11 patients with mixed plaques in the left anterior descending (LAD and left circumflex (LCx, while, in 29 patients with calcified plaques in the LAD and LCx, irregular VIE appearances were only noticed in 5 patients. Using 80° as a cut-off value to determine coronary artery disease, smooth VIE appearances were found in 95% of patients (18/19 with left bifurcation angle of less than 80°, while irregular VIE appearances were observed in nearly 50% of patients (15/31 with left bifurcation angle of more than 80°. This preliminary study shows that VIE appearances of the coronary lumen are directly related to the types of plaques.
Endovascular coil embolization in internal carotid artery bifurcation aneurysms
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Aim: To present the clinical and radiological results of coil embolization in internal carotid artery (ICA) bifurcation aneurysms (BA). Materials and methods: The records of 65 patients with 66 ICA BA were retrieved from data prospectively accrued between September 1999 and July 2013. Clinical and morphological outcomes of the aneurysms were assessed, including technical aspects of treatment. Results: The aneurysms under study were directed either superiorly (41/66, 62.1%), anteriorly (24/66, 36.4%), or posteriorly (1/66, 1.5%), and all were devoid of perforators. Aneurysmal necks were situated symmetrically at the terminal ICA (37/66, 56.1%) or slightly deviated to the proximal A1 segment (29/66, 43.9%). The steam-shaped S microcatheter (73.8%) was most commonly used to select the aneurysms, and the single microcatheter technique was most commonly applied (56.1%) to perform coil embolization, followed by balloon remodelling (21.2%), multiple microcatheter (15.1%), and stent-protection (7.6%). Successful aneurysmal occlusion was achieved in 100% of cases, with no procedure-related morbidity or mortality. Imaging performed in the course of follow-up (mean duration 27.3 months) confirmed stable occlusion of most lesions (47/53, 88.7%). Conclusion: Through tailored technical strategies, ICA BA are amenable to safe and effective endovascular coil embolization, with a tendency for stable occlusion long-term
Impact of local flow haemodynamics on atherosclerosis in coronary artery bifurcations.
Antoniadis, Antonios P; Giannopoulos, Andreas A; Wentzel, Jolanda J; Joner, Michael; Giannoglou, George D; Virmani, Renu; Chatzizisis, Yiannis S
2015-01-01
Coronary artery bifurcations are susceptible to atherosclerosis as a result of the unique local flow patterns and the subsequent endothelial shear stress (ESS) environment that are conducive to the development of plaques. Along the lateral walls of the main vessel and side branches, a distinct flow pattern is observed with local low and oscillatory ESS, while high ESS develops at the flow divider (carina). Histopathologic studies have shown that the distribution of plaque at bifurcation regions is related to the local ESS patterns. The local ESS profile also influences the outcome of percutaneous coronary interventions in bifurcation lesions. A variety of invasive and non-invasive imaging modalities have enabled 3D reconstruction of coronary bifurcations and thereby detailed local ESS assessment by computational fluid dynamics. Highly effective strategies for treatment and ultimately prevention of atherosclerosis in coronary bifurcations are anticipated with the use of advanced imaging and computational fluid dynamic techniques.
Numerical investigation of blood flow in a deformable coronary bifurcation and non-planar branch
Razavi, Seyed Esmail; Omidi, Amir Ali; Saghafi Zanjani, Massoud
2014-01-01
Introduction: Among cardiovascular diseases, arterials stenosis is recognized more commonly than the others. Hemodynamic characteristics of blood play a key role in the incidence of stenosis. This paper numerically investigates the pulsatile blood flow in a coronary bifurcation with a non-planar branch. To create a more realistic analysis, the wall is assumed to be compliant. Furthermore, the flow is considered to be three-dimensional, incompressible, and laminar. Methods: The effects of non-Newtonian blood, compliant walls and different angles of bifurcation on hemodynamic characteristics of flow were evaluated. Shear thinning of blood was simulated with the Carreau-Yasuda model. The current research was mainly focused on the flow characteristics in bifurcations since atherosclerosis occurs mostly in bifurcations. Moreover, as the areas with low shear stresses are prone to stenosis, these areas were identified. Results: Our findings indicated that the compliant model of the wall, bifurcation’s angle, and other physical properties of flow have an impact on hemodynamics of blood flow. Lower wall shear stress was observed in the compliant wall than that in the rigid wall. The outer wall of bifurcation in all models had lower wall shear stress. In bifurcations with larger angles, wall shear stress was higher in outer walls, and lower in inner walls. Conclusion: The non-Newtonian blood vessels and different angles of bifurcation on hemodynamic characteristics of flow evaluation confirmed a lower wall shear stress in the compliant wall than that in the rigid wall, while the wall shear stress was higher in outer walls but lower in inner walls in the bifurcation regions with larger angles. PMID:25671176
Baharoglu, Merih I; Lauric, Alexandra; Wu, Chengyuan; Hippelheuser, James; Malek, Adel M
2014-10-17
Cerebral aneurysms form preferentially at arterial bifurcations. The vascular optimality principle (VOP) decrees that minimal energy loss across bifurcations requires optimal caliber control between radii of parent (r₀) and daughter branches (r1 and r2): r₀(n)=r₁(n)+r₂(n), with n approximating three. VOP entails constant wall shear stress (WSS), an endothelial phenotype regulator. We sought to determine if caliber control is maintained in aneurysmal intracranial bifurcations. Three-dimensional rotational angiographic volumes of 159 middle cerebral artery (MCA) bifurcations (62 aneurysmal) were processed using 3D gradient edge-detection filtering, enabling threshold-insensitive radius measurement. Radius ratio (RR)=r₀(3)/(r₁(3)+r₂(3)) and estimated junction exponent (n) were compared between aneurysmal and non-aneurysmal bifurcations using Student t-test and Wilcoxon rank-sum analysis. The results show that non-aneurysmal bifurcations display optimal caliber control with mean RR of 1.05 and median n of 2.84. In contrast, aneurysmal bifurcations had significantly lower RR (0.76, pbifurcations revealed a daughter branch larger than its parent vessel, an absolute violation of optimality, not witnessed in non-aneurysmal bifurcations. The aneurysms originated more often off the smaller daughter (52%) vs. larger daughter branch (16%). Aneurysm size was not statistically correlated to RR or n. Aneurysmal males showed higher deviation from VOP. Non-aneurysmal MCA bifurcations contralateral to aneurysmal ones showed optimal caliber control. Aneurysmal bifurcations, in contrast to non-aneurysmal counterparts, disobey the VOP and may exhibit dysregulation in WSS-mediated caliber control. The mechanism of this focal divergence from optimality may underlie aneurysm pathogenesis and requires further study.
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ZHANG Zhen-hai; YANG Xin-jian; WU Zhong-xue; LI You-xiang; JIANG Peng
2012-01-01
This report documents the treatment of a giant aneurysm of the internal carotid artery bifurcation with a fistula to the cavernous sinus,which appeared following closed head trauma.A 39-year-old man suffered from a blunt head trauma in an automobile accident.Two weeks after the trauma,progressive chemosis of left eye was presented.Four months after the trauma,digital subtraction angiography showed an internal carotid artery bifurcation aneurysm,with drainage into the cavernous sinus.The lesion was successfully obliterated with preservation of the parent artery by using coils in conjunction with Onyx.Follow-up angiography obtained 3 months postoperatively revealed persistent obliteration of the aneurysm and fistula as well as patency of the parent artery.Endovascular treatment involving the use of coils combined with Onyx appears to be a feasible and effective option for treatment of this hard-to-treat lesion.
Bending and twisting of an in vivo coronary artery at a bifurcation.
Pao, Y C; Lu, J T; Ritman, E L
1992-03-01
Dynamic changes in the geometric shape and dimensions of a left coronary artery tree were extracted from the computer-tomographically reconstructed three-dimensional images of an in situ beating heart of an anesthetized dog. Wireframe models of the left coronary artery tree at 16 different instants of a cardiac cycle were constructed for the study of its flexing motion. For quantifying the local bending and twisting of the left coronary artery tree, the anatomic landmarks of the bifurcation points are selected as focussed locations. At these points, the space curves of the tree at different cardiac instants were first derived in parametric forms. Curvature and torsion expressions are next obtained in terms of the derivatives with respect to the parameter. This analysis revealed that during the initial contraction of the heart wall, a 2% reduction per millisecond in the radius of curvature occurred near the bifurcation point where the left circumflex coronary artery descends toward the apex of the heart. When the left ventricular chamber reached a maximum value, the radius of curvature was found to decrease at a rate of 2.3% ms-1. At the end of diastole, an increase in the radius of curvature at a rate of 5.7% ms-1 was observed. The twisting rates per unit length of artery near the bifurcation point of the selected artery were found to range from -0.62 to 0.63 degrees ms-1.
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Aim: To investigate the angle changes of the parent arteries after stent-assisted coil embolization of wide-necked intracranial bifurcation aneurysms. Materials and methods: The adjacent parent arterial angles before and after stent-assisted coil embolization were measured in 38 patients with aneurysms of the anterior communicating artery (ACoAA) and 41 patients with bifurcation aneurysms of the middle cerebral artery (MCABA). Variables were analysed in relation to the angle changes. Results: Vascular angles of the parent arteries significantly increased by 27.8° (±18.5°) immediately after stent-assisted coil embolization in 79 cases (p < 0.001), with 25.7° (±14.8°) in ACoAA and 29.7° (±21.4°) in MCABA, respectively. In 51 (64.6%) cases with follow-up angiography (mean interval 13.5 ± 4.1 months), vascular angles increased by 27.2° (±17.1°) immediately after treatment and further increased by 20.7° (±14.3°) at the last follow-up (all p < 0.001). More acute pre-stent angles of the parent arteries correlated with greater post-stent angle changes (p = 0.006). Younger age tended to be inversely related to post-stent angle changes (p = 0.091). Conclusion: Stent placement during coil embolization induced significant changes in the aneurysm–parent artery relationship. Further study is needed to elicit the association between angle change of the parent arteries and aneurysmal stability after coil embolization
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Chen, Yong, E-mail: cheny102@163.com; Ye, Peng, E-mail: thomas19871223@163.com [Southern Medical University, Department of Interventional Radiology, Nanfang Hospital (China); Jiang, Wen-jin, E-mail: 18653501187@163.com [Yantai Yuhuangding Hospital (China); Ma, Shuo-yi, E-mail: mazelong123456789@126.com; Zhao, Jian-bo, E-mail: zhaojianbohgl@163.com; Zeng, Qing-le, E-mail: doctorzengqingle@126.com [Southern Medical University, Department of Interventional Radiology, Nanfang Hospital (China)
2015-10-15
Bifurcation stenoses after end-to-side anastomosis of transplant renal artery (TRA) and external iliac artery (EIA), including stenoses at the anastomosis and the iliac artery proximal to the TRA, are rare. In the present article, we report two successfully managed cases of bifurcation stenoses after end-to-side anastomosis of the TRA and EIA using the technique of T-stenting and small protrusion (TAP stenting)
Perwaiz Khan, Samia; Gul, Pashmina; Khemani, Saleem; Yaqub, Zia
2013-01-01
Objective: To determine site specific carotid intima-media thickness: common–carotid artery and carotid bifurcation in hypercholesterolemia patients as a marker for atherosclerosis. Methods: Fifty patients with hypercholesterolemia and twenty controls were selected after getting informed consent regarding the investigation of carotid- intima media thickness by B-mode ultrasound. All the patients of hypercholesterolemia with LDL-C > 160mg/dL had family history of coronary artery diseases. This...
Suárez-Bagnasco, D.; Balay, G.; Cymberknop, L.; Armentano, R. L.; Negreira, C. A.
2013-03-01
Arterial behaviour in-vivo is influenced, amongst other factors, by the interaction between blood flow and the arterial wall endothelium, and the biomechanical properties of the arterial wall. This interaction plays an important role in pathogenic mechanisms of cardiovascular diseases such as atherosclerosis and arteriosclerosis. To quantify these interactions both from biomechanical and hemodynamical standpoints, a complete characterization and modelling of the arterial wall, blood flow, shear wall and circumferential wall stresses are needed. The development of a new multi-parameter measurement system (distances, pressures, flows, velocity profiles, temperature, viscosity) for an in-vitro characterization of the biomechanics and hemodynamics in arterial bifurcations (specially in carotid bifurcations) is described. This set-up represents an improvement relative to previous set-ups developed by the group FCIEN-FMED and is presently under development. Main subsystems interactions and environment-system interactions were identified and compensated to improve system's performance. Several interesting problems related with signal acquisition using a variety of sensors and some experimental results are shown and briefly discussed. Experimental data allow construction of meshes and parameter estimation of the biomechanical properties of the arterial wall, as well as boundary conditions, all suitable to be employed in CFD and FSI numerical simulation.
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Objective: To preliminarily evaluate the feasibility, safety and efficacy of stent placement for the treatment of wide-necked aneurysms located at internal carotid artery bifurcation. Methods: Eleven patients with wide-necked aneurysms located at internal carotid artery bifurcation, who were encountered during the period from Jan. 2004 to Dec. 2010 in hospital, were collected. A total of 16 intracranial aneurysms were detected, of which 11 were wide-necked and were located at internal carotid artery bifurcation. The diameters of the aneurysms ranged from 2.5 mm to 18 mm. Individual stent type and stenting technique was employed for each patient. Follow-up at 1, 3, 6 and 12 months after the procedure was conducted. Results: A total of 11 different stents were successfully deployed in the eleven patients. The stents included balloon expandable stent (n=1) and self-expanding stent (n=10). According to Raymond grading for the immediate occlusion of the aneurysm, grade Ⅰ (complete obliteration) was obtained in 4, grade Ⅱ (residual neck) in 2 and grade Ⅲ (residual aneurysm) in 5 cases. No procedure-related complications occurred. At the time of discharge, the modified Rankin score was 0-1 in the eleven patients. During the follow-up period lasting for 1-108 months, all the patients were in stable condition and no newly-developed neurological dysfunction or bleeding observed. Follow-up examination with angiography (1-48 months) showed that the aneurysms were cured (no visualization) in 4 cases, improved in 2 cases and in stable condition in one case. Conclusion: For the treatment of wide-necked aneurysms located at internal carotid artery bifurcation, stent implantation is clinically feasible, safe and effective. Further studies are required to evaluate its long-term efficacy. (authors)
Atherosclerosis at arterial bifurcations: evidence for the role of haemodynamics and geometry.
Morbiducci, Umberto; Kok, Annette M; Kwak, Brenda R; Stone, Peter H; Steinman, David A; Wentzel, Jolanda J
2016-03-01
Atherosclerotic plaques are found at distinct locations in the arterial system, despite the exposure to systemic risk factors of the entire vascular tree. From the study of arterial bifurcation regions, emerges ample evidence that haemodynamics are involved in the local onset and progression of the atherosclerotic disease. This observed co-localisation of disturbed flow regions and lesion prevalence at geometrically predisposed districts such as arterial bifurcations has led to the formulation of a 'haemodynamic hypothesis', that in this review is grounded to the most current research concerning localising factors of vascular disease. In particular, this review focuses on carotid and coronary bifurcations because of their primary relevance to stroke and heart attack. We highlight reported relationships between atherosclerotic plaque location, progression and composition, and fluid forces at vessel's wall, in particular shear stress and its 'easier-to-measure' surrogates, i.e. vascular geometric attributes (because geometry shapes the flow) and intravascular flow features (because they mediate disturbed shear stress), in order to give more insight in plaque initiation and destabilisation. Analogous to Virchow's triad for thrombosis, atherosclerosis must be thought of as subject to a triad of, and especially interactions among, haemodynamic forces, systemic risk factors, and the biological response of the wall.
Atherosclerosis at arterial bifurcations: evidence for the role of haemodynamics and geometry.
Morbiducci, Umberto; Kok, Annette M; Kwak, Brenda R; Stone, Peter H; Steinman, David A; Wentzel, Jolanda J
2016-03-01
Atherosclerotic plaques are found at distinct locations in the arterial system, despite the exposure to systemic risk factors of the entire vascular tree. From the study of arterial bifurcation regions, emerges ample evidence that haemodynamics are involved in the local onset and progression of the atherosclerotic disease. This observed co-localisation of disturbed flow regions and lesion prevalence at geometrically predisposed districts such as arterial bifurcations has led to the formulation of a 'haemodynamic hypothesis', that in this review is grounded to the most current research concerning localising factors of vascular disease. In particular, this review focuses on carotid and coronary bifurcations because of their primary relevance to stroke and heart attack. We highlight reported relationships between atherosclerotic plaque location, progression and composition, and fluid forces at vessel's wall, in particular shear stress and its 'easier-to-measure' surrogates, i.e. vascular geometric attributes (because geometry shapes the flow) and intravascular flow features (because they mediate disturbed shear stress), in order to give more insight in plaque initiation and destabilisation. Analogous to Virchow's triad for thrombosis, atherosclerosis must be thought of as subject to a triad of, and especially interactions among, haemodynamic forces, systemic risk factors, and the biological response of the wall. PMID:26740210
International Nuclear Information System (INIS)
Purpose: Simple rating scale for calcification in the cervical arteries and the aortic arch on multi-detector computed tomography angiography (MDCTA) was evaluated its reliability and validity. Additionally, we investigated where is the most representative location for evaluating the calcification risk of carotid bifurcation stenosis and atherosclerotic infarction in the overall cervical arteries covering from the aortic arch to the carotid bifurcation. Method: The aortic arch and cervical arteries among 518 patients (292 men, 226 women) were evaluated the extent of calcification using a 4-point grading scale for MDCTA. Reliability, validity and the concomitant risk with vascular stenosis and atherosclerotic infarction were assessed. Results: Calcification was most frequently observed in the aortic arch itself, the orifices from the aortic arch, and the carotid bifurcation. Compared with the bilateral carotid bifurcations, the aortic arch itself had a stronger inter-observer agreement for the calcification score (Fleiss’ kappa coefficients; 0.77), but weaker associations with stenosis and atherosclerotic infarction. Calcification at the orifices of the aortic arch branches had a stronger inter-observer agreement (0.74) and enough associations with carotid bifurcation stenosis and intracranial stenosis. In addition, the extensive calcification at the orifices from the aortic arch was significantly associated with atherosclerotic infarction, similar to the calcification at the bilateral carotid bifurcations. Conclusions: The orifices of the aortic arch branches were the novel representative location of the aortic arch and overall cervical arteries for evaluating the calcification extent. Thus, calcification at the aortic arch should be evaluated with focus on the orifices of 3 main branches
Energy Technology Data Exchange (ETDEWEB)
Yamada, Shigeki, E-mail: shigekiyamada3@gmail.com [Department of Neurosurgery and Stroke Center, Rakuwakai Otowa Hospital, Kyoto (Japan); Interfaculty Initiative in Information Studies/Institute of Industrial Science, The University of Tokyo, Tokyo (Japan); Department of Neurosurgery, Hamamatsu Rosai Hospital, Shizuoka (Japan); Hashimoto, Kenji, E-mail: hashiken8022@yahoo.co.jp [Department of Neurosurgery, Kishiwada Municipal Hospital, Osaka (Japan); Ogata, Hideki, E-mail: hidogata@gmail.com [Department of Neurosurgery, Hamamatsu Rosai Hospital, Shizuoka (Japan); Watanabe, Yoshihiko, E-mail: ynabe@magic.odn.ne.jp [Department of Neurosurgery, Hamamatsu Rosai Hospital, Shizuoka (Japan); Oshima, Marie, E-mail: marie@iis.u-tokyo.ac.jp [Interfaculty Initiative in Information Studies/Institute of Industrial Science, The University of Tokyo, Tokyo (Japan); Miyake, Hidenori, E-mail: hi-miyake@hamamatsuh.rofuku.go.jp [Department of Neurosurgery, Hamamatsu Rosai Hospital, Shizuoka (Japan)
2014-02-15
Purpose: Simple rating scale for calcification in the cervical arteries and the aortic arch on multi-detector computed tomography angiography (MDCTA) was evaluated its reliability and validity. Additionally, we investigated where is the most representative location for evaluating the calcification risk of carotid bifurcation stenosis and atherosclerotic infarction in the overall cervical arteries covering from the aortic arch to the carotid bifurcation. Method: The aortic arch and cervical arteries among 518 patients (292 men, 226 women) were evaluated the extent of calcification using a 4-point grading scale for MDCTA. Reliability, validity and the concomitant risk with vascular stenosis and atherosclerotic infarction were assessed. Results: Calcification was most frequently observed in the aortic arch itself, the orifices from the aortic arch, and the carotid bifurcation. Compared with the bilateral carotid bifurcations, the aortic arch itself had a stronger inter-observer agreement for the calcification score (Fleiss’ kappa coefficients; 0.77), but weaker associations with stenosis and atherosclerotic infarction. Calcification at the orifices of the aortic arch branches had a stronger inter-observer agreement (0.74) and enough associations with carotid bifurcation stenosis and intracranial stenosis. In addition, the extensive calcification at the orifices from the aortic arch was significantly associated with atherosclerotic infarction, similar to the calcification at the bilateral carotid bifurcations. Conclusions: The orifices of the aortic arch branches were the novel representative location of the aortic arch and overall cervical arteries for evaluating the calcification extent. Thus, calcification at the aortic arch should be evaluated with focus on the orifices of 3 main branches.
Model generation of coronary artery bifurcations from CTA and single plane angiography
Energy Technology Data Exchange (ETDEWEB)
Cardenes, Ruben; Diez, Jose L.; Duchateau, Nicolas; Pashaei, Ali; Frangi, Alejandro F. [Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018 (Spain); Cardiology Department, University Hospital Dr. Peset, Valencia 46017 (Spain); Hospital Clinic Provincial de Barcelona, Institut d' investigacions Biomediques August Pi i Sunyer-Universitat de Barcelona, Barcelona 08036 (Spain); Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018 (Spain); Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018, Spain and Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)
2013-01-15
Purpose: To generate accurate and realistic models of coronary artery bifurcations before and after percutaneous coronary intervention (PCI), using information from two image modalities. Because bifurcations are regions where atherosclerotic plaque appears frequently and intervention is more challenging, generation of such realistic models could be of high value to predict the risk of restenosis or thrombosis after stent implantation, and to study geometrical and hemodynamical changes. Methods: Two image modalities have been employed to generate the bifurcation models: computer tomography angiography (CTA) to obtain the 3D trajectory of vessels, and 2D conventional coronary angiography (CCA) to obtain radius information of the vessel lumen, due to its better contrast and image resolution. In addition, CCA can be acquired right before and after the intervention in the operation room; therefore, the combination of CTA and CCA allows the generation of realistic preprocedure and postprocedure models of coronary bifurcations. The method proposed is semiautomatic, based on landmarks manually placed on both image modalities. Results: A comparative study of the models obtained with the proposed method with models manually obtained using only CTA, shows more reliable results when both modalities are used together. The authors show that using preprocedure CTA and postprocedure CCA, realistic postprocedure models can be obtained. Analysis carried out of the Murray's law in all patient bifurcations shows the geometric improvement of PCI in our models, better than using manual models from CTA alone. An experiment using a cardiac phantom also shows the feasibility of the proposed method. Conclusions: The authors have shown that fusion of CTA and CCA is feasible for realistic generation of coronary bifurcation models before and after PCI. The method proposed is efficient, and relies on minimal user interaction, and therefore is of high value to study geometric and
Javadzadegan, Ashkan; Lotfi, Azadeh; Simmons, Anne; Barber, Tracie
2016-08-01
Thrombus in a femoral artery may form under stagnant flow conditions which vary depending on the local arterial waveform. Four different physiological flow waveforms - poor (blunt) monophasic, sharp monophasic, biphasic and triphasic - can exist in the femoral artery as a result of different levels of peripheral arterial disease progression. This study aims to examine the effect of different physiological waveforms on femoral artery haemodynamics. In this regard, a fluid-structure interaction analysis was carried out in idealised models of bifurcated common femoral artery. The results showed that recirculation zones occur in almost all flow waveforms; however, the sites at where these vortices are initiated, the size and structure of vortices are highly dependent on the type of flow waveform being used. It was shown that the reverse diastolic flow in biphasic and triphasic waveforms leads to the occurrence of a retrograde flow which aids in 'washout' of the disturbed flow regions. This may limit the likelihood of thrombus formation, indicating the antithrombotic role of retrograde flow in femoral arteries. Furthermore, our data revealed that the flow particles experience considerably higher residence time under blunt and sharp monophasic waveforms than under biphasic and triphasic waveforms. This confirms that the risk of atherothrombotic plaque initiation and development in femoral arteries is higher under blunt and sharp monophasic waveforms than under biphasic and triphasic flow waveforms. PMID:26582544
Effect of blood flow parameters on flow patterns at arterial bifurcations--studies in models.
Liepsch, D W
1990-01-01
Atherosclerotic lesions are found primarily at arterial bends and bifurcations. Flow disturbances at these anatomic sites play a major role in atherogenesis. How hemodynamic factors such as vessel geometry, the pulsatile nature of blood flow, vessel wall elasticity and the non-Newtonian flow behavior of blood influence the flow field at these sites must be clarified. We have performed fundamental studies using a birefringent solution in a simplified rigid 90 degree T-bifurcation and pulsatile flow. The velocity distribution was measured with a laser Doppler anemometer. Flow in an elastic abdominal aorta model has been visualized using magnetic resonance imaging. In both flow studies, zones with negative velocity were found. These model measurements demonstrate that no flow parameter can be neglected. Further detailed studies are necessary to examine the interaction between fluid dynamic and cellular surface properties. PMID:2404201
Kefayati, Sarah; Poepping, Tamie L
2013-07-01
Blood flow instabilities in the carotid artery bifurcation have been highly correlated to clot formation and mobilization resulting in ischemic stroke. In this work, PIV-measured flow velocities in normal and stenosed carotid artery bifurcation models were analyzed by means of proper orthogonal decomposition (POD). Through POD analysis, transition to more complex flow was visualized and quantified for increasing stenosis severity. While no evidence of transitional flow was seen in the normal model, the 50%-stenosed model started to show characteristics of transitional flow, which became highly evident in the 70% model, with greatest manifestation during the systolic phase of the cardiac cycle. By means of a model comparison, we demonstrate two quantitative measures of the flow complexity through the power-law decay slope of the energy spectrum and the global entropy. The more complex flow in the 70%-stenosed model showed a flatter slope of energy decay (-0.91 compared to -1.34 for 50% stenosis) and higher entropy values (0.26 compared to 0.17). Finally, the minimum temporal resolution required for POD analysis of carotid artery flow was found to be 100 Hz when determined through a more typical energy-mode convergence test, as compared to 400 Hz based on global entropy values.
Directory of Open Access Journals (Sweden)
Kweon-Ho Nam
Full Text Available Despite considerable research efforts on the relationship between arterial geometry and cardiovascular pathology, information is lacking on the pulsatile geometrical variation caused by arterial distensibility and cardiomotility because of the lack of suitable in vivo experimental models and the methodological difficulties in examining the arterial dynamics. We aimed to investigate the feasibility of using a chick embryo system as an experimental model for basic research on the pulsatile variation of arterial geometry. Optical microscope video images of various arterial shapes in chick chorioallantoic circulation were recorded from different locations and different embryo samples. The high optical transparency of the chorioallantoic membrane (CAM allowed clear observation of tiny vessels and their movements. Systolic and diastolic changes in arterial geometry were visualized by detecting the wall boundaries from binary images. Several to hundreds of microns of wall displacement variations were recognized during a pulsatile cycle. The spatial maps of the wall motion harmonics and magnitude ratio of harmonic components were obtained by analyzing the temporal brightness variation at each pixel in sequential grayscale images using spectral analysis techniques. The local variations in the spectral characteristics of the arterial wall motion were reflected well in the analysis results. In addition, mapping the phase angle of the fundamental frequency identified the regional variations in the wall motion directivity and phase shift. Regional variations in wall motion phase angle and fundamental-to-second harmonic ratio were remarkable near the bifurcation area. In summary, wall motion in various arterial geometry including straight, curved and bifurcated shapes was well observed in the CAM artery model, and their local and cyclic variations could be characterized by Fourier and wavelet transforms of the acquired video images. The CAM artery model with
NUMERICAL ANALYSIS OF THE NON-NEWTONIAN BLOOD FLOW IN THE NON-PLANAR ARTERY WITH BIFURCATION
Institute of Scientific and Technical Information of China (English)
CHEN Jie; LU Xi-yun; ZHUANG Li-xian; WANG Wen
2004-01-01
A numerical analysis of non-Newtonian fluid flow in non-planar artery with bifurcation was performed by using a finite element method to solve the three-dimensional Navier-Stokes equations coupled with the non-Newtonian constitutive models, including Carreau,Cross and Bingham models. The objective of this study is to investigate the effects of the non-Newtonian properties of blood as well as curvature and out-of-plane geometry in the non-planar daughter vessels on the velocity distribution and wall shear stress. The results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are of important in hemodynamics and play a significant role in vascular biology and pathophysiology.
Ohayon, Jacques; Gharib, Ahmed M; Garcia, Alberto; Heroux, Julie; Yazdani, Saami K; Malvè, Mauro; Tracqui, Philippe; Martinez, Miguel-Angel; Doblare, Manuel; Finet, Gérard; Pettigrew, Roderic I
2011-09-01
Coronary bifurcations represent specific regions of the arterial tree that are susceptible to atherosclerotic lesions. While the effects of vessel compliance, curvature, pulsatile blood flow, and cardiac motion on coronary endothelial shear stress have been widely explored, the effects of myocardial contraction on arterial wall stress/strain (WS/S) and vessel stiffness distributions remain unclear. Local increase of vessel stiffness resulting from wall-strain stiffening phenomenon (a local process due to the nonlinear mechanical properties of the arterial wall) may be critical in the development of atherosclerotic lesions. Therefore, the aim of this study was to quantify WS/S and stiffness in coronary bifurcations and to investigate correlations with plaque sites. Anatomic coronary geometry and cardiac motion were generated based on both computed tomography and MRI examinations of eight patients with minimal coronary disease. Computational structural analyses using the finite element method were subsequently performed, and spatial luminal arterial wall stretch (LW(Stretch)) and stiffness (LW(Stiff)) distributions in the left main coronary bifurcations were calculated. Our results show that all plaque sites were concomitantly subject to high LW(Stretch) and high LW(Stiff), with mean amplitudes of 34.7 ± 1.6% and 442.4 ± 113.0 kPa, respectively. The mean LW(Stiff) amplitude was found slightly greater at the plaque sites on the left main coronary artery (mean value: 482.2 ± 88.1 kPa) compared with those computed on the left anterior descending and left circumflex coronary arteries (416.3 ± 61.5 and 428.7 ± 181.8 kPa, respectively). These findings suggest that local wall stiffness plays a role in the initiation of atherosclerotic lesions.
Sadatomo, Takashi; Yuki, Kiyoshi; Migita, Keisuke; Imada, Yasutaka; Kuwabara, Masashi; Kurisu, Kaoru
2013-07-01
The objectives of this study were to elucidate the normal anatomy of middle cerebral artery (MCA) bifurcations and to analyze the differences in patients with MCA aneurysms. In the present study, 62 patients underwent three-dimensional magnetic resonance angiography, and no intracranial lesions were noted. The widths of M1 and the superior and inferior M2 branches, as well as their respective lateral angles, were measured. These values were used to calculate the daughter artery ratio (DA ratio; width of larger M2/width of smaller M2) and the lateral angle ratio (LA ratio; lateral angle between M1 and larger M2/lateral angle between M1 and smaller M2). The DA and LA ratios of 54 MCA aneurysm patients (34 with ruptured aneurysms, 20 with unruptured aneurysms) were also calculated, using three-dimensional digital subtraction angiography, and compared with the normal values. In normal patients, the widths of M1 and the branches of M2, the lateral angles, and the LA and DA ratios were not significantly different between the right and left sides. The bilateral superior and inferior lateral angles of normal MCAs were significantly wider than those of MCAs with aneurysms. The DA ratio was 1.5 ± 0.4 in normal MCAs and 1.7 ± 0.7 in MCAs with aneurysms; this difference was significant (p bifurcations show close to symmetric structure in the M2 branches and the lateral angles, whereas aneurysmal MCAs do not show this symmetry.
Denisenko, N. S.; Chupakhin, A. P.; Khe, A. K.; Cherevko, A. A.; Yanchenko, A. A.; Tulupov, A. A.; Boiko, A. V.; Krivoshapkin, A. L.; Orlov, K. Yu; Moshkin, M. P.; Akulov, A. E.
2016-06-01
In our experiments, we investigate a flow of a viscous fluid in the model of the common carotid artery bifurcation. The studies are carried out using three hardware equipments: two magnetic resonance scanners by Philips and Bruker, and intravascular guidewire ComboWire. The flux is generated by a special pump CompuFlow that is designed to reproduce a flow similar to the one in the blood vessels. A verification of the obtained data is carried out. Conducted research shows the capabilities of the measurement instruments and reflects the character of fluid flow inside the model.
Classification of coronary artery bifurcation lesions and treatments: Time for a consensus!
DEFF Research Database (Denmark)
Louvard, Yves; Thomas, Martyn; Dzavik, Vladimir;
2007-01-01
, heterogeneity, and inadequate description of techniques implemented. Methods: The aim is to propose a consensus established by the European Bifurcation Club (EBC), on the definition and classification of bifurcation lesions and treatments implemented with the purpose of allowing comparisons between techniques...... proposes a new classification of bifurcation lesions and their treatments to permit accurate comparisons of well described techniques in homogeneous lesion groups. (c) 2008 Wiley-Liss, Inc. Udgivelsesdato: 2007-Nov-5...
Clinical outcome after crush versus culotte stenting of coronary artery bifurcation lesions
DEFF Research Database (Denmark)
Kervinen, Kari; Niemelä, Matti; Romppanen, Hannu;
2013-01-01
The aim of the study was to compare long-term follow-up results of crush versus culotte stent techniques in coronary bifurcation lesions.......The aim of the study was to compare long-term follow-up results of crush versus culotte stent techniques in coronary bifurcation lesions....
Long-term results after simple versus complex stenting of coronary artery bifurcation lesions
DEFF Research Database (Denmark)
Maeng, Michael; Holm, Niels Ramsing; Erglis, Andrejs;
2013-01-01
Objectives This study sought to report the 5-year follow-up results of the Nordic Bifurcation Study. Background Randomized clinical trials with short-term follow-up have indicated that coronary bifurcation lesions may be optimally treated using the optional side branch stenting strategy. Methods ...
Saho, Tatsunori; Onishi, Hideo
2016-07-01
In this study, we evaluated the hemodynamics of carotid artery bifurcation with various geometries using simulated and volunteer models based on magnetic resonance imaging (MRI). Computational fluid dynamics (CFD) was analyzed by use of OpenFOAM. The velocity distribution, streamline, and wall shear stress (WSS) were evaluated in a simulated model with known bifurcation angles (30°, 40°, 50°, 60°, derived from patients' data) and in three-dimensional (3D) healthy volunteer models. Separated flow was observed at the outer side of the bifurcation, and large bifurcation models represented upstream transfer of the point. Local WSS values at the outer bifurcation [both simulated (100 Pa). The bifurcation angle had a significant negative correlation with the WSS value (p<0.05). The results of this study show that the carotid artery bifurcation angle is related to the WSS value. This suggests that hemodynamic stress can be estimated based on the carotid artery geometry. The construction of a clinical database for estimation of developing atherosclerosis is warranted. PMID:27255300
Townsend, Jacob C; Steinberg, Daniel H; Nielsen, Christopher D; Todoran, Thomas M; Patel, Chetan P; Leonardi, Robert A; Wolf, Bethany J; Brilakis, Emmanouil S; Shunk, Kendrick A; Goldstein, James A; Kern, Morton J; Powers, Eric R
2013-08-01
Atherosclerosis has been shown to develop preferentially at sites of coronary bifurcation, yet culprit lesions resulting in ST-elevation myocardial infarction do not occur more frequently at these sites. We hypothesized that these findings can be explained by similarities in intracoronary lipid and that lipid and lipid core plaque would be found with similar frequency in coronary bifurcation and nonbifurcation segments. One hundred seventy bifurcations were identified, 156 of which had comparative nonbifurcation segments proximal and/or distal to the bifurcation. We compared lipid deposition at bifurcation and nonbifurcation segments in coronary arteries using near-infrared spectroscopy (NIRS), a novel method for the in vivo detection of coronary lipid. Any NIRS signal for the presence of lipid was found with similar frequency in bifurcation and nonbifurcation segments (79% vs 74%, p = NS). Lipid core burden index, a measure of total lipid quantity indexed to segment length, was similar across bifurcation segments as well as their proximal and distal controls (lipid core burden index 66.3 ± 106, 67.1 ± 116, and 66.6 ± 104, p = NS). Lipid core plaque, identified as a high-intensity focal NIRS signal, was found in 21% of bifurcation segments, and 20% of distal nonbifurcation segments (p = NS). In conclusion, coronary bifurcations do not appear to have higher levels of intracoronary lipid or lipid core plaque than their comparative nonbifurcation regions.
Energy Technology Data Exchange (ETDEWEB)
Goltz, Jan Peter, E-mail: janpeter.goltz@uksh.de; Loesaus, Julia; Frydrychowicz, Alex; Barkhausen, Jörg [University Hospital of Schleswig-Holstein, Department for Radiology and Nuclear Medicine (Germany); Wiedner, Marcus [University Hospital of Schleswig-Holstein, Clinic for Surgery (Germany)
2016-02-15
We report an endovascular technique for the treatment of type Ia endoleak after a plain tubular stentgraft had been implanted for a large common iliac artery aneurysm with an insufficient proximal landing zone and without occlusion of the hypogastric in another hospital. CT follow-up showed an endoleak with continuous sac expansion over 12 months. This was classified as type Ia by means of dynamic contrast-enhanced MRI. Before a bifurcated stentgraft was implanted to relocate the landing zone more proximally, the still perfused ipsilateral hypogastric artery was embolized to prevent a type II endoleak. A guidewire was manipulated alongside the indwelling stentgraft. The internal iliac artery could then be selectively intubated followed by successful plug embolization of the vessel’s orifice despite the stentgraft being in place.
Energy Technology Data Exchange (ETDEWEB)
Yamada, Shigeki, E-mail: shigekiyamada3@gmail.com [Department of Neurosurgery and Stroke Center, Rakuwakai Otowa Hospital, Otowachinji-cho 2, Yamashina-ku, Kyoto 607-8602 (Japan); Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan); Interfaculty Initiative in Information Studies/Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Oshima, Marie, E-mail: marie@iis.u-tokyo.ac.jp [Interfaculty Initiative in Information Studies/Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Watanabe, Yoshihiko, E-mail: ynabe@magic.odn.ne.jp [Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan); Ogata, Hideki, E-mail: hidogata@gmail.com [Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan); Hashimoto, Kenji, E-mail: hashiken8022@yahoo.co.jp [Department of Neurosurgery, Kishiwada Municipal Hospital, 1001 Gakuhara-cho, Kishiwada city, Osaka 596-8501 (Japan); Miyake, Hidenori, E-mail: hi-miyake@hamamatsuh.rofuku.go.jp [Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan)
2014-06-15
Purpose: The purpose of this study was to investigate the association between internal carotid artery (ICA) stenosis and intramural location and size of calcification at the ICA origins and the origins of the cervical arteries proximal to the ICA. Method: A total of 1139 ICAs were evaluated stenosis and calcification on the multi-detector row CT angiography. The intramural location was categorized into none, outside and inside location. The calcification size was evaluated on the 4-point grading scale. The multivariate analyses were adjusted for age, serum creatinine level, hypertension, hyperlipidemia, diabetes mellitus, smoking and alcohol habits. Results: Outside calcification at the ICA origins showed the highest multivariate odds ratio (OR) for the presence of ICA stenosis (30.0) and severe calcification (a semicircle or more of calcification at the arterial cross-sectional surfaces) did the second (14.3). In the subgroups of >70% ICA stenosis, the multivariate OR of outside location increased to 44.8 and that of severe calcification also increased to 32.7. Four of 5 calcified carotid plaque specimens extracted by carotid endarterectomy were histologically confirmed to be calcified burdens located outside the internal elastic lamia which were defined as arterial medial calcification. Conclusions: ICA stenosis was strongly associated with severe calcification located mainly outside the carotid plaque. Outside calcification at the ICA origins should be evaluated separately from inside calcification, as a marker for the ICA stenosis. Additionally, we found that calcification at the origins of the cervical arteries proximal to the ICA was significantly associated with the ICA stenosis.
International Nuclear Information System (INIS)
Purpose: The purpose of this study was to investigate the association between internal carotid artery (ICA) stenosis and intramural location and size of calcification at the ICA origins and the origins of the cervical arteries proximal to the ICA. Method: A total of 1139 ICAs were evaluated stenosis and calcification on the multi-detector row CT angiography. The intramural location was categorized into none, outside and inside location. The calcification size was evaluated on the 4-point grading scale. The multivariate analyses were adjusted for age, serum creatinine level, hypertension, hyperlipidemia, diabetes mellitus, smoking and alcohol habits. Results: Outside calcification at the ICA origins showed the highest multivariate odds ratio (OR) for the presence of ICA stenosis (30.0) and severe calcification (a semicircle or more of calcification at the arterial cross-sectional surfaces) did the second (14.3). In the subgroups of >70% ICA stenosis, the multivariate OR of outside location increased to 44.8 and that of severe calcification also increased to 32.7. Four of 5 calcified carotid plaque specimens extracted by carotid endarterectomy were histologically confirmed to be calcified burdens located outside the internal elastic lamia which were defined as arterial medial calcification. Conclusions: ICA stenosis was strongly associated with severe calcification located mainly outside the carotid plaque. Outside calcification at the ICA origins should be evaluated separately from inside calcification, as a marker for the ICA stenosis. Additionally, we found that calcification at the origins of the cervical arteries proximal to the ICA was significantly associated with the ICA stenosis
An Experimental Investigation of the Aeroacoustics of a Two-Dimensional Bifurcated Supersonic Inlet
LI, S.-M.; HANUSKA, C. A.; NG, W. F.
2001-11-01
An experiment was conducted on a two-dimensional bifurcated, supersonic inlet to investigate the aeroacoustics at take-off and landing conditions. A 104·1 mm (4·1 in) diameter turbofan simulator was coupled to the inlet to generate the noise typical of a turbofan engine. Aerodynamic and acoustic data were obtained in an anechoic chamber under ground-static conditions (i.e., no forward flight effect). Results showed that varying the distance between the trailing edge of the bifurcated ramp of the inlet and the fan face had negligible effect on the total noise level. Thus, one can have a large freedom to design the bifurcated ramp mechanically and aerodynamically, with minimum impact on the aeroacoustics. However, the effect of inlet guide vanes' (IGV) axial spacing to the fan face has a first order effect on the aeroacoustics for the bifurcated 2-D inlet. As much as 5 dB reduction in the overall sound pressure level and as much as 15 dB reduction in the blade passing frequency tone were observed when the IGV was moved from 0·8 chord of rotor blade upstream of the fan face to 2·0 chord of the blade upstream. The wake profile similarity of the IGV was also found in the flow environment of the 2-D bifurcated inlet, i.e., the IGV wakes followed the usual Gauss' function.
Institute of Scientific and Technical Information of China (English)
Jiang Junhao; Chen Bin; Dong Zhihui; Shi Yun; Li Weimiao; Yue Jianing
2014-01-01
Background Crossover stenting across the origin of the profunda femoral artery (PFA) and occasionally into the common femoral artery (CFA) is commonly used after suboptimal balloon angioplasty of ostial occlusive lesions of the superficial femoral artery (SFA) involving the bifurcation.Late stent occlusion at the bifurcation is not rare and results in severe lower extremity ischemia.Therefore,we tried to assess its possible causes,prevention and reintervention.Methods Using a prospectively maintained single-center database,12-month femoral bifurcation patency was retrospectively compared and lesion and procedural predictors of stent occlusion were determined among 63 patients (64 lesions) who between July 2011 and February 2013 underwent crossover (36 non-jailed and 15 jailed SFA,and 12 distal and 1 complete CFA) stenting of de novo ostial SFA lesions.Results Twelve-month overall patency rate at the femoral bifurcation was 88％,with no significant difference between jailed-ostial SFA (80％) and distal CFA (67％) stenting (P=0.731),and significant differences between either and non-jailed ostial stenting (100％,P=0.035 and 0.002).When PFA ostium was jailed by the stent,patients with preexisting CFA or PFA lesions had a 12-month bifurcation patency rate of 20％,significantly lower than those with simple ostial SFA lesions (83％,P=0.015).Stent induced intimal hyperplasia caused bifurcation occlusion in 6 surgical reintervention cases.Conclusions In crossover stenting of ostial lesions in SFA,bifurcation patency loss was significantly higher in distal CFA and jailed ostial SFA stenting than non-jailed ostial SFA stenting.Preexisting CFA or PFA lesion is a significant risk factor for bifurcation patency loss when PFA ostium is jailed by crossover stenting.
Institute of Scientific and Technical Information of China (English)
Xu-Wei Zheng; Dong-Hui Zhao; Hong-Yu Peng; Qian Fan; Qin Ma; Zhen-Ye Xu; Chao Fan
2016-01-01
Background:The crush and the culotte stenting were both reported to be effective for complex bifurcation lesion treatment.However,their comparative performance remains elusive.Methods:A total of 300 patients with coronary bifurcation lesions were randomly assigned to crush (n =150) and culotte (n =150) treatment.The primary endpoint was the occurrence of major adverse cardiac events (MACEs) at 12 months including cardiac death,myocardial infarction,stent thrombosis,and target vessel revascularization.Index lesion restenosis at 12 months was a secondary endpoint.The surface integrals of time-averaged wall shear stress at bifurcation sites were also be quantified.Results:There were no significant differences in MACE rates between the two groups at 12-month follow-up:Crush 6.7％,culotte 5.3％ (P =0.48).The rates of index lesion restenosis were 12.7％ versus 6.0％ (P =0.047) in the crush and the culotte groups,respectively.At 12-month follow-up,the surface integrals of time-averaged wall shear stress at bifurcation sites in the crush group were significantly lower than the culotte group ([5.01 ± 0.95] × 10-4 Newton and [6.08 ± 1.16] × 10 4 Newton,respectively;P =0.003).Conclusions:Both the crush and the culotte bifurcation stenting techniques showed satisfying clinical and angiographic results at 12-month follow-up.Bifurcation lesions treated with the culotte technique tended to have lower restenosis rates and more favorable flow patterns.
DK crush technique: modified treatment of bifurcation lesions in coronary artery
Institute of Scientific and Technical Information of China (English)
CHEN Shao-liang; GE Jun-bo; YE Fei; ZHANG Jun-jie; ZHU Zhong-sheng; LIN Song; SHAN Shou-jie; LIU Zhi-zhong; LIU Yan; DUAN Bao-xiang
2005-01-01
@@ Bifurcation lesions are still technically challenging even in the era of modern stents.1 High incidence of restenosis both in main vessel and side branch limits the long-term prognosis although several kinds of techniques have been identified to be successful for coronary bifurcations.2-5 Reports have demonstrated the main reason for higher incidence of ostial side branch even though drug-eluting stent used in side vessel lies in that there were gaps in metal coverage and drug application.6-9 Therefore, new technique ensuring complete vessel scaffolding without gaps in drug delivery at the bifurcation is crush technique which is similar to other techniques including T- and Y- stenting still needing postdilatation of kissing balloon angioplasty to expand the stent fully in the ostial side branch and to prevent stent distortion in main vessel.10 As a result, kissing balloon angioplasty is a key step to improve the final result and to reduce the restenosis after stenting bifurcation lesions. However, kissing angioplasty is difficult to be underwent or impossible because operators usually fail to rewire two layers of metal strut, which would result in suboptimal stent deployment, a main reason of high incidence of restenosis, and acute- or-late-thrombosus. The present study reports modified DK crush technique improving success rate of kissing balloon angioplasty under the guidance of intravascular ultrasound (IVUS).
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We present a case of a 73-year-old man in whom a celiac trunk aneurysm close to the hepato-splenic bifurcation was discovered and treated by using celiac-hepatic stent-grafts implantation and splenic artery embolization
AN ACCESSORY/ABERRANT LEFT INFERIOR POLAR ARTERY AR ISING FROM THE AORTIC BIFURCATION
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Sreekanth
2013-04-01
Full Text Available ABSTRACT: The frequently to rarely occurring wide range of va riations in the renal vasculature are considered critical issue that surgeons should have a thorough envision and appreciation of the condition. During the routine prosection hours for the preclinical MBBS students at Shadan Institute of Medical Sciences, Teaching Hospital and Research Centre, while dissecting a male cadaver revealed an interesting variation. The Main Renal Artery (MRA was arising from the aorta about 1.8 cm below the Superior Mesentric Arte ry (SMA extending laterally towards the hilum of the kidney. At about 1.5 cm below the orig in of the Inferior Mesenteric Artery (IMA from the antero lateral aspect of the Aortic Bifurca tion, an aberrant renal artery measuring 4.5 cm in length, was seen coursing upwards, backwards a nd laterally & made its portal of entry by penetrating into the medial border and extending on to the posterior surface by piercing the capsule just half cm. above its lower pole. The urete r and the gonadal vessels were superficial to it. A thorough knowledge of the variations of renal vascular anatomy has importance in exploration and treatment of renal trauma, renal tra nsplantation, renal artery embolization, surgery for abdominal aortic aneurysm and conservat ive or radical renal surgery.
Non-local investigation of bifurcations of solutions of non-linear elliptic equations
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Il' yasov, Ya Sh
2002-12-31
We justify the projective fibration procedure for functionals defined on Banach spaces. Using this procedure and a dynamical approach to the study with respect to parameters, we prove that there are branches of positive solutions of non-linear elliptic equations with indefinite non-linearities. We investigate the asymptotic behaviour of these branches at bifurcation points. In the general case of equations with p-Laplacian we prove that there are upper bounds of branches of positive solutions with respect to the parameter.
Directory of Open Access Journals (Sweden)
Patrick Bastos Metzger
2014-03-01
Full Text Available Embolization due to a firearm projectile entering the bloodstream is a rare event that is unlikely to be suspected during initial treatment of trauma patients. We describe and discuss a case of bullet embolism of the abdominal aortic bifurcation, complicated by a pseudoaneurysm of the thoracoabdominal aorta and occlusion of the right common iliac artery, but successfully treated using a combination of endovascular methods and conventional surgery.
The clinical application of 64-slice spiral CT angiography in carotid artery bifurcation disease
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Objective: To explore the clinical value of 64-slice spiral CT angiography (CTA) in carotid stenosis and atherosclerotic plaque. Methods: 40 patients (80 carotid arteries) underwent CTA and DSA. These two examinations within one week. The results of CTA were compared with that of DSA, the sensitivity and specificity of CTA and DSA were figured out. Results: CTA performed well in the detection of mild (0% to 29%) carotid stenosis, as well as carotid occlusion, with values for sensitivity and specificity both near 100%. In determining that a stenosis was >50% by DSA measurement, CTA with a sensitivity, specificity of 89% and 91% respectively. While CTA was quite specific in identifying degrees of stenoses in either the 50% to 69% or the 70% to 99% ranges, in this task it was much less sensitive: 65% and 73% respectively. CTA can detect all kinds of ulcers while DSA can not. Conclusions: 64-slice CTA and DSA were correctly identified in detecting carotid stenosis. CTA could demonstrate ulcers associated with the carotid stenosis, hut DSA only show stenosis. (authors)
Single umbilical artery in fetopathological investigations.
Joó, József Gábor; Beke, Artúr; Papp, Zoltán; Rigó, János; Papp, Csaba
2008-01-01
Single umbilical artery (SUA) is a relatively common malformation that may call attention to the possibility of associated malformations (often chromosome aberrations). The current study aimed at surveying malformations associated with SUA on the basis of fetopathological investigations, analyzing the role of history, summarizing the clinically important factors emerging together with this malformation. In this study, we processed the details of 204 cases in which SUA was confirmed fetopathologically after miscarriage or induced abortion between 1990 and 2007. In our sample, SUA occurred in 7.38% of the cases. The history was positive in almost 30% of the cases. The majority of the cases had a positive obstetric and the minority of them a positive genetic history. The highest association of SUA with other malformations was found for craniospinal ones, but an association with cardiovascular malformations should also be mentioned. Regarding the individual types of malformation, SUA was most commonly associated with hydrocephalus, but Potter's sequence, trisomy 21, and atrioventricular septal defect also reached a higher rate in associated SUA. Previously published articles dealing with associated malformations found that urogenital malformations were most commonly associated with SUA. 'Itemizing' the different non-chromosomal malformations in association with SUA, we found that hydrocephalus, Potter's sequence, and atrioventricular septal defect were the most frequent malformations, while in earlier studies, the association with non-chromosomal malformations such as vertebral malformations, imperforated anus, cheilognathopalatoschisis, and renal agenesis occurred more frequently than usual.
Lykov, Kirill; Li, Xuejin; Lei, Huan; Pivkin, Igor V; Karniadakis, George Em
2015-08-01
When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the "all-or-nothing" phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.
Directory of Open Access Journals (Sweden)
Kirill Lykov
2015-08-01
Full Text Available When blood flows through a bifurcation, red blood cells (RBCs travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the "all-or-nothing" phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.
Chiastra, Claudio; Wu, Wei; Dickerhoff, Benjamin; Aleiou, Ali; Dubini, Gabriele; Otake, Hiromasa; Migliavacca, Francesco; LaDisa, John F
2016-07-26
The optimal stenting technique for coronary artery bifurcations is still debated. With additional advances computational simulations can soon be used to compare stent designs or strategies based on verified structural and hemodynamics results in order to identify the optimal solution for each individual's anatomy. In this study, patient-specific simulations of stent deployment were performed for 2 cases to replicate the complete procedure conducted by interventional cardiologists. Subsequent computational fluid dynamics (CFD) analyses were conducted to quantify hemodynamic quantities linked to restenosis. Patient-specific pre-operative models of coronary bifurcations were reconstructed from CT angiography and optical coherence tomography (OCT). Plaque location and composition were estimated from OCT and assigned to models, and structural simulations were performed in Abaqus. Artery geometries after virtual stent expansion of Xience Prime or Nobori stents created in SolidWorks were compared to post-operative geometry from OCT and CT before being extracted and used for CFD simulations in SimVascular. Inflow boundary conditions based on body surface area, and downstream vascular resistances and capacitances were applied at branches to mimic physiology. Artery geometries obtained after virtual expansion were in good agreement with those reconstructed from patient images. Quantitative comparison of the distance between reconstructed and post-stent geometries revealed a maximum difference in area of 20.4%. Adverse indices of wall shear stress were more pronounced for thicker Nobori stents in both patients. These findings verify structural analyses of stent expansion, introduce a workflow to combine software packages for solid and fluid mechanics analysis, and underscore important stent design features from prior idealized studies. The proposed approach may ultimately be useful in determining an optimal choice of stent and position for each patient. PMID:26655589
Chiastra, Claudio; Wu, Wei; Dickerhoff, Benjamin; Aleiou, Ali; Dubini, Gabriele; Otake, Hiromasa; Migliavacca, Francesco; LaDisa, John F
2016-07-26
The optimal stenting technique for coronary artery bifurcations is still debated. With additional advances computational simulations can soon be used to compare stent designs or strategies based on verified structural and hemodynamics results in order to identify the optimal solution for each individual's anatomy. In this study, patient-specific simulations of stent deployment were performed for 2 cases to replicate the complete procedure conducted by interventional cardiologists. Subsequent computational fluid dynamics (CFD) analyses were conducted to quantify hemodynamic quantities linked to restenosis. Patient-specific pre-operative models of coronary bifurcations were reconstructed from CT angiography and optical coherence tomography (OCT). Plaque location and composition were estimated from OCT and assigned to models, and structural simulations were performed in Abaqus. Artery geometries after virtual stent expansion of Xience Prime or Nobori stents created in SolidWorks were compared to post-operative geometry from OCT and CT before being extracted and used for CFD simulations in SimVascular. Inflow boundary conditions based on body surface area, and downstream vascular resistances and capacitances were applied at branches to mimic physiology. Artery geometries obtained after virtual expansion were in good agreement with those reconstructed from patient images. Quantitative comparison of the distance between reconstructed and post-stent geometries revealed a maximum difference in area of 20.4%. Adverse indices of wall shear stress were more pronounced for thicker Nobori stents in both patients. These findings verify structural analyses of stent expansion, introduce a workflow to combine software packages for solid and fluid mechanics analysis, and underscore important stent design features from prior idealized studies. The proposed approach may ultimately be useful in determining an optimal choice of stent and position for each patient.
Computational simulations in coronary bifurcations: Paving the future of interventional planning.
Collet, Carlos; Serruys, Patrick W
2016-06-01
Anatomical evaluation is of paramount importance in the treatment of bifurcation lesions. Left main coronary artery bifurcation geometry differs from left anterior descending artery/diagonal and circumflex artery/obtuse marginal bifurcations. Individualized approach with pre-procedural planning has the potential to improve outcomes after bifurcation treatment.
Laboratory Experiments to Investigate Breakout and Bifurcation of Lava Flows on Mars
Miyamoto, H.; Zimbelman, J. R.; Tokunaga, T.; Tosaka, H.
2001-05-01
Mars Orbiter Camera (MOC) images show that many lava flows on Mars have morphologies quite similar to aa lava flows. Such flows often have many lobes and branches that overlap each other, making a compound flow unit. These features cannot be explained by any simple flow model because longer effusion duration will simply make the flow longer, although actual lavas often will bifurcate to make additonal flow units. Similarly, formation of a lava tube is difficult to predict by a model that does not contain preset conditions for their formation. Treatment of the surface crust is very important to the flow morphology, especially for effusion over a long duration. To understand the effect of a crust on flow morphology, paraffin wax is especially useful in laboratory experiments. In our experiments, a flow on a constant slope typically progresses with a constant width at first. Then, the flow front cools to form a crust, which inhibits the progress of the flow. At that time, the flow sometimes becomes sinuous or ceases its movement. With a sufficient flux after that, uplift of thickness (inflation) can occur. Uplift sometimes attains a sufficient thickening to produce a breakout at the side of the flow, bifurcating to form a new cooling unit. Bifurcated flows do not always follow the main flow (some branches moved several cm away from the initial flow). The bifurcations continue to develop into a complicated flow field, given a sufficiently long duration of effusion. Although the movement of the flow with a surface crust is difficult to predict, our simple analysis suggests that the maximum thickness attained by the inflation (by fluid continuing to enter a stopped flow) before a breakout can occur is roughly estimated by a balance between the overpressure and the crust tensile strength. The maximum extent of a bifurcated flow after a breakout can probably be constrained, which will be a significant goal for future modeling of compound flows.
Ghalichi, Farzan; Deng, Xiaoyan
2003-01-01
The pulsatile blood flow in a partially blocked artery is significantly altered as the flow regime changes through the cardiac cycle. This paper reports on the application of a low-Reynolds turbulence model for computation of physiological pulsatile flow in a healthy and stenosed carotid artery bifurcation. The human carotid artery was chosen since it has received much attention because atherosclerotic lesions are frequently observed. The Wilcox low-Re k-omega turbulence model was used for the simulation since it has proven to be more accurate in describing transition from laminar to turbulent flow. Using the FIDAP finite element code a validation showed very good agreement between experimental and numerical results for a steady laminar to turbulent flow transition as reported in a previous publication by the same authors. Since no experimental or numerical results were available in the literature for a pulsatile and turbulent flow regime, a comparison between laminar and low-Re turbulent calculations was made to further validate the turbulence model. The results of this study showed a very good agreement for velocity profiles and wall shear stress values for this imposed pulsatile laminar flow regime. To explore further the medical aspect, the calculations showed that even in a healthy or non-stenosed artery, small instabilities could be found at least for a portion of the pulse cycle and in different sections. The 40% and 55% diameter reduction stenoses did not significantly change the turbulence characteristics. Further results showed that the presence of 75% stenoses changed the flow properties from laminar to turbulent flow for a good portion of the cardiac pulse. A full 3D simulation with this low-Re-turbulence model, coupled with Doppler ultrasound, can play a significant role in assessing the degree of stenosis for cardiac patients with mild conditions.
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Peters, John W.; Miller, Anne-Frances; Jones, Anne K.; King, Paul W.; Adams, Michael W. W.
2016-04-01
Electron bifurcation is the recently recognized third mechanism of biological energy conservation. It simultaneously couples exergonic and endergonic oxidation-reduction reactions to circumvent thermodynamic barriers and minimize free energy loss. Little is known about the details of how electron bifurcating enzymes function, but specifics are beginning to emerge for several bifurcating enzymes. To date, those characterized contain a collection of redox cofactors including flavins and iron-sulfur clusters. Here we discuss the current understanding of bifurcating enzymes and the mechanistic features required to reversibly partition multiple electrons from a single redox site into exergonic and endergonic electron transfer paths.
Long-term follow-up of crush versus no crush technique for coronary artery bifurcation lesions
Institute of Scientific and Technical Information of China (English)
GAO Zhan; YANG Yue-jin; XU Bo; CHEN Ji-lin; QIAO Shu-bin; LI Jian-jun; QIN Xue-wen; YAO Min; WU Yong-jian; YUAN Jin-qing; CHEN Jue; LIU Hai-bo; DAI Jun; GAO Run-lin
2009-01-01
Background Lesions at coronary bifurcations always are a big challenge for interventionists even with the advent of drug eluting stents (DES). Even as more clinical trials are published, operators still can not confirm that one strategy is more efficient than another. Selection of patients and short term follow-up contribute to the difficulty in comparing strategies.Methods From April 2004 to April 2008, 505 consecutive Chinese patients underwent DES implantation for true bifurcation lesions; including 258 using crush strategy (213 male, (56.7±10.8) years old) and 247 using no crush strategy (206 male, (58.1±10.1 ) years old) were analyzed.Results The follow-up period ranged from 237 to 1223 days, average (537±340) days for the crush group and (538±351) days for the no crush group. There was no significant difference of major adverse cardiac events (MACE) rate between the two groups (10.1% vs 12.1%; P=0.481), nor in cardiac death, nonfatal myocardial infarction (MI) or in the target vessel revascularization (TVR) (0.4% vs 1.6%; P=0.207, 2.7% vs 2.8; P=1.000 and 7.0% MS 7.7%; P=0.865). The stent thrombosis rate was similar in the two groups (1.6% vs 2.0%; P=0.409), late and very late stent thrombosis in both groups were very low (0.4% vs 0.4%; P=1.000). Seven-month angiographic follow-up showed no significant difference of the restenosis rate between the two groups (11.0% vs 13.5%; P=0.786). During the follow-up, cardiac death, nonfatal MI, TVR and ST free survival rate showed no significant difference between the two groups. The only variant identified as a predictor of MACE was percutaneous coronary intervention (PCI) in the first two years, which accounted for 47% of patients of all cases in four years.Conclusion Crush technique showed similar long-term clinical effect compared with other two DES techniques for coronary bifurcation lesions, the surgeons' skills are very important for reducing clinical events.
The Boundary Element Analysis on Y Bifurcation Arterial Hemodynamic Characteristics%Y型血管血流动力学边界元分析
Institute of Scientific and Technical Information of China (English)
彭红梅; 杨德全
2011-01-01
目的:通过数值计算,判断Y型动脉血管中,血流动力学特性对分叉处粥样斑块病变产生和发展的影响.方法:利用边界元方法[4,5],计算了Y型动脉血管,主管病变前后的血液流场、血管壁切应力、压力等血液流体动力学特性,通过对计算结果的分析和比较对粥样病变产生和发展的原因做出了分析.边界元方法由于只在边界离散时作了近似,因而计算精度较高,对于象分叉血管这类复杂边界问题,有较强的适应性.结果:计算结果显示,分叉处管壁切应力明显大于主管壁切应力,说明了分叉处易产生粥样斑块的流体动力学原因；而病变的产生使血管腔变窄,病变斑块顶部血流速度、切应力变大,上、下游血流速度、切应力变小,说明了粥样斑块变厚和附壁延伸的流体动力学原因[7]；另外,病变前后血管壁压力的计算结果显示,病变的产生对动脉血压有一定的影响.结论:通过对Y型分叉血管血液流体动力学特性的计算,进一步说明,边界元方法对分叉血管,以及分叉处有病变血管,这类复杂边界问题的计算,方便、快捷、精度高、节约机时,可为生物流体力学的深入研究提供一种可靠、有效的方法[8,9].%Objective: Ifs judged that the effect of hemodynamic characteristics for the cause and development of theatherosclerotic lesion in Y bifurcation arterial by numerical. Methods: A kind of Y bifurcation arterial's hemodynamic characteristics such as blood flowing velocity vector, the shear stress and pressure at the vessel wall are calculated .studied and compared with the boundary element method. The method has higher precision because it is only approximate on the border, and it has a strong adaptability for complex border issue. Results: The hemodynamic reasons of lesions producing and developing are reasonably explained. It is shown that the blood hydrokinetic characteristics play a great important role
An Experimental and Numerical Investigation of Bifurcations in a Kolmogorov-Like Flow
Tithof, Jeffrey; Pallantla, Ravi; Grigoriev, Roman O; Schatz, Michael F
2016-01-01
We present a combined experimental and numerical study of the primary and secondary bifurcations for a Kolmogorov-like flow. The experimental system is a quasi-two-dimensional incompressible fluid flow consisting of two immiscible layers of fluid for which electromagnetic forces drive a shear flow that approximates Kolmogorov flow. The two-dimensional (2D) direct numerical simulations (DNS) integrate a depth-averaged version of the full three-dimensional Navier-Stokes equations Suri ${\\it et}$ ${\\it al.}$ (2014), which contains a (non-unity) prefactor on the advection term, previously unaccounted for in all studies. Specifically, we present three separate 2D DNS: one that is doubly-periodic, one that is singly-periodic, and one that is non-periodic (i.e. no-slip is imposed at the lateral boundaries). All parameters are directly calculated or measured from experimental quantities. We show that inclusion of the advection term prefactor substantially improves agreement between experiment and numerics. However, g...
Feng, J; Rajeswaran, T; He, S; Wilkinson, F L; Serracino-Inglott, F; Azzawi, M; Parikh, V; Miraftab, M; Alexander, M Y
2015-08-01
Stroke is mainly caused by a narrowing of the carotid artery from a build-up of plaque. The risk of plaque rupture and subsequent stroke is dependent on plaque composition. Advances in imaging modalities offer a non-invasive means to assess the health of blood vessels and detect damage. However, the current diagnosis fails to identify patients with soft lipid plaque that are more susceptible to fissure, resulting in stroke. The aim of this study was to use waveform analysis to identify plaque composition and the risk of rupture. We have investigated pressure and flow by combining an artificial blood flow circuit with tubing containing different materials, to simulate plaques in a blood vessel. We used fat and bone to model lipid and calcification respectively to determine if the composition of plaques can be identified by arterial waveforms. We demonstrate that the arterial plaque models with different percentages of calcification and fat, results in significantly different arterial waveforms. These findings imply that arterial waveform analysis has the potential for further development to identify the vulnerable plaques prone to rupture. These findings could have implications for improved patient prognosis by speed of detection and a more appropriate treatment strategy. PMID:26736431
1991-01-01
Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambe...
Liu, Yu; Jiang, Lanlan; Zhu, Ningjun; Zhao, Yuechao; Zhang, Yi; Wang, Dayong; Yang, Mingjun; Zhao, Jiafei; Song, Yongchen
2015-09-01
The study of immiscible fluid displacement between aqueous-phase liquids and non-aqueous-phase liquids in porous media is of great importance to oil recovery, groundwater contamination, and underground pollutant migration. Moreover, the attendant viscous, capillary, and gravitational forces are essential to describing the two-phase flows. In this study, magnetic resonance imaging was used to experimentally examine the detailed effects of the viscous, capillary, and gravitational forces on water-oil flows through a vertical straight capillary, bifurcate channel, and monolayered glass-bead pack. Water flooding experiments were performed at atmospheric pressure and 37.8°C, and the evolution of the distribution and saturation of the oil as well as the characteristics of the two-phase flow were investigated and analyzed. The results showed that the flow paths, i.e., the fingers of the displacing phase, during the immiscible displacement in the porous medium were determined by the viscous, capillary, and gravitational forces as well as the sizes of the pores and throats. The experimental results afford a fundamental understanding of immiscible fluid displacement in a porous medium. PMID:25940392
Multiple Bifurcations in the Periodic Orbit around Eros
Ni, Yanshuo; Baoyin, Hexi
2016-01-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real ...
Lee, Sang Hoon; Choi, Hyoung Gwon; Yoo, Jung Yul
2012-11-01
The effect of artery wall hypertrophy and stiffness on the flow field is investigated using three-dimensional finite element method for simulating the blood flow. To avoid the complexity due to the necessity of additional mechanical constraints, we use the combined formulation which includes both the fluid and structural equations of motion into single coupled variational equation. A P2P1 Galerkin finite element method is used to solve the Navier-Stokes equations for fluid flow and arbitrary Lagrangian-Eulerian formulation is used to achieve mesh movement. The Newmark method is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics. The pulsatile, incompressible flows of Newtonian fluids constrained in the flexible wall are analyzed with Womersley velocity profile at the inlet and constant pressure at the outlet. The study shows that the stiffness of carotid artery wall affects significantly the flow phenomena during the pulse cycle. Similarly, it is found that the flow field is also strongly influenced by wall hypertrophy. This work was supported by Mid-career Researcher Program and Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0079936 & 2011-0029613).
Global Bifurcations With Symmetry
Porter, J B
2001-01-01
Symmetry is a ubiquitous feature of physical systems with profound implications for their dynamics. This thesis investigates the role of symmetry in global bifurcations. In particular, the structure imposed by symmetry can encourage the formation of complex solutions such as heteroclinic cycles and chaotic invariant sets. The first study focuses on the dynamics of 1:n steady-state mode interactions in the presence of O(2) symmetry. The normal form equations considered are relevant to a variety of physical problems including Rayleigh-Bénard convection with periodic boundary conditions. In open regions of parameter space these equations contain structurally stable heteroclinic cycles composed of connections between standing wave, pure mode, and trivial solutions. These structurally stable cycles exist between two global bifurcations, the second of which involves an additional mixed mode state and creates as many as four distinct kinds of structurally unstable heteroclinic cycles. The various cycles c...
A Novel Tram Stent Method in the Treatment of Coronary Bifurcation Lesions - Finite Element Study.
Directory of Open Access Journals (Sweden)
Mark C Arokiaraj
Full Text Available A novel stent was designed for the treatment of coronary bifurcation lesion, and it was investigated for its performance by finite element analysis. This study was performed in search of a novel method of treatment of bifurcation lesion with provisional stenting. A bifurcation model was created with the proximal vessel of 3.2 mm diameter, and the distal vessel after the side branch (2.3 mm was 2.7 mm. A novel stent was designed with connection links that had a profile of a tram. Laser cutting and shape setting of the stent was performed, and thereafter it was crimped and deployed over a balloon. The contact pressure, stresses on the arterial wall, stresses on the stent, the maximal principal log strain of the main artery and the side-branch were studied. The study was performed in Abaqus, Simulia. The stresses on the main branch and the distal branch were minimally increased after deployment of this novel stent. The side branch was preserved, and the stresses on the side branch were lesser; and at the confluence of bifurcation on either side of the side branch origin the von-Mises stress was marginally increased. The stresses and strain at the bifurcation were significantly lesser than the stresses and strain of the currently existing techniques used in the treatment of bifurcation lesions though the study was primarily focused only on the utility of the new technology. There is a potential for a novel Tram-stent method in the treatment of coronary bifurcation lesions.
A Novel Tram Stent Method in the Treatment of Coronary Bifurcation Lesions – Finite Element Study
Arokiaraj, Mark C.; De Santis, Gianluca; De Beule, Matthieu; Palacios, Igor F.
2016-01-01
A novel stent was designed for the treatment of coronary bifurcation lesion, and it was investigated for its performance by finite element analysis. This study was performed in search of a novel method of treatment of bifurcation lesion with provisional stenting. A bifurcation model was created with the proximal vessel of 3.2 mm diameter, and the distal vessel after the side branch (2.3 mm) was 2.7 mm. A novel stent was designed with connection links that had a profile of a tram. Laser cutting and shape setting of the stent was performed, and thereafter it was crimped and deployed over a balloon. The contact pressure, stresses on the arterial wall, stresses on the stent, the maximal principal log strain of the main artery and the side-branch were studied. The study was performed in Abaqus, Simulia. The stresses on the main branch and the distal branch were minimally increased after deployment of this novel stent. The side branch was preserved, and the stresses on the side branch were lesser; and at the confluence of bifurcation on either side of the side branch origin the von-Mises stress was marginally increased. The stresses and strain at the bifurcation were significantly lesser than the stresses and strain of the currently existing techniques used in the treatment of bifurcation lesions though the study was primarily focused only on the utility of the new technology. There is a potential for a novel Tram-stent method in the treatment of coronary bifurcation lesions. PMID:26937643
A Novel Tram Stent Method in the Treatment of Coronary Bifurcation Lesions - Finite Element Study.
Arokiaraj, Mark C; De Santis, Gianluca; De Beule, Matthieu; Palacios, Igor F
2016-01-01
A novel stent was designed for the treatment of coronary bifurcation lesion, and it was investigated for its performance by finite element analysis. This study was performed in search of a novel method of treatment of bifurcation lesion with provisional stenting. A bifurcation model was created with the proximal vessel of 3.2 mm diameter, and the distal vessel after the side branch (2.3 mm) was 2.7 mm. A novel stent was designed with connection links that had a profile of a tram. Laser cutting and shape setting of the stent was performed, and thereafter it was crimped and deployed over a balloon. The contact pressure, stresses on the arterial wall, stresses on the stent, the maximal principal log strain of the main artery and the side-branch were studied. The study was performed in Abaqus, Simulia. The stresses on the main branch and the distal branch were minimally increased after deployment of this novel stent. The side branch was preserved, and the stresses on the side branch were lesser; and at the confluence of bifurcation on either side of the side branch origin the von-Mises stress was marginally increased. The stresses and strain at the bifurcation were significantly lesser than the stresses and strain of the currently existing techniques used in the treatment of bifurcation lesions though the study was primarily focused only on the utility of the new technology. There is a potential for a novel Tram-stent method in the treatment of coronary bifurcation lesions. PMID:26937643
International Nuclear Information System (INIS)
This work aims to study effects of toroidal flow on the L-H transition phenomenon in tokamak plasmas using bifurcation concept. Two-field (thermal and particle) transport equations with both neoclassical and turbulent effects included are solved simultaneously. The transport suppression mechanism used in this work is flow shear, which is assumed to affect only the turbulent transport. The flow shear can be calculated from the force balance equation with toroidal flow as a main contributor. The toroidal velocity profile is calculated using three different models. The first model is an empirical model in which the velocity is dependent on local ion temperature. The second model is based on neoclassical toroidal viscosity theory in which the velocity is driven by ion temperature gradient. In the third model, the velocity is dependent on current density flow in plasma. The two transport equations are solved both analytically and numerically using MATLAB to study the criteria for H-mode formation, pedestal width and its dynamics. The results from three toroidal velocity models are compared and analyzed with respect to bifurcation behavior and plasma performance.
BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW
Institute of Scientific and Technical Information of China (English)
LiuFei; YangYiren
2005-01-01
Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given.
Homoclinic Bifurcation Properties near Eight－figure Homoclinic Orbit
Institute of Scientific and Technical Information of China (English)
邹永魁; 佘彦
2002-01-01
In this paper paper we investigate the homoclinic bifurcation properties near an eight-figure homoclinic orbit of co-dimension two of a planar dynamical system.The corresponding local bifurcation diagram is also illustrated by numerical computation.
Local bifurcation analysis of a four-dimensional hyperchaotic system
Institute of Scientific and Technical Information of China (English)
Wu Wen-Juan; Chen Zeng-Qiang; Yuan Zhu-Zhi
2008-01-01
Local bifurcation phenomena in a four-dimensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
Institute of Scientific and Technical Information of China (English)
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
Multiple bifurcations in the periodic orbit around Eros
Ni, Yanshuo; Jiang, Yu; Baoyin, Hexi
2016-05-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real saddle bifurcation, two tangent bifurcations, and two period-doubling bifurcations.
Sprinkler Bifurcations and Stability
Sorensen, Jody; Rykken, Elyn
2010-01-01
After discussing common bifurcations of a one-parameter family of single variable functions, we introduce sprinkler bifurcations, in which any number of new fixed points emanate from a single point. Based on observations of these and other bifurcations, we then prove a number of general results about the stabilities of fixed points near a…
Directory of Open Access Journals (Sweden)
JA Mitchell
2009-06-01
Full Text Available Blood flow to the hindbrain, via the paired vertebral arteries, must be uncompromised for adequate neurological functioning of its vital centres. Therefore, it would seem unlikely that the intracranial vertebral artery would need to vasoconstrict, thus reducing its blood flow. In order to investigate the existence and location of a noradrenaline-mediated constrictor mechanism in the wall of the intracranial vertebral artery, transverse sections of ten baboon and ten monkey vessels were stained with sucrose-potassium phosphate-glyoxylic acid (counterstained with malachite-green. This method allows the visualisation of catecholaminergic nerves when the sections are exposed to ultraviolet light. In this study of primate vascular tissue, however, none of the monkey or baboon vertebral artery sections showed the presence of noradrenergic nerves in the tunica media – tunica adventitia junction or penetrating the tunica media of the arteries. These findings indicate that the intracranial vertebral artery does not have a neurogenic vasomotor function in primates.
Tang, Abraham Yik-Sau; Chung, Wai-Choi; Liu, Eric Tian-Yang; Qu, Jie-Qiong; Tsang, Anderson Chun-On; Leung, Gilberto Ka-Kit; Leung, Kar-Ming; Yu, Alfred Cheuk-Hang; Chow, Kwok-Wing
2015-01-01
An intracranial aneurysm, abnormal swelling of the cerebral artery, may lead to undesirable rates of mortality and morbidity upon rupture. Endovascular treatment involves the deployment of a flow-diverting stent that covers the aneurysm orifice, thereby reducing the blood flow into the aneurysm and mitigating the risk of rupture. In this study, computational fluid dynamics analysis is performed on a bifurcation model to investigate the change in hemodynamics with various side branch diameters...
About Bifurcational Parametric Simplification
Gol'dshtein, V; Yablonsky, G
2015-01-01
A concept of "critical" simplification was proposed by Yablonsky and Lazman in 1996 for the oxidation of carbon monoxide over a platinum catalyst using a Langmuir-Hinshelwood mechanism. The main observation was a simplification of the mechanism at ignition and extinction points. The critical simplification is an example of a much more general phenomenon that we call \\emph{a bifurcational parametric simplification}. Ignition and extinction points are points of equilibrium multiplicity bifurcations, i.e., they are points of a corresponding bifurcation set for parameters. Any bifurcation produces a dependence between system parameters. This is a mathematical explanation and/or justification of the "parametric simplification". It leads us to a conjecture that "maximal bifurcational parametric simplification" corresponds to the "maximal bifurcation complexity." This conjecture can have practical applications for experimental study, because at points of "maximal bifurcation complexity" the number of independent sys...
Alternate Pacing of Border-Collision Period-Doubling Bifurcations.
Zhao, Xiaopeng; Schaeffer, David G
2007-11-01
Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise C1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision period-doubling bifurcations. We apply a subharmonic perturbation to the bifurcation parameter, which is also known as alternate pacing, and we investigate the response under such pacing near the original bifurcation point. The resulting behavior is characterized quantitatively by a gain, which is the ratio of the response amplitude to the applied perturbation amplitude. The gain in a border-collision period-doubling bifurcation has a qualitatively different dependence on parameters from that of a classical period-doubling bifurcation. Perhaps surprisingly, the differences are more readily apparent if the gain is plotted vs. the perturbation amplitude (with the bifurcation parameter fixed) than if plotted vs. the bifurcation parameter (with the perturbation amplitude fixed). When this observation is exploited, the gain under alternate pacing provides a useful experimental tool to identify a border-collision period-doubling bifurcation.
Patient-specific simulations of stenting procedures in coronary bifurcations: two clinical cases.
Morlacchi, Stefano; Colleoni, Sebastian George; Cárdenes, Rubén; Chiastra, Claudio; Diez, Jose Luis; Larrabide, Ignacio; Migliavacca, Francesco
2013-09-01
Computational simulations of stenting procedures in idealized geometries can only provide general guidelines and their use in the patient-specific planning of percutaneous treatments is inadequate. Conversely, image-based patient-specific tools that are able to realistically simulate different interventional options might facilitate clinical decision-making and provide useful insights on the treatment for each individual patient. The aim of this work is the implementation of a patient-specific model that uses image-based reconstructions of coronary bifurcations and is able to replicate real stenting procedures following clinical indications. Two clinical cases are investigated focusing the attention on the open problems of coronary bifurcations and their main treatment, the provisional side branch approach. Image-based reconstructions are created combining the information from conventional coronary angiography and computed tomography angiography while structural finite element models are implemented to replicate the real procedure performed in the patients. First, numerical results show the biomechanical influence of stents deployment in the coronary bifurcations during and after the procedures. In particular, the straightening of the arterial wall and the influence of two overlapping stents on stress fields are investigated here. Results show that a sensible decrease of the vessel tortuosity occurs after stent implantation and that overlapping devices result in an increased stress state of both the artery and the stents. Lastly, the comparison between numerical and image-based post-stenting configurations proved the reliability of such models while replicating stent deployment in coronary arteries.
Anomalous origin of the occipital artery diagnosed by magnetic resonance angiography
Energy Technology Data Exchange (ETDEWEB)
Uchino, Akira; Saito, Naoko; Mizukoshi, Waka; Okada, Yoshitaka [Saitama Medical University International Medical Center, Department of Diagnostic Radiology, Hidaka, Saitama (Japan)
2011-11-15
It is well known that the occipital artery (OA) can arise from the internal carotid artery (ICA) or vertebral artery (VA). However, the incidence of an anomalously originating OA has not been reported. We investigate its incidence and characteristic features on magnetic resonance angiography (MRA). We retrospectively reviewed MRA images of 2,866 patients that included the carotid bifurcation; images were obtained using a standard noncontrast MRA protocol and two 1.5-T MR units. We diagnosed six cases (seven arteries) of anomalously originating OA, which represented an incidence of 0.21%. The OA arose from the ICA in four patients (five arteries), from the carotid bifurcation in one, and from the VA in one. Five of the seven arteries occurred on the right. Anomalously originating OA is rare and occurs with right-side predominance. Correct diagnosis is necessary before or during cerebral angiography, especially when selective catheterization to the OA is required. (orig.)
Torus Bifurcation Under Discretization
Institute of Scientific and Technical Information of China (English)
邹永魁; 黄明游
2002-01-01
Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torns bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Fredholm theory in Banach spaces is applied to obtain the global torns bifurcation. Our results complement those on the study of discretization effects of global bifurcation.
Codimension-Two Bifurcation Analysis in Hindmarsh-Rose Model with Two Parameters
Institute of Scientific and Technical Information of China (English)
DUAN Li-Xia; LU Qi-Shao
2005-01-01
@@ Bifurcation phenomena in a Hindmarsh-Rose neuron model are investigated. Special attention is paid to the bifurcation structures off two parameters, where codimension-two generalized-Hopf bifurcation and fold-Hopf bifurcation occur. The classification offiring patterns as well as the transition mechanism in different regions on the parameter plane are obtained.
分叉血管有绕流物血液流分析%Analysis on Bifurcation Arterial Flow Around a Body
Institute of Scientific and Technical Information of China (English)
彭红梅; 杨德全
2011-01-01
In this paper,the blood hydrokinetic characteristics in the bifurcation blood vessel have been studied with the viscosity fluid boundary element methods.Besides the movement laws of the bloodstream in the branch tube,the changes of the blood flow have been studied when there is flow-round particle in the blood vessel.And some situations are indicted,such as the velocity vector distribution of the blood flow,the pressure distribution on the surface of the flow-round particle.The results show that the particle unsteadies at the main axis.It can move towards the high speed direction when it deviates due to some disturbances.The conclusion is consistent with the test result of the literature.The method of the paper turns the problem of handling about viscous flow from the area into the boundary so as to lower one dimension in calculation.It is very flexible and convenient to divide solving inner point value from the boundary.It needs less EMS memory,but with great accuracy.It provides a worthy approach for numerical calculation of bio-fluid engineering and other correlation domains.%用粘性流动边界元方法,研究了一类对称分叉血管中有绕流物时血液流问题.对血液在分叉血管内的流动规律,及血管内积存颗粒状绕流物的问题作了研究,给出了颗粒状绕流物处于不同位置时血液流场,及颗粒状绕流物表面的压力分布.计算中将粘性流体在区域上的求解问题化为边界上的求解问题,使问题的求解降低一个维度,由于内点值与边界值分开计算只在边界上作了近似因而精度较高,可为生物流的数值计算提供一种可靠方法.
Unfolding the Riddling Bifurcation
DEFF Research Database (Denmark)
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated,with the flow speed as the bifurcation parameter.The center manifold theory and complex normal form method are used to obtain the bifurcation equation.Interestingly,for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical.It is found,mathematically,this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter.The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.
Hemodynamics of Stent Implantation Procedures in Coronary Bifurcations: an in vitro study
Brindise, Melissa C; Burzotta, Francesco; Migliavacca, Francesco; Vlachos, Pavlos P
2016-01-01
Stent implantation in coronary bifurcations presents unique challenges and currently there is no universally accepted stent deployment approach. Despite clinical and computational studies, to date, the effect of each stent implantation method on the coronary artery hemodynamics is not well understood. In this study the hemodynamics of stented coronary bifurcations under pulsatile flow conditions were investigated experimentally. Three implantation methods, provisional side branch (PSB), culotte (CUL), and crush (CRU), were investigated using time-resolved particle image velocimetry (PIV) to measure the velocity fields. Subsequently, hemodynamic parameters including wall shear stress (WSS), oscillatory shear index (OSI), and relative residence time (RRT) were calculated and the pressure field through the vessel was non-invasively quantified. The effects of each stented case were evaluated and compared against an un-stented case. CRU provided the lowest compliance mismatch, but demonstrated detrimental stent in...
The Bifurcation Behavior of CO Coupling Reactor
Institute of Scientific and Technical Information of China (English)
徐艳; 马新宾; 许根慧
2005-01-01
The bifurcation behavior of the CO coupling reactor was examined based on the one-dimensional pseudohomogeneous axial dispersion dynamic model. The method of finite difference was used for solving the boundary value problem; the continuation technique and the direct method were applied to determine the bifurcation diagram.The effects of dimensionless adiabatic temperature rise, Damkoehler number, activation energy, heat transfer coefficient and feed ratio on the bifurcation behavior were investigated. It was shown that there existed static bifurcation and the oscillations did not occur in the reactor. The result also revealed that the reactor exhibited at most 1-3-1 multiplilicity patterns within the range of practical possible parameters and the measures, such as weakening the axial dispersion of reactor, enhancing heat transfer, decreasing the concentration of ethyl nitrite, were efficient for avoiding the possible risk of multiple steady states.
Wall shear stress in intracranial aneurysms and adjacent arteries
Institute of Scientific and Technical Information of China (English)
Fuyu Wang; Bainan Xu; Zhenghui Sun; Chen Wu; Xiaojun Zhang
2013-01-01
Hemodynamic parameters play an important role in aneurysm formation and growth. However, it is difficult to directly observe a rapidly growing de novo aneurysm in a patient. To investigate possible associations between hemodynamic parameters and the formation and growth of intracranial aneurysms, the present study constructed a computational model of a case with an internal carotid artery aneurysm and an anterior communicating artery aneurysm, based on the CT angiography findings of a patient. To simulate the formation of the anterior communicating artery aneurysm and the growth of the internal carotid artery aneurysm, we then constructed a model that virtually removed the anterior communicating artery aneurysm, and a further two models that also progressively decreased the size of the internal carotid artery aneurysm. Computational simulations of the fluid dynamics of the four models were performed under pulsatile flow conditions, and wall shear stress was compared among the different models. In the three aneurysm growth models, increasing size of the aneurysm was associated with an increased area of low wall shear stress, a significant decrease in wall shear stress at the dome of the aneurysm, and a significant change in the wall shear stress of the parent artery. The wall shear stress of the anterior communicating artery remained low, and was significantly lower than the wall shear stress at the bifurcation of the internal carotid artery or the bifurcation of the middle cerebral artery. After formation of the anterior communicating artery aneurysm, the wall shear stress at the dome of the internal carotid artery aneurysm increased significantly, and the wall shear stress in the upstream arteries also changed significantly. These findings indicate that low wall shear stress may be associated with the initiation and growth of aneurysms, and that aneurysm formation and growth may influence hemodynamic parameters in the local and adjacent arteries.
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Codimension two bifurcation of a vibro-bounce system
Institute of Scientific and Technical Information of China (English)
Guanwei Luo; Yandong Chu; Yanlong Zhang; Jianhua Xie
2005-01-01
A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one singleimpact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.
Saaski, E. W.
1974-01-01
The effect of noncondensable gases on high-performance arterial heat pipes was investigated both analytically and experimentally. Models have been generated which characterize the dissolution of gases in condensate, and the diffusional loss of dissolved gases from condensate in arterial flow. These processes, and others, were used to postulate stability criteria for arterial heat pipes under isothermal and non-isothermal condensate flow conditions. A rigorous second-order gas-loaded heat pipe model, incorporating axial conduction and one-dimensional vapor transport, was produced and used for thermal and gas studies. A Freon-22 (CHCIF2) heat pipe was used with helium and xenon to validate modeling. With helium, experimental data compared well with theory. Unusual gas-control effects with xenon were attributed to high solubility.
Bifurcations and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcing is investigated. The conditions of existence of primary resonance, second-order, third-order subharmonics, m-order subharmonics and chaos are given by using the second-averaging method, the Melnikov method and bifurcation theory. Numerical simulations including bifurcation diagram, bifurcation surfaces and phase portraits show the consistence with the theoretical analysis. The numerical results also exhibit new dynamical behaviors including onset of chaos, chaos suddenly disappearing to periodic orbit, cascades of inverse period-doubling bifurcations, period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, symmetry-breaking of periodic orbits, interleaving occurrence of chaotic behaviors and period-one orbit, a great abundance of periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaotic attractors. Our results show that many dynamical behaviors are strictly departure from the behaviors of the Duffing equation with odd-nonlinear restoring force.
Bifurcations analysis of oscillating hypercycles.
Guillamon, Antoni; Fontich, Ernest; Sardanyés, Josep
2015-12-21
We investigate the dynamics and transitions to extinction of hypercycles governed by periodic orbits. For a large enough number of hypercycle species (n>4) the existence of a stable periodic orbit has been previously described, showing an apparent coincidence of the vanishing of the periodic orbit with the value of the replication quality factor Q where two unstable (non-zero) equilibrium points collide (named QSS). It has also been reported that, for values below QSS, the system goes to extinction. In this paper, we use a suitable Poincaré map associated to the hypercycle system to analyze the dynamics in the bistability regime, where both oscillatory dynamics and extinction are possible. The stable periodic orbit is identified, together with an unstable periodic orbit. In particular, we are able to unveil the vanishing mechanism of the oscillatory dynamics: a saddle-node bifurcation of periodic orbits as the replication quality factor, Q, undergoes a critical fidelity threshold, QPO. The identified bifurcation involves the asymptotic extinction of all hypercycle members, since the attractor placed at the origin becomes globally stable for values Qbifurcation, these extinction dynamics display a periodic remnant that provides the system with an oscillating delayed transition. Surprisingly, we found that the value of QPO is slightly higher than QSS, thus identifying a gap in the parameter space where the oscillatory dynamics has vanished while the unstable equilibrium points are still present. We also identified a degenerate bifurcation of the unstable periodic orbits for Q=1.
Bifurcation analysis in single-species population model with delay
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A single-species population model is investigated in this paper.Firstly,we study the existence of Hopf bifurcation at the positive equilibrium.Furthermore,an explicit algorithm for determining the direction of the Hopf bifurcation and stability of the bifurcation periodic solutions are derived by using the normal form and the center manifold theory.At last,numerical simulations to support the analytical conclusions are carried out.
Bifurcation Analysis in a Delayed Diffusive Leslie-Gower Model
Directory of Open Access Journals (Sweden)
Shuling Yan
2013-01-01
Full Text Available We investigate a modified delayed Leslie-Gower model under homogeneous Neumann boundary conditions. We give the stability analysis of the equilibria of the model and show the existence of Hopf bifurcation at the positive equilibrium under some conditions. Furthermore, we investigate the stability and direction of bifurcating periodic orbits by using normal form theorem and the center manifold theorem.
Bifurcation property and persistence of configurations for parallel mechanisms
Institute of Scientific and Technical Information of China (English)
王玉新; 王仪明; 刘学深
2003-01-01
The configuration of parallel mechanisms at the singularity position is uncertain. How to control the mechanism through the singularity position with a given configuration is one of the key problems of the robot controlling. In this paper the bifurcation property and persistence of configurations at the singularity position is investigated for 3-DOF parallel mechanisms. The dimension of the bifurcation equations is reduced by Liapunov-Schmidt reduction method. According to the strong equivalence condition, the normal form which is consistent with the bifurcation condition of the original equation is selected. Through universal unfolding of the bifurcation equation, the influences of the disturbance factors, such as the influence of length of the input component on the configuration persistence at the bifurcation position, are analyzed. Using this method we can obtain the bifurcation curve in which the configuration will be held when the mechanism passes through the singularity position. Therefore, the configuration is under control in this way.
Codimension 2 reversible heteroclinic bifurcations with inclination flips
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, the heteroclinic bifurcation problem with real eigenvalues and two incli- nation-flips is investigated in a four-dimensional reversible system. We perform a detailed study of this case by using the method originally established in the papers "Problems in Homoclinic Bifurcation with Higher Dimensions" and "Bifurcation of Heteroclinic Loops," and obtain fruitful results, such as the existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic loops, R-symmetric homoclinic orbit and R-symmetric periodic orbit. The double R-symmetric homoclinic bifurcation (i.e., two-fold R-symmetric homoclinic bifurcation) for reversible heteroclinic loops is found, and the existence of infinitely many R-symmetric periodic orbits accumulating onto a homoclinic orbit is demonstrated. The relevant bifurcation surfaces and the existence regions are also located.
Codimension 2 reversible heteroclinic bifurcations with inclination flips
Institute of Scientific and Technical Information of China (English)
XU YanCong; ZHU DeMing; DENG GuiFeng
2009-01-01
In this paper,the heteroclinic bifurcation problem with real eigenvalues and two inclination-flips is investigated in a four-dimensional reversible system.We perform a detailed study of this case by using the method originally established in the papers "Problems in Homoclinic Bifurcation with Higher Dimensions" and "Bifurcation of Heteroclinic Loops," and obtain fruitful results,such as the existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic loops,R-symmetric homoclinic orbit and R-symmetric periodic orbit.The double R-symmetric homoclinic bifurcation (i.e.,two-fold R-symmetric homoclinic bifurcation) for reversible heteroclinic loops is found,and the existence of infinitely many R-symmetric periodic orbits accumulating onto a homoclinic orbit is demonstrated.The relevant bifurcation surfaces and the existence regions are also located.
Diffusion-driven instability and Hopf bifurcation in Brusselator system
Institute of Scientific and Technical Information of China (English)
LI Bo; WANG Ming-xin
2008-01-01
The Hopf bifurcation for the Brusselator ordinary-differential-equation (ODE)model and the corresponding partial-differential-equation(PDE)model are investigated by using the Hopf bifurcation theorem.The stability of the Hopf bifurcation periodic solution is di8cu88ed by applying the normal form theory and the center manifold theorem.When parameters satisfy some conditions,the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable.Our results show that if parameters are properly chosen,Hopf bifurcation does not occur for the ODE system,but occurs for the PDE system.
Bifurcation Analysis for Neural Networks in Neutral Form
Chen, Hong-Bing; Sun, Xiao-Ke
2016-06-01
In this paper, a system of neural networks in neutral form with time delay is investigated. Further, by introducing delay τ as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ is across some critical values. The direction of the Hopf bifurcations and the stability are determined by using normal form method and center manifold theory. Next, the global existence of periodic solution is established by using a global Hopf bifurcation result. Finally, an example is given to support the theoretical predictions.
LOCAL STABILITY AND BIFURCATION IN A THREE—UNIT DELAYED NEURAL NETWORK
Institute of Scientific and Technical Information of China (English)
LINYiping; LIJibin; 等
2003-01-01
A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given.
BIFURCATION OF LIMIT CYCLES FROM A DOUBLE HOMOCLINIC LOOP WITH A ROUGH SADDLE
Institute of Scientific and Technical Information of China (English)
HAN MAOAN; BI PING
2004-01-01
This paper concerns with the bifurcation of limit cycles from a double bomoclinic loop under multiple parameter perturbations for general planar systems. The existence conditions of 4 homoclinic bifurcation curves and small and large limit cycles are especially investigated.
Experimental investigations of the steady flow through an idealized model of a femoral artery bypass
Directory of Open Access Journals (Sweden)
Giurgea Corina
2014-03-01
Full Text Available The present paper presents the steps taken by the authors in the first stage of an experimental program within a larger national research project whose objective is to characterize the flow through a femoral artery bypass with a view to finding solutions for its optimization. The objective of the stage is to investigate by means of the PIV method the stationary flow through a bypass model with an idealized geometry. A bypass assembly which reunites the idealized geometry models of the proximal and distal anastomoses, and which respects the lengths of a femoral artery bypass was constructed on the basis of data for a real patient provided by medical investigations. With the aim of testing the model and the established experimental set-up with regard to their suitability for the assessment of the velocity field associated to the steady flow through the bypass, three zones that can restore the whole distal anastomosis were PIV investigated. The measurements were taken in the conditions of maintained inflow at the bypass entry of 0.9 l / min (Re = 600. The article presents comparatively the flow spectra and the velocity fields for each zone obtained in two situations: with the femoral artery completely occluded and completely open.
Influence of perturbations on period-doubling bifurcation
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1987-01-01
The influence of noise and resonant perturbation on a dynamical system in the vicinity of a period-doubling bifurcation is investigated. It is found that the qualitative dynamics can be revealed by simple considerations of the Poincaré map. These considerations lead to a shift of the bifurcation...
Bifurcation of hyperbolic planforms
Chossat, Pascal; Faugeras, Olivier
2010-01-01
Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperbolic plane D (Poincar\\'e disc). We make use of the concept of periodic lattice in D to further reduce the problem to one on a compact Riemann surface D/T, where T is a cocompact, torsion-free Fuchsian group. The knowledge of the symmetry group of this surface allows to carry out the machinery of equivariant bifurcation theory. Solutions which generically bifurcate are called "H-planforms", by analogy with the "planforms" introduced for pattern formation in Euclidean space. This concept is applied to the case of an octagonal periodic pattern, where we are able to classify all possible H-planforms satisfying the hypotheses o...
Minton, Roland; Pennings, Timothy J.
2007-01-01
When a dog (in this case, Tim Pennings' dog Elvis) is in the water and a ball is thrown downshore, it must choose to swim directly to the ball or first swim to shore. The mathematical analysis of this problem leads to the computation of bifurcation points at which the optimal strategy changes.
The Analysis of PPG Morphology: Investigating the Effects of Aging on Arterial Compliance
Yousef, Q.; Reaz, M. B. I.; Ali, M. A. M.
2012-12-01
This study presents the variations of photoplethysmogram (PPG) morphology with age. PPG measurement is done noninvasively at the index finger on both right and left hands for a sample of erectile dysfunction (ED) subjects. Some parameters are derived from the analysis of PPG contour showed in association with age. The age is found to be an important factor that affects the contour of PPG signals which accelerates the disappearance of PPG’s dicrotic notch and PPG’s inflection point as well. Arterial compliance is found to be degraded with age due to the fall of arterial elasticity. This study approaches the establishment of usefulness of PPG’s contour analysis as an investigator to the changes in the elastic properties of the vascular system, and as a detector of early sub-clinical atherosclerosis.
Bifurcations and Chaos in a Discrete Predator-prey System with Holling Type-Ⅳ Functional Response
Institute of Scientific and Technical Information of China (English)
Ji-cai Huang
2005-01-01
A discrete predator-prey system with Holling type-Ⅳ functional response obtained by the Euler method is first investigated. The conditions of existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory. Furthermore, we give the condition for the occurrence of codimension-two bifurcation called the Bogdanov-Takens bifurcation for fixed points and present approximate expressions for saddle-node, Hopf and homoclinic bifurcation sets near the Bogdanov-Takens bifurcation point. We also show, the existence of degenerated fixed point with codimension three at least. The numerical simulations, including bifurcation diagrams, phase portraits, and computation of maximum Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors such as the attracting invariant circle, period-doubling bifurcation from period-2,3,4 orbits,interior crisis, intermittency mechanic, and sudden disappearance of chaotic dynamic.
STABILITY AND BIFURCATION OF A HUMAN RESPIRATORY SYSTEM MODEL WITH TIME DELAY
Institute of Scientific and Technical Information of China (English)
沈启宏; 魏俊杰
2004-01-01
The stability and bifurcation of the trivial solution in the two-dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem. Furthermore, numerical simulation was carried out.
Stability of the Bifurcation Solutions for a Predator-Prey Model
Institute of Scientific and Technical Information of China (English)
孟义杰; 王一夫
2003-01-01
The bifurcation solution of the nonnegative steady-state of a reaction-diffusion system was investigated. The combination of the sturm-type eigenvalue and the theorem of bifurcation was used to study the local coexistence solutions, and obtain the stability of bifurcation solutions. The system model describes predator-prey interaction in an unstirred chemostat.
Stability and bifurcations in a nonlocal delayed reaction-diffusion population model
Chen, Shanshan; Yu, Jianshe
2016-01-01
A nonlocal delayed reaction-diffusion equation with Dirichlet boundary condition is considered in this paper. It is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium. The stability/instability of the bifurcated positive equilibrium and associated Hopf bifurcation are investigated, providing us with a complete picture of the dynamics.
Equilibrium Point Bifurcation and Singularity Analysis of HH Model with Constraint
2014-01-01
We present the equilibrium point bifurcation and singularity analysis of HH model with constraints. We investigate the effect of constraints and parameters on the type of equilibrium point bifurcation. HH model with constraints has more transition sets. The Matcont toolbox software environment was used for analysis of the bifurcation points in conjunction with Matlab. We also illustrate the stability of the equilibrium points.
Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay
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Xiaojian Zhou
2012-01-01
Full Text Available We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.
Stability and Hopf bifurcation in a symmetric Lotka-Volterra predator-prey system with delays
Directory of Open Access Journals (Sweden)
Jing Xia
2013-01-01
Full Text Available This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.
Stability and Bifurcation Analysis in a Diffusive Brusselator-Type System
Liao, Maoxin; Wang, Qi-Ru
2016-06-01
In this paper, the dynamic properties for a Brusselator-type system with diffusion are investigated. By employing the theory of Hopf bifurcation for ordinary and partial differential equations, we mainly obtain some conditions of the stability and Hopf bifurcation for the ODE system, diffusion-driven instability of the equilibrium solution, and the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions for the PDE system. Finally, some numerical simulations are presented to verify our results.
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations
Saputra, Kie Van Ivanky
2015-06-01
We investigate a dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analyzed and yield the transcritical bifurcation as the codimension-one bifurcation while the saddle-node-transcritical interaction and the Hopf-transcritical interactions as the codimension-two bifurcations. The unfolding of this degeneracy is also analyzed and reveal global bifurcations such as homoclinic and heteroclinic bifurcations. We apply our results to a modified Lotka-Volterra model and to an infection model in HIV diseases.
Post-Treatment Hemodynamics of a Basilar Aneurysm and Bifurcation
Energy Technology Data Exchange (ETDEWEB)
Ortega, J; Hartman, J; Rodriguez, J; Maitland, D
2008-01-16
Aneurysm re-growth and rupture can sometimes unexpectedly occur following treatment procedures that were initially considered to be successful at the time of treatment and post-operative angiography. In some cases, this can be attributed to surgical clip slippage or endovascular coil compaction. However, there are other cases in which the treatment devices function properly. In these instances, the subsequent complications are due to other factors, perhaps one of which is the post-treatment hemodynamic stress. To investigate whether or not a treatment procedure can subject the parent artery to harmful hemodynamic stresses, computational fluid dynamics simulations are performed on a patient-specific basilar aneurysm and bifurcation before and after a virtual endovascular treatment. The simulations demonstrate that the treatment procedure produces a substantial increase in the wall shear stress. Analysis of the post-treatment flow field indicates that the increase in wall shear stress is due to the impingement of the basilar artery flow upon the aneurysm filling material and to the close proximity of a vortex tube to the artery wall. Calculation of the time-averaged wall shear stress shows that there is a region of the artery exposed to a level of wall shear stress that can cause severe damage to endothelial cells. The results of this study demonstrate that it is possible for a treatment procedure, which successfully excludes the aneurysm from the vascular system and leaves no aneurysm neck remnant, to elevate the hemodynamic stresses to levels that are injurious to the immediately adjacent vessel wall.
Spiral blood flow in aorta-renal bifurcation models.
Javadzadegan, Ashkan; Simmons, Anne; Barber, Tracie
2016-01-01
The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta-renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta-renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta-renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries. PMID:26414530
Energy Technology Data Exchange (ETDEWEB)
Kim, Chang Hun [Dept. of Neurology, Stroke Center, Myongji Hospital, Goyang (Korea, Republic of); Cho, Young Dae; Kang, Hyun Seung; Kim, Jeong Eun; Han, Moon Hee [Seoul National University Hospital, Seoul National University College of Medicine, Seoul (Korea, Republic of); Jung, Seung Chai [Dept. of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul (Korea, Republic of); Ahn, Jun Hyong [Dept. of Neurosurgery, Hallym University Sacred Heart Hospital, Hallym University College of Medicine, Anyang (Korea, Republic of)
2015-08-15
Two angiographic instances of anomalous external carotid artery (ECA) and internal carotid artery (ICA) anastomosis are described, each occurring at the C2-3 level and bearing remnants of proximal ICA. The ICA remnant of one patient (identifiable immediately upon bifurcation of the common carotid artery) was hypoplastic, and that of the other patient was an occluded arterial stump. These features are not typical of non-bifurcating ICA. The occipital artery originated from an anomalous connection in one instance and from the main trunk of the ECA (just past the ECA-ICA connection) in the other.
Noise induced Hopf bifurcation
Shuda, I. A.; Borysov, S S; A.I. Olemskoi
2008-01-01
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle in dependence of relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest vari...
Symmetric/asymmetric bifurcation behaviours of a bogie system
DEFF Research Database (Denmark)
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue;
2013-01-01
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel–rail contact relation are investigated in detail by the ‘resultant bifurcation diagram’ method...... with slowly increasing and decreasing speed. It is found that the stationary equilibrium solution and the periodic motions coexist due to the sub-critical Hopf bifurcation in the railway bogie system. It is also found that multiple solutions coexist in many speed ranges. The coexistence of multiple solutions...... may result in a jump and hysteresis of the oscillating amplitude for different kinds of disturbances. It should be avoided in the normal operation. Furthermore, it is found that symmetry-breaking of the system through a pitchfork bifurcation leads to asymmetric chaotic motions in the railway bogie...
Bifurcation behaviours of peak current controlled PFC boost converter
Institute of Scientific and Technical Information of China (English)
Ren Hai-Peng; Liu Ding
2005-01-01
Bifurcation behaviours of the peak current controlled power-factor-correction (PFC) boost converter, including fast-scale instability and low-frequency bifurcation, are investigated in this paper. Conventionally, the PFC converter is analysed in continuous conduction mode (CCM). This prevents us from recognizing the overall dynamics of the converter. It has been pointed out that the discontinuous conduction mode (DCM) can occur in the PFC boost converter, especially in the light load condition. Therefore, the DCM model is employed to analyse the PFC converter to cover the possible DCM operation. By this way, the low-frequency bifurcation diagram is derived, which makes the route from period-double bifurcation to chaos clear. The bifurcation diagrams versus the load resistance and the output capacitance also indicate the stable operation boundary of the converter, which is useful for converter design.
Bifurcation behaviours of peak current controlled PFC boost converter
Ren, Hai-Peng; Liu, Ding
2005-07-01
Bifurcation behaviours of the peak current controlled power-factor-correction (PFC) boost converter, including fast-scale instability and low-frequency bifurcation, are investigated in this paper. Conventionally, the PFC converter is analysed in continuous conduction mode (CCM). This prevents us from recognizing the overall dynamics of the converter. It has been pointed out that the discontinuous conduction mode (DCM) can occur in the PFC boost converter, especially in the light load condition. Therefore, the DCM model is employed to analyse the PFC converter to cover the possible DCM operation. By this way, the low-frequency bifurcation diagram is derived, which makes the route from period-double bifurcation to chaos clear. The bifurcation diagrams versus the load resistance and the output capacitance also indicate the stable operation boundary of the converter, which is useful for converter design.
Institute of Scientific and Technical Information of China (English)
余琛; 熊建群; 李应华
2013-01-01
目的 探讨成人颈动脉分叉高度的超声测量与体重指数、颈内动脉形态变异的关系.方法 联合高、低频超声前瞻性检查728例受试者的双侧颈动脉,按照Wain的方法测量颈动脉分又高度及进行颈内动脉形态分型,分析颈动脉分叉高度与体重指数、颈内动脉形态变异发生率的关系.结果 体重指数≤24时,高位分叉占14.8％ (149/1010),＞24时占17.5％(78/446),两者差异无统计学意义(P＞0.05).在高位分叉组中,颈内动脉形态变异发生率约41.4％ (94/227),而正常分叉组中颈内动脉形态变异发生率约27.4％ (335/1221,P＜0.05),颈内动脉形态变异发生率与分叉高度呈正相关.结论 双侧颈动脉分叉高度与体重指数无显著相关,与形态变异相关.%Objective To explore relationship among the height of carotid bifurcation measured by duplex ultrasonography,body mass index (BMI) and morphological variations of the internal carotid arteries (ICA).Methods 728 subjects were examined by combination of high-and low-frequency ultrasonography.The height of carotid bifurcation was measured and morphological variations of the ICA were classified prospectively according to the criteria by Wain.Relationship among the height of carotid bifurcation,BMI,and morphological variations of the ICA were analyzed statistically.Results High bifurcation (≤ 1.5 cm) was not significantly (P＞ 0.05)different with BM1 below 24 (14.8％,149/1010)from that with BMI above 24 (17.5％,78/446).The prevalence of morphological variations of the ICA (41.4％,94/227) was significantly higher (P ＜ 0.05) in subjects with high carotid bifurcation than normal subjects (27.4％,335/1221).There was positive correlation between morphological variation of ICA and height of carotid bifurcation.Conclusions There is positive correlation between high carotid bifurcation and morphological variations of the ICA without correlation with BMI.
Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension
Institute of Scientific and Technical Information of China (English)
Shun ZHONG; Yu-shu CHEN
2009-01-01
A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established.Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory.Transition sets of the system and 40 groups of bifurcation diagrams are obtained.The local bifurcation is found,and shows the overall characteristics of bifurcation.Based on the relationship between parameters and the topological bifurcation solutions,motion characteristics with different parameters are obtained.The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.
International Nuclear Information System (INIS)
Objective: To investigate and analyze the cause of the tumble which occurs after transcatheter arterial chemoembolization (TACE), and to discuss its related factors. Methods: During the period from January 2003 to February 2010 in the Department of Interventional Radiology of Union Hospital (Wuhan city), post-TACE tumble occurred in 28 patients. The causes of the tumble were investigated and analyzed. Results: (1) The total number of the tumble occurrence after TACE was declining with the year. (2) Certain relationship existed between the occurrence of post-TACE tumble and the patient's age, drugs used in surgery, unit environment, nurse's shift, etc. Conclusion: Based on the patient's individual condition, intentionally enhancing the perioperative nursing care and adjusting the nurse's shift are very important measures to prevent the occurrence of post-TACE tumble. (authors)
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-01-01
Full Text Available Hopf bifurcation of a delayed predator-prey system with prey infection and the modified Leslie-Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifurcation in the system. In addition, direction of Hopf bifurcation and stability of the bifurcated periodic solutions of the controlled system are obtained by using normal form and center manifold theory. Finally, numerical simulation results are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation.
Synchronization and Bifurcation of General Complex Dynamical Networks
Institute of Scientific and Technical Information of China (English)
SUN Wei-Gang; XU Cong-Xiang; LI Chang-Pin; FANG Jin-Qing
2007-01-01
In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.
Delay Induced Hopf Bifurcation of Small-World Networks
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the stability and the Hopf bifurcation of small-world networks with time delay are studied. By analyzing the change of delay, we obtain several sufficient conditions on stable and unstable properties. When the delay passes a critical value, a Hopf bifurcation may appear. Furthermore, the direction and the stability of bifurcating periodic solutions are investigated by the normal form theory and the center manifold reduction. At last, by numerical simulations, we further illustrate the effectiveness of theorems in this paper.
Systematic experimental exploration of bifurcations with noninvasive control.
Barton, D A W; Sieber, J
2013-05-01
We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular noninvasive control schemes, such as (Pyragas) time-delayed or washout-filtered feedback control, can be overcome for tracking equilibria or forced periodic orbits in experiments. To demonstrate the use of our noninvasive control, we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability, around two saddle-node bifurcations (folds) and a cusp bifurcation.
Neural Excitability and Singular Bifurcations.
De Maesschalck, Peter; Wechselberger, Martin
2015-12-01
We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov-Takens/SNIC bifurcation while type II excitability is associated with a singular Andronov-Hopf bifurcation. In both cases, canards play an important role in the understanding of the unfolding of these singular bifurcation structures. We also explain the transition between the two excitability types and highlight all bifurcations involved, thus providing a complete analysis of excitability based on geometric singular perturbation theory.
Directory of Open Access Journals (Sweden)
Weiguo Rui
2015-01-01
Full Text Available By using Frobenius’ idea together with integral bifurcation method, we study a third order nonlinear equation of generalization form of the modified KdV equation, which is an important water wave model. Some exact traveling wave solutions such as smooth solitary wave solutions, nonsmooth peakon solutions, kink and antikink wave solutions, periodic wave solutions of Jacobian elliptic function type, and rational function solution are obtained. And we show their profiles and discuss their dynamic properties aim at some typical solutions. Though the types of these solutions obtained in this work are not new and they are familiar types, they did not appear in any existing literatures because the equation ut+ux+νuxxt+βuxxx + αuux+1/3να(uuxxx+2uxuxx+3μα2u2ux+νμα2(u2uxxx+ux3+4uuxuxx + ν2μα2(ux2uxxx+2uxuxx2 = 0 is very complex. Particularly, compared with the cited references, all results obtained in this paper are new.
Hopf bifurcations in a predator-prey system with multiple delays
Energy Technology Data Exchange (ETDEWEB)
Hu Guangping [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); School of Mathematics and Physics, Nanjing University of Information and Technology, Nanjing 210044 (China); Li Wantong [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)], E-mail: wtli@lzu.edu.cn; Yan Xiangping [Department of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070 (China)
2009-10-30
This paper is concerned with a two species Lotka-Volterra predator-prey system with three discrete delays. By regarding the gestation period of two species as the bifurcation parameter, the stability of positive equilibrium and Hopf bifurcations of nonconstant periodic solutions are investigated. Furthermore, the direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs). In addition, the global existence of bifurcated periodic solutions are also established by employing the topological global Hopf bifurcation theorem, which shows that the local Hopf bifurcations imply the global ones after the second critical value of parameter. Finally, to verify our theoretical predictions, some numerical simulations are also included.
Multi-Bifurcation Effect of Blood Flow by Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
RAO Yong; NI Yu-Shan; LIU Chao-Feng
2008-01-01
The multi-bifurcation effect of blood flow is investigated by lattice Boltzmann method at Re = 200 with six different bifurcation angles α, which are 22.5°, 25°, 28°, 30°, 33°, 35°, respectively. The velocities and ratios of average velocity at various bifurcations are discussed. It is indicated that the maximum velocity at the section near the first divider increases and shifts towards the walls of branch with the increase of α. At the first bifurcation, the average horizontal velocities increase with the increase of α. The average horizontal velocities of outer branches at the secondary bifurcation decrease at 22.5°≤α≤30° and increase at 30°≤α≤35°, whereas those of inner branches at the secondary bifurcation have the opposite variation, as the same as the above variations of the ratios of average horizontal velocities at various bifurcations. The ratios of average vertical velocities of branch at first bifurcation to that of outer branches at the secondary bifurcation increase at 22.5°≤α≤30° and decrease at 30°≤α≤35°, whereas the ratios of average vertical velocities of branch at first bifurcation to that of inner branches at the secondary bifurcation always decrease.
Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model.
Dtchetgnia Djeundam, S R; Yamapi, R; Kofane, T C; Aziz-Alaoui, M A
2013-09-01
We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.
Introduction to bifurcation theory
International Nuclear Information System (INIS)
Bifurcation theory is a subject with classical mathematical origins. The modern development of the subject starts with Poincare and the qualitative theory of differential equations. In recent years, the theory has undergone a tremendous development with the infusion of new ideas and methods from dynamical systems theory, singularity theory, group theory, and computer-assisted studies of dynamics. As a result, it is difficult to draw the boundaries of the theory with any confidence. In this review, the objects in question will be parameterized families of dynamical systems (vector fields or maps). In the sciences these families commonly arise when one formulates equations of motion to model a physical system. We specifically analyze how the time evolution near an equilibrium can change as parameters are varied; for simplicity we consider the case of a single parameter only
Bifurcation structure of the C-type period-doubling transition
DEFF Research Database (Denmark)
Laugesen, Jakob Lund; Mosekilde, Erik; Zhusubaliyev, Zhanybai T.
2012-01-01
(Arneodo et al. (1983) [15]). Using the Rössler system as an example, we present a detailed analysis of the bifurcation structure associated with the forcing of a three-dimensional period-doubling system. We explain how this structure is related to the recently discovered phenomenon of multi-layered tori...... and discuss different bifurcation scenarios that transform a resonance torus into a period-doubled ergodic torus. Similar bifurcation phenomena have recently been observed in a biologically relevant model of kidney blood flow regulation in response to fluctuations in arterial pressure....
Clip reconstruction of a large right MCA bifurcation aneurysm. Case report
Directory of Open Access Journals (Sweden)
Giovani A.
2014-06-01
Full Text Available We report a case of complex large middle cerebral artery (MCA bifurcation aneurysm that ruptured during dissection from the very adherent MCA branches but was successfully clipped and the MCA bifurcation reconstructed using 4 Yasargill clips. Through a right pterional craniotomy the sylvian fissure was largely opened as to allow enough workspace for clipping the aneurysm and placing a temporary clip on M1. The pacient recovered very well after surgery and was discharged after 1 week with no neurological deficit. Complex MCA bifurcation aneurysms can be safely reconstructed using regular clips, without the need of using fenestrated clips or complex by-pass procedures.
Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems
Harb, Ahmad M.
1996-01-01
A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA$#$ generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical co...
Bifurcations sights, sounds, and mathematics
Matsumoto, Takashi; Kokubu, Hiroshi; Tokunaga, Ryuji
1993-01-01
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, howev...
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
The influence of perturbations (a small, near-resonant signal and noise) on a driven dissipative dynamical system that is close to undergoing a period-doubling bifurcation is investigated. It is found that the system is very sensitive, and that periodic perturbations change its stability in a wel...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Directory of Open Access Journals (Sweden)
Emanuel Dias
2010-12-01
gluteal claudication, intestinal ischemia, vesical and intestinal disfunction, neurologic deficits and impotence. The use of branched endoprothesis with preservation of the hypgastric artery is a recente innovation to reduce such complications. Clinical case: A 63 year-old male, previously submitted to an open repair of an abdominal aortic aneurysm with an aorto-aortic prothesis, was admitted for endovascular treatment of an aneurysm of the right common and internal iliac arteries with 3,3cm. A Zenith® branched endoprothesis with a branch to the iliac bifurcation was deployed via right femoral access, thus assuring preservation of the hypogastric artery. Conclusion: Hypogastric preservation necessity during EVAR in aorto-iliac aneurysms may be achieved in a secure and simple way through the placement of endoprothesis to the iliac bifurcation.
Bifurcation theory for hexagonal agglomeration in economic geography
Ikeda, Kiyohiro
2014-01-01
This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distri...
Bifurcation behaviors of catalytic combustion in a micro-channel
Institute of Scientific and Technical Information of China (English)
Wen Zeng; Maozhao Xie; Hongan Maa; Wei Xua
2008-01-01
Bifurcation analysis of ignition and extinction of catalytic combustion in a short micro-channel is carried out with the laminar flow model incorporated as the flow model. The square of transverse Thiele modulus and the realdence time are used as bifurcation parameters. The influences of different parameters on ignition and extinction behavior are investigated. It is shown that all these parameters have great effects on the bifurcation behaviors of ignition and extinction in the short micro-channel. The effects of flow models on bifurcation behaviors of combustion are also analyzed. The results show that in comparison with the fiat velocity profile model, for the case of the laminar flow model, the temperatures of ignition and extinction of combustion ate higher and the unsteady multiple solution region is larger.
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings. PMID:27586627
Grazing bifurcation and chaos in response of rubbing rotor
International Nuclear Information System (INIS)
This paper investigates the grazing bifurcation in the nonlinear response of a complex rotor system. For a rotor with overhung disc, step diameter shaft and elastic supports, the motion equations are derived based on the Transition Matrix Method. When the rotor speed increases, the disc will touch the case and lead to rubbing of rotor. When the disc rubs with the case, the elastic force and friction force of the case will make the rotor exhibit nonlinear characteristics. For the piecewise ODEs, the numerical method is applied to obtain its nonlinear response. From the results, the grazing bifurcation, which happens at the moment of touching between disc and case, can be observed frequently. The grazing bifurcation can lead to the jump between periodic orbits. The response can go to chaos from periodic motion under grazing bifurcation. When grazing occurs, response can become quasi-period from period
Bifurcation dynamics of the tempered fractional Langevin equation
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study
International Nuclear Information System (INIS)
There is recent interest in the role of carotid bifurcation anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis. Certain anatomical and geometric configurations at the carotid bifurcation have been linked to disturbed flow. It has been proposed that vascular dimensions are selected to minimize energy required to maintain blood flow, and that this occurs when an exponent of 3 relates the radii of parent and daughter arteries. We evaluate whether the dimensions of bifurcation of the extracranial carotid artery follow this principle of minimum work. This study involved subjects who had computed tomographic angiography (CTA) at our institution between 2006 and 2007. Radii of the common, internal and external carotid arteries were determined. The exponent was determined for individual bifurcations using numerical methods and for the sample using nonlinear regression. Mean age for 45 participants was 56.9 ± 16.5 years with 26 males. Prevalence of vascular risk factors was: hypertension-48%, smoking-23%, diabetes-16.7%, hyperlipidemia-51%, ischemic heart disease-18.7%. The value of the exponent ranged from 1.3 to 1.6, depending on estimation methodology. The principle of minimum work (defined by an exponent of 3) may not apply at the carotid bifurcation. Additional factors may play a role in the relationship between the radii of the parent and daughter vessels
Institute of Scientific and Technical Information of China (English)
Ji-cai Huang; Dong-mei Xiao
2004-01-01
In this paper the dynamical behaviors of a predator-prey system with Holling Type-IV functional response are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numerical simulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stable limit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddlenode bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibrium and the existence of homoclinic orbit by using numerical simulation.
Bifurcation Adds Flavor to Basketball
Min, Byeong June
2016-01-01
We report an emergence of bifurcation in basketball, a single-particle system governed by Newtonian mechanics. When shooting the basketball, the obvious control parameters are the launch speed and the launch angle. We propose to use the three-dimensional velocity phase-space volume associated with the given launch parameters to quantify the difficulty of the shooting. The optimal launch angle that maximizes the associated phase-space volume undergoes a bifurcation as the launch speed is increased, if the shooter is farther than a critical distance away from the hoop. Thus, the bifurcation makes it very important to control the launch speed accurately. If the air resistance is removed, the bifurcation disappears and the phase-space volume distribution becomes dispersionless and shrinks in magnitude.
Pathological observation of brain arteries and spontaneous aneurysms in hypertensive rats
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Objective To investigate the role of hypertension in the pathogenesis of cerebral aneurysms in rats.Methods Twenty spontaneous hypertensive rats (SHR) and 10 Wistar-Kyoto rats (WKY) were included in this observational study. Animals were fed with normal diet and drinking water. No experimental modifications were undertaken in either group. They were sacrificed at one year of age, the bifurcations of the circle of Willis were dissected and longitudinal serial sections were prepared for light microscopic and transmission electron microscopic study.Results In the SHR group, 2 of the 20 rats formed an aneurysm respectively at the bifurcations of the basilar artery. As revealed by electron microscopy, injury at the bifurcation of the artery first occurred on the steeper side of the intimal pad. Furthermore, loss of endothelial cells, small depressions on the intima, disruptive internal elastic lamina and lymphocytes or red blood cells infiltration were noted at the steeper side of the intimal pad. No significant changes were observed in WKY group.Conclusions Cerebral aneurysms can form spontaneously in SHR without ligation of the common carotid artery and without a diet containing β-aminoproprionitrile. Long-standing systemic arterial hypertension is one of the etiological factors that contributes to aneurysm formation in SHR rats.
Bifurcations, instabilities, degradation in geomechanics
Exadaktylos, George
2007-01-01
Leading international researchers and practitioners of bifurcations and instabilities in geomechanics debate the developments and applications which have occurred over the last few decades. The topics covered include modeling of bifurcation, structural failure of geomaterials and geostructures, advanced analytical, numerical and experimental techniques, and application and development of generalised continuum models etc. In addition analytical solutions, numerical methods, experimental techniques, and case histories are presented. Beside fundamental research findings, applications in geotechni
Rarefaction and blood pressure in systemic and pulmonary arteries.
Olufsen, Mette S; Hill, N A; Vaughan, Gareth D A; Sainsbury, Christopher; Johnson, Martin
2012-08-01
The effects of vascular rarefaction (the loss of small arteries) on the circulation of blood are studied using a multiscale mathematical model that can predict blood flow and pressure in the systemic and pulmonary arteries. We augmented a model originally developed for the systemic arteries (Olufsen et al. 1998, 1999, 2000, 2004) to (a) predict flow and pressure in the pulmonary arteries, and (b) predict pressure propagation along the small arteries in the vascular beds. The systemic and pulmonary arteries are modelled as separate, bifurcating trees of compliant and tapering vessels. Each tree is divided into two parts representing the `large' and `small' arteries. Blood flow and pressure in the large arteries are predicted using a nonlinear cross-sectional area-averaged model for a Newtonian fluid in an elastic tube with inflow obtained from magnetic resonance measurements. Each terminal vessel within the network of the large arteries is coupled to a vascular bed of small `resistance' arteries, which are modelled as asymmetric structured trees with specified area and asymmetry ratios between the parent and daughter arteries. For the systemic circulation, each structured tree represents a specific vascular bed corresponding to major organs and limbs. For the pulmonary circulation, there are four vascular beds supplied by the interlobar arteries. This manuscript presents the first theoretical calculations of the propagation of the pressure and flow waves along systemic and pulmonary large and small arteries. Results for all networks were in agreement with published observations. Two studies were done with this model. First, we showed how rarefaction can be modelled by pruning the tree of arteries in the microvascular system. This was done by modulating parameters used for designing the structured trees. Results showed that rarefaction leads to increased mean and decreased pulse pressure in the large arteries. Second, we investigated the impact of decreasing vessel
ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN L(é)VY NOISES
Institute of Scientific and Technical Information of China (English)
Chen Huiqin; Duan Jinqiao; Zhang Chengjian
2012-01-01
Nonlinear dynamical systems are sometimes under the influence of random fluctuations.It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.@@A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable Lévy motions,by examining the changes in stationary probability density functions for the solution orbits of this stochastic system.The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically.This allows numerically investigating phenomenological bifurcation,or P-bifurcation,for stochastic differential equations with non-Gaussian Lévy noises.
Fast automatic algorithm for bifurcation detection in vascular CTA scans
Brozio, Matthias; Gorbunova, Vladlena; Godenschwager, Christian; Beck, Thomas; Bernhardt, Dominik
2012-02-01
Endovascular imaging aims at identifying vessels and their branches. Automatic vessel segmentation and bifurcation detection eases both clinical research and routine work. In this article a state of the art bifurcation detection algorithm is developed and applied on vascular computed tomography angiography (CTA) scans to mark the common iliac artery and its branches, the internal and external iliacs. In contrast to other methods our algorithm does not rely on a complete segmentation of a vessel in the 3D volume, but evaluates the cross-sections of the vessel slice by slice. Candidates for vessels are obtained by thresholding, following by 2D connected component labeling and prefiltering by size and position. The remaining candidates are connected in a squared distanced weighted graph. With Dijkstra algorithm the graph is traversed to get candidates for the arteries. We use another set of features considering length and shape of the paths to determine the best candidate and detect the bifurcation. The method was tested on 119 datasets acquired with different CT scanners and varying protocols. Both easy to evaluate datasets with high resolution and no apparent clinical diseases and difficult ones with low resolution, major calcifications, stents or poor contrast between the vessel and surrounding tissue were included. The presented results are promising, in 75.7% of the cases the bifurcation was labeled correctly, and in 82.7% the common artery and one of its branches were assigned correctly. The computation time was on average 0.49 s +/- 0.28 s, close to human interaction time, which makes the algorithm applicable for time-critical applications.
Effects of Bifurcations on Aft-Fan Engine Nacelle Noise
Nark, Douglas M.; Farassat, Fereidoun; Pope, D. Stuart; Vatsa, Veer N.
2004-01-01
Aft-fan engine nacelle noise is a significant factor in the increasingly important issue of aircraft community noise. The ability to predict such noise within complex duct geometries is a valuable tool in studying possible noise attenuation methods. A recent example of code development for such predictions is the ducted fan noise propagation and radiation code CDUCT-LaRC. This work focuses on predicting the effects of geometry changes (i.e. bifurcations, pylons) on aft fan noise propagation. Beginning with simplified geometries, calculations show that bifurcations lead to scattering of acoustic energy into higher order modes. In addition, when circumferential mode number and the number of bifurcations are properly commensurate, bifurcations increase the relative importance of the plane wave mode near the exhaust plane of the bypass duct. This is particularly evident when the bypass duct surfaces include acoustic treatment. Calculations involving more complex geometries further illustrate that bifurcations and pylons clearly affect modal content, in both propagation and radiation calculations. Additionally, results show that consideration of acoustic radiation results may provide further insight into acoustic treatment effectiveness for situations in which modal decomposition may not be straightforward. The ability of CDUCT-LaRC to handle complex (non-axisymmetric) multi-block geometries, as well as axially and circumferentially segmented liners, allows investigation into the effects of geometric elements (bifurcations, pylons).
LOCAL AND GLOBAL HOPF BIFURCATIONS IN A DELAYED HUMAN RESPIRATORY SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper considers a delayed human respiratory model. Firstly, the stability of the equilibrium of the model is investigated and the occurrence of a sequence of Hopf bifurcations of the model is proved. Secondly, the explicit algorithms which determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by applying the normal form method and the center manifold theory. Finally, the existence of the global periodic solutions is showed under some ass...
Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting
Directory of Open Access Journals (Sweden)
Fengying Wei
2014-01-01
Full Text Available A kind of delayed predator-prey system with harvesting is considered in this paper. The influence of harvesting and delay is investigated. Our results show that Hopf bifurcations occur as the delay τ passes through critical values. By using of normal form theory and center manifold theorem, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are obtained. Finally, numerical simulations are given to support our theoretical predictions.
Complex dynamics in biological systems arising from multiple limit cycle bifurcation.
Yu, P; Lin, W
2016-12-01
In this paper, we study complex dynamical behaviour in biological systems due to multiple limit cycles bifurcation. We use simple epidemic and predator-prey models to show exact routes to new types of bistability, that is, bistability between equilibrium and periodic oscillation, and bistability between two oscillations, which may more realistically describe the real situations. Bifurcation theory and normal form theory are applied to investigate the multiple limit cycles bifurcating from Hopf critical point. PMID:27042877
Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems
Directory of Open Access Journals (Sweden)
Jinglei Tian
2014-01-01
Full Text Available Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis.
Prediction of fibre architecture and adaptation in diseased carotid bifurcations.
LENUS (Irish Health Repository)
Creane, Arthur
2011-12-01
Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.
Bifurcation analysis of a predator–prey model with anti-predator behaviour
International Nuclear Information System (INIS)
We investigated a predator–prey model with a nonmonotonic functional response and anti-predator behaviour such that the adult prey can attack vulnerable predators. By analyzing the existence and stability of all possible equilibria and conducting a bifurcation analysis, we obtained the global dynamics of the proposed system. The system could undergo a saddle-node bifurcation, (supercritical and subcritical) Hopf bifurcation, homoclinic bifurcation and a Bogdanov–Takens bifurcation of codimension 2. Further, we obtained a generic family unfolding for the system by choosing the environmental carrying capacity of the prey and the death rate of the predator as bifurcation parameters. Numerical studies showed that anti-predator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predator–prey oscillations. Therefore, anti-predator behaviour helps the prey population to resist predator aggression
Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge
Directory of Open Access Journals (Sweden)
Qingsong Liu
2014-01-01
Full Text Available A modified Leslie-Gower predator-prey system with two delays is investigated. By choosing τ1 and τ2 as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed. Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
Dynamic bifurcation of a modified Kuramoto-Sivashinsky equation with higher-order nonlinearity
Institute of Scientific and Technical Information of China (English)
Huang Qiong-Wei; Tang Jia-Shi
2011-01-01
Under the periodic boundary condition,dynamic bifurcation and stability in the modified Kuramoto-Sivashinsky equation with a higher-order nonlinearity p(ux)Puxx are investigated by using the centre manifold reduction procedure.The result shows that as the control parameter crosses a critical value,the system undergoes a bifurcation from the trivial solution to produce a cycle consisting of locally asymptotically stable equilibrium points. Furthermore,for cases in which the distances to the bifurcation points are small enough,one-order approximations to the bifurcation solutions are obtained.
Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays
Directory of Open Access Journals (Sweden)
Xin-You Meng
2014-01-01
Full Text Available A class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998. Numerical simulations are given to support the theoretical results.
Control of Fold Bifurcation Application on Chemostat around Critical Dilution Rate
DEFF Research Database (Denmark)
Pedersen, Kurt; Jørgensen, Sten Bay
1999-01-01
Based on a bifurcation analysis of a process it is possible to point out where there might be operational problems due to change of stability of the process. One such change is investigated, Fold bifurcations. This type of bifurcation is associated with hysteresis/multiple steady states, which...... complicates operation close to these bifurcations. Typically only one of the steady states is interesting from a production point of view. A novel control law is proposed herein which is able to cope with the operational problems of the process....
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,an introduction to the bifurcation theory and its applicability to the study of sub-synchronous resonance (SSR) phenomenon in power system are presented. The continuation and bifurcation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.
Institute of Scientific and Technical Information of China (English)
DUAN XianZhong; WEN JinYu; CHENG ShiJie
2009-01-01
In this paper, an introduction to the bifurcation theory and its applicability to the study of sub-syn-chronous resonance (SSR) phenomenon in power system are presented. The continuation and bifur-cation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.
The Flatness of Bifurcations in 3D Dendritic Trees: An Optimal Design.
van Pelt, Jaap; Uylings, Harry B M
2011-01-01
The geometry of natural branching systems generally reflects functional optimization. A common property is that their bifurcations are planar and that daughter segments do not turn back in the direction of the parent segment. The present study investigates whether this also applies to bifurcations in 3D dendritic arborizations. This question was earlier addressed in a first study of flatness of 3D dendritic bifurcations by Uylings and Smit (1975), who used the apex angle of the right circular cone as flatness measure. The present study was inspired by recent renewed interest in this measure. Because we encountered ourselves shortcomings of this cone angle measure, the search for an optimal measure for flatness of 3D bifurcation was the second aim of our study. Therefore, a number of measures has been developed in order to quantify flatness and orientation properties of spatial bifurcations. All these measures have been expressed mathematically in terms of the three bifurcation angles between the three pairs of segments in the bifurcation. The flatness measures have been applied and evaluated to bifurcations in rat cortical pyramidal cell basal and apical dendritic trees, and to random spatial bifurcations. Dendritic and random bifurcations show significant different flatness measure distributions, supporting the conclusion that dendritic bifurcations are significantly more flat than random bifurcations. Basal dendritic bifurcations also show the property that their parent segments are generally aligned oppositely to the bisector of the angle between their daughter segments, resulting in "symmetrical" configurations. Such geometries may arise when during neuronal development the segments at a newly formed bifurcation are subjected to elastic tensions, which force the bifurcation into an equilibrium planar shape. Apical bifurcations, however, have parent segments oppositely aligned with one of the daughter segments. These geometries arise in the case of side
International Nuclear Information System (INIS)
Congenital absence of the unilateral internal carotid artery (ICA) was found in a patient during MR imaging examination for right trigeminal neuralgia. Magnetic resonance angiography showed complete absence of the right ICA and a large tortuous basilar artery (BA). The source images revealed a deformed right trigeminal nerve resulting from compression by the BA. Computed tomography of the skull base showed absence of the right carotid canal, suggesting agenesis of the right ICA. Longstanding hemodynamic stress may have caused the BA to become extremely tortuous, resulting in the trigeminal neuralgia. (orig.)
Uchino, A; Sawada, A; Hirakawa, N; Totoki, T; Kudo, S
2002-09-01
Congenital absence of the unilateral internal carotid artery (ICA) was found in a patient during MR imaging examination for right trigeminal neuralgia. Magnetic resonance angiography showed complete absence of the right ICA and a large tortuous basilar artery (BA). The source images revealed a deformed right trigeminal nerve resulting from compression by the BA. Computed tomography of the skull base showed absence of the right carotid canal, suggesting agenesis of the right ICA. Longstanding hemodynamic stress may have caused the BA to become extremely tortuous, resulting in the trigeminal neuralgia. PMID:12195492
Energy Technology Data Exchange (ETDEWEB)
Uchino, A.; Sawada, A.; Kudo, S. [Department of Radiology, Saga Medical School, 5-1-1, Nabeshima, Saga (Japan); Hirakawa, N.; Totoki, T. [Department of Anesthesiology, Saga Medical School, 5-1-1, Nabeshima, Saga (Japan)
2002-09-01
Congenital absence of the unilateral internal carotid artery (ICA) was found in a patient during MR imaging examination for right trigeminal neuralgia. Magnetic resonance angiography showed complete absence of the right ICA and a large tortuous basilar artery (BA). The source images revealed a deformed right trigeminal nerve resulting from compression by the BA. Computed tomography of the skull base showed absence of the right carotid canal, suggesting agenesis of the right ICA. Longstanding hemodynamic stress may have caused the BA to become extremely tortuous, resulting in the trigeminal neuralgia. (orig.)
E. V. Nikolaeva; I. A. Kurmukov; N N Yudkina; A. V. Volkov
2015-01-01
Pulmonary arterial hypertension (PAH) associated with systemic connective tissue diseases (SCTD) is a poor prognostic manifestation of the latter that result in death if untreated. The invasive determination of hemodynamic parameters is prominent in diagnosing the disease and determining its treatment policy and prognosis.Objective: to analyze the results of catheterization in PAH-SCTD patients admitted to the V.A. Nasonova Research Institute of Rheumatology.Subjects and methods. The investig...
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.
Controlling hopf bifurcations: Discrete-time systems
Directory of Open Access Journals (Sweden)
Guanrong Chen
2000-01-01
Full Text Available Bifurcation control has attracted increasing attention in recent years. A simple and unified state-feedback methodology is developed in this paper for Hopf bifurcation control for discrete-time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.
Multiple Bifurcations of a Cylindrical Dynamical System
Han Ning; Cao Qingjie
2016-01-01
This paper focuses on multiple bifurcations of a cylindrical dynamical system, which is evolved from a rotating pendulum with SD oscillator. The rotating pendulum system exhibits the coupling dynamics property of the bistable state and conventional pendulum with the ho- moclinic orbits of the first and second type. A double Andronov-Hopf bifurcation, two saddle-node bifurcations of periodic orbits and a pair of homoclinic bifurcations are detected by using analytical analysis and nu- merical ...
Bifurcations associated with sub-synchronous resonance
Mitani, Yasunori; K. Tsuji; M.Varghese; Wu, F. F.; VARAIYA, P
1998-01-01
This paper describes a set of results of detecting nonlinear phenomena appearing in a turbine generator power system with series-capacitor compensation. The analysis was based on the Floquet theory as well as the Hopf bifurcation theorem. After the first Hopf bifurcation, the stable limit cycle bifurcates to a stable torus and an unstable limit cycle which connects to a stable limit cycle by a supercritical torus bifurcation. The stable limit cycle joins with an unstable limit cycle at a cycl...
Delayed Hopf bifurcation in time-delayed slow-fast systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems.Here the two delayed’s have different meanings.The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point,but at some other point which is above the bifurcation point by an obvious distance.In a time-delayed system,the evolution of the system depends not only on the present state but also on past states.In this paper,the time-delayed slow-fast system is firstly simplified to a slow-fast system without time delay by means of the center manifold reduction,and then the so-called entry-exit function is defined to characterize the delayed bifurcation on the basis of Neishtadt’s theory.It shows that delayed Hopf bifurcation exists in time-delayed slow-fast systems,and the theoretical prediction on the exit-point is in good agreement with the numerical calculation,as illustrated in the two illustrative examples.
Bifurcation analysis of polynomial models for longitudinal motion at high angle of attack
Institute of Scientific and Technical Information of China (English)
Shi Zhongke; Fan Li
2013-01-01
To investigate the longitudinal motion stability of aircraft maneuvers conveniently,a new stability analysis approach is presented in this paper.Based on describing longitudinal aerodynamics at high angle-of-attack (α ＜ 50°) motion by polynomials,a union structure of two-order differential equation is suggested.By means of nonlinear theory and method,analytical and global bifurcation analyses of the polynomial differential systems are provided for the study of the nonlinear phenomena of high angle-of-attack flight.Applying the theories of bifurcations,many kinds of bifurcations,such as equilibrium,Hopf,homoclinic (heteroclinic) orbit and double limit cycle bifurcations are discussed and the existence conditions for these bifurcations as well as formulas for calculating bifurcation curves are derived.The bifurcation curves divide the parameter plane into several regions; moreover,the complete bifurcation diagrams and phase portraits in different regions are obtained.Finally,our conclusions are applied to analyzing the stability and bifurcations of a practical example of a high angle-of-attack flight as well as the effects of elevator deflection on the asymptotic stability regions of equilibrium.The model and analytical methods presented in this paper can be used to study the nonlinear flight dynamic of longitudinal stall at high angle of attack.
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Institute of Scientific and Technical Information of China (English)
Xin Qi; Shi Zhongke
2015-01-01
Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To pre-dict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynam-ics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurca-tion and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders ser-ies of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.
Thermodynamic geometry and critical aspects of bifurcations.
Mihara, A
2016-07-01
This work presents an exploratory study of the critical aspects of some well-known bifurcations in the context of thermodynamic geometry. For each bifurcation its normal form is regarded as a geodesic equation of some model analogous to a thermodynamic system. From this hypothesis it is possible to calculate the corresponding metric and curvature and analyze the critical behavior of the bifurcation.
Solution and transcritical bifurcation of Burgers equation
Institute of Scientific and Technical Information of China (English)
Tang Jia-Shi; Zhao Ming-Hua; Han Feng; Zhang Liang
2011-01-01
Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics. We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region. The transcritical bifurcation exists in the (2 + 1)-dimensional Burgers equation.
Institute of Scientific and Technical Information of China (English)
ZHANG Zi-Zhen; YANG Hui-Zhong
2013-01-01
In this paper,we consider a predator-prey system with modified Leslie-Gower and Holling type III schemes.By regarding the time delay as the bifurcation parameter,the local asymptotic stability of the positive equilibrium is investigated.And we find that Hopf bifurcations can occur as the time delay crosses some critical values.In particular,special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions.In addition,the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result.Finally,numerical simulations are carried out to illustrate the main theoretical results.
Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay
Directory of Open Access Journals (Sweden)
Yahong Peng
2014-01-01
Full Text Available We consider a model for gene expression with one or two time delays and diffusion. The local stability and delay-induced Hopf bifurcation are investigated. We also derive the formulas determining the direction and the stability of Hopf bifurcations by calculating the normal form on the center manifold.
Bifurcations of a predator-prey model with non-monotonic response function
Broer, H.W.; Naudot, Vincent; Roussarie, Robert; Saleh, Khairul
2005-01-01
A 2-dimensional predator-prey model with five parameters is investigated, adapted from the Volterra-Lotka system by a non-monotonic response function. A description of the various domains of structural stability and their bifurcations is given. The bifurcation structure is reduced to four organising
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
Energy Technology Data Exchange (ETDEWEB)
Song Yongli E-mail: songyl@sjtu.edu.cn; Han Maoan; Peng Yahong
2004-12-01
We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Hopf bifurcation in a dynamic IS-LM model with time delay
Energy Technology Data Exchange (ETDEWEB)
Neamtu, Mihaela [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: mihaela.neamtu@fse.uvt.ro; Opris, Dumitru [Department of Applied Mathematics, Faculty of Mathematics, West University of Timisoara, Bd. V. Parvan, nr. 4, 300223 Timisoara (Romania)]. E-mail: opris@math.uvt.ro; Chilarescu, Constantin [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: cchilarescu@rectorat.uvt.ro
2007-10-15
The paper investigates the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. We show when the system is stable with respect to the delay. Some numerical examples are given to confirm the theoretical results.
Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gomp ertz Mo del
Institute of Scientific and Technical Information of China (English)
XU Chang-jin; CHEN Da-xue
2013-01-01
A delayed predator-prey Gompertz model is investigated. The stability is ana-lyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.
NEW BIFURCATION PATTERNS IN ELEMENTARY BIFURCATION PROBLEMS WITH SINGLE-SIDE CONSTRAINT
Institute of Scientific and Technical Information of China (English)
吴志强; 陈予恕
2001-01-01
Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results about it. As the complement to singularity theory and the first step to study on constrained bifurcations, here are given the transition sets and persistent perturbed bifurcation diagrams of 10 elementary bifurcation of codimension no more than three.
Hahn, C; Mahajan, A; Chu, T; Schoen, M
2007-08-01
This paper presents a lumped-parameter model for the big-toe region that investigates the effect of plantar pressure on the diameter of the blood vessels, specifically the arteries, in the presence of arterial and/or tissue changes. The model developed in this paper uses a multi-domain energy system approach to develop the lumped-parameter differential equations. Blood flow is modelled as fluidic flow through compliant pipes that have inertia, stiffness, and damping. The tissue material is treated as a soft compliant material that transmits the external force to the blood vessels. Conclusions have been drawn to show the effect of plantar pressure, tissue damage, and their combination on the diameter of the blood vessels. The principles used here can be used to model the entire foot and the model used to investigate the effect of plantar pressure, tissue damage, and arterial changes on different parts of the foot. The work presented here may also have applications in other vascular diseases. PMID:17937206
Optimal Revascularization Strategy on Medina 0,1,0 Left Main Bifurcation Lesions in Type 2 Diabetes
Zheng, Xuwei; Peng, Hongyu; Zhao, Donghui; Ma, Qin; Fu, Kun; Chen, Guo
2016-01-01
Aim. Diabetes mellitus (DM) is a major risk factor for cardiovascular disease. The implications of a diagnosis of DM are as severe as the diagnosis of coronary artery disease. For many patients with complex coronary artery disease, optimal revascularization strategy selection and optimal medical therapy are equally important. In this study, we compared the hemodynamic results of different stenting techniques for Medina 0,1,0 left main bifurcation lesions. Methods. We use idealized left main bifurcation models and computational fluid dynamics analysis to evaluate hemodynamic parameters which are known to affect the risk of restenosis and thrombosis at stented bifurcation. The surface integrals of time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) at bifurcation site were quantified. Results. Crossover stenting without final kissing balloon angioplasty provided the most favorable hemodynamic results (integrated values of TAWSS = 2.96 × 10−4 N, OSI = 4.75 × 10−6 m2) with bifurcation area subjected to OSI values >0.25, >0.35, and >0.45 calculated as 0.39 mm2, 0.06 mm2, and 0 mm2, respectively. Conclusion. Crossover stenting only offers hemodynamic advantages over other stenting techniques for Medina 0,1,0 left main bifurcation lesions and large bifurcation angle is associated with unfavorable flow profiles. PMID:27777957
Research on bifurcation characters of rotor-SMA bearing system
International Nuclear Information System (INIS)
Based on Landau-Devonshire model, the bifurcation characteristic of rotor-shape memory alloy bearings(SMAB) system was investigated in this paper. Heteronomous system was transformed into autonomous system in averaging method and Van der Pol transformation, and the existence of Hopf bifurcation was proved in theory. The concept of broadened set of equilibrium point was introduced to improve centre manifold method to be adapted to heteronomous system. The equation of the flow on the centre manifold of rotor-SMAB system was obtained, and the existence of transcritical bifurcation and supercritical pitchfork bifurcation was proved in theory. Finally the results in centre manifold method and averaging method were compared with each other. The comparison shows that the results of the two methods were both the parts of global dynamic characteristic of rotor-SMAB system, while centre manifold method can be applied to research bifurcation behavior in the case of more dimensions. It means that the two methods both have limitation, and global dynamic characteristic must be obtained in kinds of method
Full system bifurcation analysis of endocrine bursting models.
Tsaneva-Atanasova, Krasimira; Osinga, Hinke M; Riess, Thorsten; Sherman, Arthur
2010-06-21
Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis. PMID:20307553
Backward bifurcations, turning points and rich dynamics in simple disease models.
Zhang, Wenjing; Wahl, Lindi M; Yu, Pei
2016-10-01
In this paper, dynamical systems theory and bifurcation theory are applied to investigate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous investigations of epidemiology, in-host disease, and autoimmunity. These closely related models display interesting dynamical behaviors including bistability, recurrence, and regular oscillations, each of which has possible clinical or public health implications. In this contribution we elucidate the key role of backward bifurcations in the parameter regimes leading to the behaviors of interest. We demonstrate that backward bifurcations with varied positions of turning points facilitate the appearance of Hopf bifurcations, and the varied dynamical behaviors are then determined by the properties of the Hopf bifurcation(s), including their location and direction. A Maple program developed earlier is implemented to determine the stability of limit cycles bifurcating from the Hopf bifurcation. Numerical simulations are presented to illustrate phenomena of interest such as bistability, recurrence and oscillation. We also discuss the physical motivations for the models and the clinical implications of the resulting dynamics.
ROBUST CONTROL OF PERIODIC BIFURCATION SOLUTIONS
Institute of Scientific and Technical Information of China (English)
梁建术; 陈予恕; 梁以德
2004-01-01
The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method.According to obtained bifurcation diagrams and combining control theory,the method of robust control of periodic bifurcation was presented,which differs from generic methods of bifurcation control.It can make the existing motion pattern into the goal motion pattern.Because the method does not make strict requirement about parametric values of the controller,it is convenient to design and make it.Numerical simulations verify validity of the method.
Insight into Phenomena of Symmetry Breaking Bifurcation
Institute of Scientific and Technical Information of China (English)
FANG Tong; ZHANG Ying
2008-01-01
@@ We show that symmetry-breaking (SB) bifurcation is just a transition of different forms of symmetry, while still preserving system's symmetry. SB bifurcation always associates with a periodic saddle-node bifurcation, identifiable by a zero maximum of the top Lyapunov exponent of the system. In addition, we show a significant phase portrait of a newly born periodic saddle and its stable and unstable invariant manifolds, together with their neighbouring flow pattern of Poincaré mapping points just after the periodic saddle-node bifurcation, thus gaining an insight into the mechanism of SB bifurcation.
High resolution wavenumber analysis for investigation of arterial pulse wave propagation
Hasegawa, Hideyuki; Sato, Masakazu; Irie, Takasuke
2016-07-01
The propagation of the pulse wave along the artery is relatively fast (several m/s), and a high-temporal resolution is required to measure pulse wave velocity (PWV) in a regional segment of the artery. High-frame-rate ultrasound enables the measurement of the regional PWV. In analyses of wave propagation phenomena, the direction and propagation speed are generally identified in the frequency-wavenumber space using the two-dimensional Fourier transform. However, the wavelength of the pulse wave is very long (1 m at a propagation velocity of 10 m/s and a temporal frequency of 10 Hz) compared with a typical lateral field of view of 40 mm in ultrasound imaging. Therefore, PWV cannot be identified in the frequency-wavenumber space owing to the low resolution of the two-dimensional Fourier transform. In the present study, PWV was visualized in the wavenumber domain using phases of arterial wall acceleration waveforms measured by high-frame-rate ultrasound.
Bifurcations analysis of turbulent energy cascade
Energy Technology Data Exchange (ETDEWEB)
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com
2015-03-15
This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.
Numerical bifurcation of Hamiltonian relative periodic orbits
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2009-01-01
-breaking bifurcations of RPOs in Hamiltonian systems with compact symmetry group and show how they can be detected and computed numerically. These are turning points of RPOs and relative period-doubling and relative period-halving bifurcations along branches of RPOs. In a comoving frame the latter correspond...... to symmetry-breaking/symmetry-increasing pitchfork bifurcations or to period-doubling/period-halving bifurcations. We apply our methods to the family of rotating choreographies which bifurcate from the famous figure eight solution of the three-body problem as angular momentum is varied. We find...... that the family of choreographies rotating around the $e^2$-axis bifurcates to the family of rotating choreographies that connects to the Lagrange relative equilibrium. Moreover, we compute several relative period-doubling bifurcations and a turning point of the family of planar rotating choreographies, which...
Escape statistics for parameter sweeps through bifurcations.
Miller, Nicholas J; Shaw, Steven W
2012-04-01
We consider the dynamics of systems undergoing parameter sweeps through bifurcation points in the presence of noise. Of interest here are local codimension-one bifurcations that result in large excursions away from an operating point that is transitioning from stable to unstable during the sweep, since information about these "escape events" can be used for system identification, sensing, and other applications. The analysis is based on stochastic normal forms for the dynamic saddle-node and subcritical pitchfork bifurcations with a time-varying bifurcation parameter and additive noise. The results include formulation and numerical solution for the distribution of escape events in the general case and analytical approximations for delayed bifurcations for which escape occurs well beyond the corresponding quasistatic bifurcation points. These bifurcations result in amplitude jumps encountered during parameter sweeps and are particularly relevant to nano- and microelectromechanical systems, for which noise can play a significant role.
Description of the celiac artery in domestic pigeons (Columba livia
Directory of Open Access Journals (Sweden)
Cibele Geeverghese
2012-06-01
Full Text Available This paper aimed to define the origin and distribution of the celiac artery and its collateral branches in 15 fowls from the Columba livia species, which were obtained from the Zoonosis Control Center of Brasilia, Brazil. In order to mark the arterial system of the specimens, the left brachiocephalic trunk was canullated and a colored water-latex solution was injected there. Afterwards, fowls were fixed in a 10% v/v formaldehyde solution and dissected with appropriate equipment, presenting the results described in this paper. The celiac artery originated from the ventral face of the descendent aorta. The first collateral branch arose from the celiac artery itself, forming the esophageal artery. Then, the celiac artery has bifurcated into two branches, named left and right branches of the celiac artery. The left branch emitted the proventricular ventral artery, followed by the splenic arteries, proventricular dorsal artery, and the left hepatic artery. The left branch has bifurcated into two branches, known as ventral and left gastric arteries. The right branch emitted the right hepatic artery, followed by the ileal artery and the right gastric artery. Finally, the right branch turned into the pancreaticoduodenal artery. Our findings showed a great similarity with the avian lineages of the Gallus gallus species, except for the lack of ileocecal artery, cystic branches, and dorsal gastric artery.
Fluid dynamics in airway bifurcations: II. Secondary currents.
Martonen, T B; Guan, X; Schreck, R M
2001-04-01
As the second component of a systematic investigation on flows in bifurcations reported in this journal, this work focused on secondary currents. The first article addressed primary flows and the third discusses localized conditions (both in this issue). Secondary flow patterns were studied in two lung bifurcation models (Schreck, 1972) using FIDAP with the Cray T90 supercomputer. The currents were examined at different prescribed distances distal to the carina. Effects of inlet conditions, Reynolds numbers, and diameter ratios and orientations of airways were addressed. The secondary currents caused by the presence of the carina and inclination of the daughter tubes exhibited symmetric, multivortex patterns. The intensities of the secondary currents became stronger for larger Reynolds numbers and larger angles of bifurcation.
Bifurcations in the optimal elastic foundation for a buckling column
International Nuclear Information System (INIS)
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcations in the optimal elastic foundation for a buckling column
Rayneau-Kirkhope, Daniel; Farr, Robert; Ding, K.; Mao, Yong
2010-12-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcations in the optimal elastic foundation for a buckling column
Rayneau-Kirkhope, Daniel; Ding, K; Mao, Yong
2010-01-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Hopf bifurcation and chaos in macroeconomic models with policy lag
International Nuclear Information System (INIS)
In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael;
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior......-time Lyapunov exponents. As a special case we study an isolated branch in the bifurcation diagram brought into existence by a 1:3 subharmonic resonance. On this isola it is only possible to determine stability using one of the three methods, which is due to the fact that only this method guarantees...
Bifurcation Analysis for Surface Waves Generated by Wind
Schweizer, Ben
2001-01-01
We study the generation of surface waves on water as a bifurcation phenomenon. For a critical wind-speed there appear traveling wave solutions. While linear waves do not transport mass (in the mean), nonlinear effects create a shear-flow and result in a net mass transport in the direction of the wind. We derive an asymptotic formula for the average tangential velocity along the free surface. Numerical investigations confirm the appearance of the shear-flow and yield results on the bifurcation...
Yeh, J.-R.; Lin, T.-Y.; Shieh, J.-S.; Chen, Y.; Huang, N. E.; Wu, Z.; Peng, C.-K.
2008-02-01
In this investigation, surgical operations of blocked intestinal artery have been conducted on pigs to simulate the condition of acute mesenteric arterial occlusion. The empirical mode decomposition method and the algorithm of linguistic analysis were applied to verify the blood pressure signals in simulated situation. We assumed that there was some information hidden in the high-frequency part of the blood pressure signal when an intestinal artery is blocked. The empirical mode decomposition method (EMD) has been applied to decompose the intrinsic mode functions (IMF) from a complex time series. But, the end effects and phenomenon of intermittence damage the consistence of each IMF. Thus, we proposed the complementary ensemble empirical mode decomposition method (CEEMD) to solve the problems of end effects and the phenomenon of intermittence. The main wave of blood pressure signals can be reconstructed by the main components, identified by Monte Carlo verification, and removed from the original signal to derive a riding wave. Furthermore, the concept of linguistic analysis was applied to design the blocking index to verify the pattern of riding wave of blood pressure using the measurements of dissimilarity. Blocking index works well to identify the situation in which the sampled time series of blood pressure signal was recorded. Here, these two totally different algorithms are successfully integrated and the existence of the existence of information hidden in high-frequency part of blood pressure signal has been proven.
Evolution and stability of tidal river bifurcations
Kleinhans, M. G.
2011-12-01
At bifurcations, water and sediment are partitioned, so that long-term evolution of fluvial and deltaic channels is determined by the bifurcation stability. Recent work in fluvial environments showed that bifurcations are commonly unstable so that avulsion results. For tidal rivers it could be argued that the discharge fluctuation enhances transport so that it simply closes of faster than in steady flow, but it could also be argued that tidal phase differences between the bifurcates cause a residual flow that counteracts the closing trend and keeps both bifurcates open. A physics-based numerical model (Delft3D) was used to model fixed-bank fork-shaped bifurcations with and without tides, and with short and long length relative to tidal wavelength. In all cases the bifurcations remained as unstable as without tides and ended invariably in avulsion. Tidal bifurcations unbalanced more rapidly than fluvial bifurcations, because of the increased ebb current and nonlinearity of sediment transport. On the other hand, discharge partitioning at the final bifurcation was much less asymmetrical with tides than without. Tidal wave deformation and production of higher harmonics in the longer channels affected sediment partitioning in the unstable phase but seems to have no effect on equilibrium morphology. Significant phase differences between the bifurcates caused a tidal floss effect, which scoured the bifurcation. In conclusion, symmetrical bifurcations affected by tides are unstable, but their final equilibrium is more symmetrical than without tides unless bifurcates have significant tidal phase differences. Furthermore I modelled growing deltas with self-formed distributary channels with and without cohesive sediment and with and without tides. Here, tides cause the flow to be more focussed in fewer and larger channels, whilst the few bifurcations are relatively stable. Combined fluvial discharge and tidal ebb flow in the channels transports more sediment than in fluvial
Scale dependence of branching in arterial and bronchial trees
Restrepo, J G; Hunt, B R; Restrepo, Juan G.; Ott, Edward; Hunt, Brian R.
2005-01-01
Although models of branching in arterial and bronchial trees often predict a dependence of bifurcation parameters on the scale of the bifurcating vessels, direct verifications of this dependence with data are uncommon. We compare measurements of bifurcation parameters in airways and arterial trees of different mammals as a function of scale to general features predicted by theoretical models. We find that the size dependence is more complex than existing theories based solely on energy minimization explain, and suggest additional factors that may govern the branching at different scales.
Anatomy and function relation in the coronary tree: from bifurcations to myocardial flow and mass.
Kassab, Ghassan S; Finet, Gerard
2015-01-01
The study of the structure-function relation of coronary bifurcations is necessary not only to understand the design of the vasculature but also to use this understanding to restore structure and hence function. The objective of this review is to provide quantitative relations between bifurcation anatomy or geometry, flow distribution in the bifurcation and degree of perfused myocardial mass in order to establish practical rules to guide optimal treatment of bifurcations including side branches (SB). We use the scaling law between flow and diameter, conservation of mass and the scaling law between myocardial mass and diameter to provide geometric relations between the segment diameters of a bifurcation, flow fraction distribution in the SB, and the percentage of myocardial mass perfused by the SB. We demonstrate that the assessment of the functional significance of an SB for intervention should not only be based on the diameter of the SB but also on the diameter of the mother vessel as well as the diameter of the proximal main artery, as these dictate the flow fraction distribution and perfused myocardial mass, respectively. The geometric and flow rules for a bifurcation are extended to a trifurcation to ensure optimal therapy scaling rules for any branching pattern.
Simulation of bifurcated stent grafts to treat abdominal aortic aneurysms (AAA)
Egger, J.; Großkopf, S.; Freisleben, B.
2007-03-01
In this paper a method is introduced, to visualize bifurcated stent grafts in CT-Data. The aim is to improve therapy planning for minimal invasive treatment of abdominal aortic aneurysms (AAA). Due to precise measurement of the abdominal aortic aneurysm and exact simulation of the bifurcated stent graft, physicians are supported in choosing a suitable stent prior to an intervention. The presented method can be used to measure the dimensions of the abdominal aortic aneurysm as well as simulate a bifurcated stent graft. Both of these procedures are based on a preceding segmentation and skeletonization of the aortic, right and left iliac. Using these centerlines (aortic, right and left iliac) a bifurcated initial stent is constructed. Through the implementation of an ACM method the initial stent is fit iteratively to the vessel walls - due to the influence of external forces (distance- as well as balloonforce). Following the fitting process, the crucial values for choosing a bifurcated stent graft are measured, e.g. aortic diameter, right and left common iliac diameter, minimum diameter of distal neck. The selected stent is then simulated to the CT-Data - starting with the initial stent. It hereby becomes apparent if the dimensions of the bifurcated stent graft are exact, i.e. the fitting to the arteries was done properly and no ostium was covered.
BIFURCATION ANALYSIS OF A MITOTIC MODEL OF FROG EGGS
Institute of Scientific and Technical Information of China (English)
吕金虎; 张子范; 张锁春
2003-01-01
The mitotic model of frog eggs established by Borisuk and Tyson is qualitatively analyzed. The existence and stability of its steady states are further discussed. Furthermore, the bifurcation of above model is further investigated by using theoretical analysis and numerical simulations. At the same time, the numerical results of Tyson are verified by theoretical analysis.
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos
Lee, B. H. K.; Price, S. J.; Wong, Y. S.
1999-04-01
Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary differential equations suitable for numerical simulations and analytical investigation of the system stability. The onset of Hopf-bifurcation, and amplitudes and frequencies of limit cycle oscillations are investigated, with examples given for a cubic hardening spring. For various geometries of the freeplay, bifurcations and chaos are discussed via the phase plane, Poincaré maps, and Lyapunov spectrum. The route to chaos is investigated from bifurcation diagrams, and for the freeplay nonlinearity it is shown that frequency doubling is the most commonly observed route. Examples of aerodynamic nonlinearities arising from transonic flow and dynamic stall are discussed, and special attention is paid to numerical simulation results for dynamic stall using a time-synthesized method for the unsteady aerodynamics. The assumption of uniform flow is usually not met in practice since perturbations in velocities are encountered in flight. Longitudinal atmospheric turbulence is introduced to show its effect on both the flutter boundary and the onset of Hopf-bifurcation for a cubic restoring force.
Experiments on the bifurcation behaviour of a forced nonlinear pendulum
Beckert, S.; Schock, U.; Schulz, C.-D.; Weidlich, T.; Kaiser, F.
1985-02-01
A mechanical system (forced nonlinear torsion pendulum) is investigated. The state diagram is given as a function of both the external driving frequency and the damping parameter. A bifurcation diagram is measured showing period doubling, chaos and periodic windows. The results are in qualitative agreement with the recent theory.
Complete bifurcation analysis of DC-DC converters under current mode control
Pikulin, D.
2014-03-01
The purpose of this research is to investigate to what extend application of novel method of complete bifurcation groups to the analysis of global dynamics of piecewise-smooth hybrid systems enables one to highlight new nonlinear effects before periodic and chaotic regimes. Results include the construction of complete one and two-parameter bifurcation diagrams, detection of various types of bifurcation groups and investigation of their interactions, localization of rare attractors, and the investigation of different principles of birth of chaotic attractors. Effectiveness of the approach is illustrated in respect to one of the most widely used switching systems-boost converter under current mode control operating in continuous current mode.
Oscillatory flow in bifurcating tubes
International Nuclear Information System (INIS)
Respiratory fluid mechanics is characterized by flow through bifurcating, Y-shaped, tubes. Steady flow through such geometries has been studied in detail by several authors. However, the recent widespread use of high frequency mechanical assistance of ventilation has generated interest in unsteady flows. A symmetric, singly branching pipe has been constructed, with its bifurcation shaped to model pulmonary conditions. The form of the bifurcation is based on CAT scans of human tracheal carinas. Its features include an area change of the parent tube from circular to roughly elliptical near the junction, a pinch-off effect on the parent tube, smoothly curved outer walls at the junction, and a sharp flow divider. Parent and daughter tubes have an l/d ratio of > 50, so that entrance effects are avoided. In order to better understand the effects of unsteadiness, piston driven, laminar, purely oscillatory flow has been established in the pipe for a variety of Womersley numbers. By appropriate choices of flow frequency and amplitude, fluid viscosity, and pipe diameter, tracheal Reynolds and Womersley numbers have been matched for resting breathing (tidal volume of 600 ml to 0.25 Hz), high frequency breathing (50 ml at 5 Hz), and intermediate breathing levels
Xiao, Min; Zheng, Wei Xing; Jiang, Guoping; Cao, Jinde
2015-12-01
In this paper, a fractional-order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated, such as the stability, Hopf bifurcations, and undamped oscillations. The stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate-order neural network. Based on the stability analysis, the critical values of the fractional order are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state. Then, the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate-order networks. Meanwhile, it is shown that the incommensurate-order neural network can also exhibit a Hopf bifurcation as the network parameter passes through a critical value which can be determined exactly. The frequency and amplitude of bifurcated oscillations are determined.
Bifurcation mechanisms of regular and chaotic network signaling in brain astrocytes
Matrosov, V. V.; Kazantsev, V. B.
2011-06-01
Bifurcation mechanisms underlying calcium oscillations in the network of astrocytes are investigated. Network model includes the dynamics of intracellular calcium concentration and intercellular diffusion of inositol 1,4,5-trisphosphate through gap junctions. Bifurcation analysis of underlying nonlinear dynamical system is presented. Parameter regions and principle bifurcation boundaries have been delineated and described. We show how variations of the diffusion rate can lead to generation of network calcium oscillations in originally nonoscillating cells. Different scenarios of regular activity and its transitions to chaotic dynamics have been obtained. Then, the bifurcations have been associated with statistical characteristics of calcium signals showing that different bifurcation scenarios yield qualitative changes in experimentally measurable quantities of the astrocyte activity, e.g., statistics of calcium spikes.
Natsis, Konstantinos; Raikos, Athanasios; Foundos, Ioannis; Noussios, George; Lazaridis, Nikolaos; Njau, Samouel N
2011-09-01
Studies on the origin of the superior thyroid artery, define that it could originate either from the external carotid artery, (at the level of common carotid bifurcation), or from the common carotid artery. However, there is a classical anatomic knowledge that the superior thyroid artery is a branch of the external carotid artery. Variability in the anatomy of the superior thyroid artery was studied on 100 carotids. Moreover, a review about the origin of superior thyroid artery between recent and previous cadaveric, autopsy, and angiographic studies, on adults and fetuses, was carried out. The superior thyroid artery originated from the external carotid artery in 39% and at the level of carotid bifurcation and common carotid artery in 61% of cases. The anterior branches of the external carotid artery were separate in 76% of cases, while common trunks between the arteries were found in 24% of the specimens. A new classification proposal on the origin of the superior thyroid artery is also suggested. In this study, the origin of superior thyroid artery is considered at the level of the carotid bifurcation and not from the external carotid artery as stated in many classical anatomy textbooks. This has a great impact on the terminology when referring to the anterior branches of the external carotid artery, which could be termed as anterior branches of the cervical carotid artery. Head and neck surgeons must be familiar with anatomical variations of the superior thyroid artery in order to achieve a better surgical outcome.
The Effect of Alternating Bars Migration on River Bifurcation Dynamics
Miori, S.; Bertoldi, W.; Repetto, R.; Zanoni, L.; Tubino, M.
2007-12-01
Recent theoretical analysis, field and laboratory observations pointed out that fluvial bifurcation show an intrinsic instability, leading to the establishment of an unbalanced flow and sediments distribution in the downstream branches. The existence of equilibrium configurations has been proved, which mainly depend on the hydraulic and morphologic conditions of the upstream flow. However, flow and sediment transport in braided networks are highly unsteady, so that the bifurcation can hardly reach an equilibrium configuration. One of the main causes of temporal fluctuations is the migration of alternate bars in the upstream channel, that can affect and control the flow partition in the distributaries. We analysed the bar - bifurcation interactions by experimental and analytical investigations. We performed a set of flume experiments on a Y shaped fixed banks and movable bed bifurcation. Laboratory results show that bar formation in the upstream channel perturbs the discharge distribution with a series of fluctuations strictly related to the period of bar migration. Four different behaviours have been identified, characterised by small perturbations of the equilibrium state (balanced or unbalanced), by the occurrence of large fluctuations or by the closure of one of the distributaries. The character of the bifurcation is controlled by the amplitude and speed of alternate bars that directly influence the amplitude and period of discharge oscillations. Consequently, at large values of the aspect ratio (high bars) and low sediment mobility (slow bars) the bifurcation dynamics is likely to be dominated by bars migration. Extending the one-dimensional model proposed by Bolla Pittaluga et al. (2003), we introduce the effect of bars migrating in the upstream channel. In the present model, the bifurcation is forced with spatial crosswise fluctuations of feeding conditions, in order to reproduce the transverse distribution of sediment and water of an alternate bar pattern as
The 'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device.
Peach, Thomas; Cornhill, J Frederick; Nguyen, Anh; Riina, Howard; Ventikos, Yiannis
2014-01-01
We present flow-based results from the early stage design cycle, based on computational modeling, of a prototype flow-diverter device, known as the 'Sphere', intended to treat bifurcation aneurysms of the cerebral vasculature. The device is available in a range of diameters and geometries and is constructed from a single loop of NITINOL(®) wire. The 'Sphere' reduces aneurysm inflow by means of a high-density, patterned, elliptical surface that partially occludes the aneurysm neck. The device is secured in the healthy parent vessel by two armatures in the shape of open loops, resulting in negligible disruption of parent or daughter vessel flow. The device is virtually deployed in six anatomically accurate bifurcation aneurysms: three located at the Basilar tip and three located at the terminus bifurcation of the Internal Carotid artery (at the meeting of the middle cerebral and anterior cerebral arteries). Both steady state and transient flow simulations reveal that the device presents with a range of aneurysm inflow reductions, with mean flow reductions falling in the range of 30.6-71.8% across the different geometries. A significant difference is noted between steady state and transient simulations in one geometry, where a zone of flow recirculation is not captured in the steady state simulation. Across all six aneurysms, the device reduces the WSS magnitude within the aneurysm sac, resulting in a hemodynamic environment closer to that of a healthy vessel. We conclude from extensive CFD analysis that the 'Sphere' device offers very significant levels of flow reduction in a number of anatomically accurate aneurysm sizes and locations, with many advantages compared to current clinical cylindrical flow-diverter designs. Analysis of the device's mechanical properties and deployability will follow in future publications.
Stability and Bifurcation in a Delayed Reaction-Diffusion Equation with Dirichlet Boundary Condition
Guo, Shangjiang; Ma, Li
2016-04-01
In this paper, we study the dynamics of a diffusive equation with time delay subject to Dirichlet boundary condition in a bounded domain. The existence of spatially nonhomogeneous steady-state solution is investigated by applying Lyapunov-Schmidt reduction. The existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues. The direction of Hopf bifurcation and stability of the bifurcating periodic solution are also investigated by means of normal form theory and center manifold reduction. Moreover, we illustrate our general results by applications to the Nicholson's blowflies models with one- dimensional spatial domain.
Einstein's Field Equations as a Fold Bifurcation
Kohli, Ikjyot Singh
2016-01-01
It is shown that Einstein's field equations for \\emph{all} perfect-fluid $k=0$ FLRW cosmologies have the same form as the topological normal form of a fold bifurcation. In particular, we assume that the cosmological constant is a bifurcation parameter, and as such, fold bifurcation behaviour is shown to occur in a neighbourhood of Minkowski spacetime in the phase space. We show that as this cosmological constant parameter is varied, an expanding and contracting de Sitter universe \\emph{emerge} via this bifurcation.
Bifurcation and instability problems in vortex wakes
DEFF Research Database (Denmark)
Aref, Hassan; Brøns, Morten; Stremler, Mark A.
2007-01-01
A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...
Bifurcation Tools for Flight Dynamics Analysis and Control System Design Project
National Aeronautics and Space Administration — Modern bifurcation analysis methods have been proposed for investigating flight dynamics and control system design in highly nonlinear regimes and also for the...
Hassan, Natalia; Maldonado-Valderrama, Julia; Gunning, A Patrick; Morris, V J; Ruso, Juan M
2011-10-15
Propanolol is a betablocker drug used in the treatment of arterial hypertension related diseases. In order to achieve an optimal performance of this drug it is important to consider the possible interactions of propanolol with plasma proteins. In this work, we have used several experimental techniques to characterise the effect of addition of the betablocker propanolol on the properties of bovine plasma fibrinogen (FB). Differential scanning calorimeter (DSC), circular dichroism (CD), dynamic light scattering (DLS), surface tension techniques and atomic force microscopy (AFM) measurements have been combined to carry out a detailed physicochemical and surface characterization of the mixed system. As a result, DSC measurements show that propranolol can play two opposite roles, either acting as a structure stabilizer at low molar concentrations or as a structure destabilizer at higher concentrations, in different domains of fibrinogen. CD measurements have revealed that the effect of propanolol on the secondary structure of fibrinogen depends on the temperature and the drug concentration and the DLS analysis showed evidence for protein aggregation. Interestingly, surface tension measurements provided further evidence of the conformational change induced by propanolol on the secondary structure of FB by importantly increasing the surface tension of the system. Finally, AFM imaging of the fibrinogen system provided direct visualization of the protein structure in the presence of propanolol. Combination of these techniques has produced complementary information on the behavior of the mixed system, providing new insights into the structural properties of proteins with potential medical interest.
Energy Technology Data Exchange (ETDEWEB)
Nagata, Shun-ichi; Kazekawa, Kiyoshi; Matsubara, Shuko [Fukuoka University Chikushi Hospital, Department of Neurosurgery, Chikushino, Fukuoka (Japan); Sugata, Sei [Bironoki Neurosurgical Hospital, Shibushi, Kagoshima (Japan)
2006-08-15
Obstructions of the supraaortic vessels are an important cause of morbidity associated with a variety of symptoms. Percutaneous transluminal angioplasty has evolved as an effective and safe treatment modality for occlusive lesions of the supraaortic vessels. However, the endovascular management of an innominate bifurcation has not previously been reported. A 53-year-old female with a history of systematic hypertension, diabetes mellitus and hypercholesterolemia presented with left hemiparesis and dysarthria. Angiography of the innominate artery showed a stenosis of the innominate bifurcation. The lesion was successfully treated using the retrograde kissing stent technique via a brachial approach and an exposed direct carotid approach. The retrograde kissing stent technique for the treatment of a stenosis of the innominate bifurcation was found to be a safe and effective alternative to conventional surgery. (orig.)
Cutrì, Elena; Zunino, Paolo; Morlacchi, Stefano; Chiastra, Claudio; Migliavacca, Francesco
2013-08-01
The treatment of coronary bifurcation lesions represents a challenge for the interventional cardiologists due to the lower rate of procedural success and the higher risk of restenosis. The advent of drug-eluting stents (DES) has dramatically reduced restenosis and consequently the request for re-intervention. The aim of the present work is to provide further insight about the effectiveness of DES by means of a computational study that combines virtual stent implantation, fluid dynamics and drug release for different stenting protocols currently used in the treatment of a coronary artery bifurcation. An explicit dynamic finite element model is developed in order to obtain realistic configurations of the implanted devices used to perform fluid dynamics analysis by means of a previously developed finite element method coupling the blood flow and the intramural plasma filtration in rigid arteries. To efficiently model the drug release, a multiscale strategy is adopted, ranging from lumped parameter model accounting for drug release to fully 3-D models for drug transport to the artery. Differences in drug delivery to the artery are evaluated with respect to local drug dosage. This model allowed to compare alternative stenting configurations (namely the Provisional Side Branch, the Culotte and the Inverted Culotte techniques), thus suggesting guidelines in the treatment of coronary bifurcation lesions and addressing clinical issues such as the effectiveness of drug delivery to lesions in the side branch, as well as the influence of incomplete strut apposition and overlapping stents.
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Directory of Open Access Journals (Sweden)
Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Bifurcations and Patterns in Nonlinear Dissipative Systems
Energy Technology Data Exchange (ETDEWEB)
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System
Directory of Open Access Journals (Sweden)
Xiaojun Liu
2014-01-01
Full Text Available The Hopf bifurcation of a fractional-order Van der Pol (VDP for short system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
Institute of Scientific and Technical Information of China (English)
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS
Institute of Scientific and Technical Information of China (English)
HuangWentao; LiuYirong
2004-01-01
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated. Two recursive formulas to compute singular quantities at infinity and at the origin are given. The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles. Two fifth degree systems are constructed. One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity. The other perturbs six limit cycles at the origin.
Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
KANG Xiu-Ying; LIU Da-He; ZHOU Jing; JIN Yong-Juan
2005-01-01
@@ The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in awide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation arepresented in detail. The flow separation zones revealed with increase of Reynolds number are located in theareas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particularblood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmannmethod is adaptive to simulating the flow in larger vessels under a high Reynolds number.
Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method
Kang, Xiu-Ying; Liu, Da-He; Zhou, Jing; Jin, Yong-Juan
2005-11-01
The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in a wide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation are presented in detail. The flow separation zones revealed with increase of Reynolds number are located in the areas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particular blood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmann method is adaptive to simulating the flow in larger vessels under a high Reynolds number.
Synchronization and Bifurcation Analysis in Coupled Networks of Discrete-Time Systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Synchronization and bifurcation analysis in coupled networks of discrete-time systems are investigated in the present paper. We mainly focus on some special coupling matrix, i.e., the sum of each row equals a nonzero constant u and the network connection is directed. A result that the network can reach a new synchronous state, which is not the asymptotic limit set determined by the node state equation, is derived. It is interesting that the network exhibits bifurcation if we regard the constant u as a bifurcation parameter at the synchronous state. Numerical simulations are given to show the efficiency of our derived conclusions.
Bifurcation in a thin liquid film flowing over a locally heated surface
Katkar, Harshwardhan H
2014-01-01
We investigate the non-linear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of Marangoni number using linear stability theory. Continuation along the Marangoni number using non-linear evolution equation is used to trace bifurcation diagram associated with the oscillatory instability. Hysteresis, a characteristic attribute of a sub-critical Hopf bifurcation, is observed in a critical parametric region. The bifurcation is universally observed for both, a non-volatile film and a volatile film.
Bifurcations, chaos, and sensitivity to parameter variations in the Sato cardiac cell model
Otte, Stefan; Berg, Sebastian; Luther, Stefan; Parlitz, Ulrich
2016-08-01
The dynamics of a detailed ionic cardiac cell model proposed by Sato et al. (2009) is investigated in terms of periodic and chaotic action potentials, bifurcation scenarios, and coexistence of attractors. Starting from the model's standard parameter values bifurcation diagrams are computed to evaluate the model's robustness with respect to (small) parameter changes. While for some parameters the dynamics turns out to be practically independent from their values, even minor changes of other parameters have a very strong impact and cause qualitative changes due to bifurcations or transitions to coexisting attractors. Implications of this lack of robustness are discussed.
Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback
Yang, Jihua; Zhang, Erli; Liu, Mei
2016-06-01
We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.
Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model
Páez Chávez, Joseph; Wiercigroch, Marian
2013-09-01
We investigate complex dynamics occurring in a non-smooth model of a Jeffcott rotor with a bearing clearance. A bifurcation analysis of the rotor system is carried out by means of the software TC-HAT [25], a toolbox of AUTO 97 [6] allowing path-following and detection of bifurcations of periodic trajectories of non-smooth dynamical systems. The study reveals a rich variety of dynamics, which includes grazing-induced fold and period-doubling bifurcations, as well as hysteresis loops produced by a cusp singularity. Furthermore, an analytical expression predicting grazing incidences is derived.
Stability and bifurcation analysis for a delayed Lotka-Volterra predator-prey system
Yan, Xiang-Ping; Chu, Yan-Dong
2006-11-01
The present paper deals with a delayed Lotka-Volterra predator-prey system. By linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation, we find the necessary conditions that the parameters should verify in order to have the oscillations in the system. In addition, the normal form of the Hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these Hopf bifurcations. To verify the obtained conditions, a special numerical example is also included.
Stability and bifurcation analysis on a three-species food chain system with two delays
Cui, Guo-Hu; Yan, Xiang-Ping
2011-09-01
The present paper deals with a three-species Lotka-Volterra food chain system with two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Furthermore, by using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.
STABILITY AND LOCAL BIFURCATION IN A SIMPLY-SUPPORTED BEAM CARRYING A MOVING MASS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The stability and local bifurcation of a simply-supported flexible beam (Bernoulli-Euler type) carrying a moving mass and subjected to harmonic axial excitation are investigated.In the theoretical analysis, the partial differential equation of motion with the fifth-order nonlinear term is solved using the method of multiple scales (a perturbation technique). The stability and local bifurcation of the beam are analyzed for 1/2 sub harmonic resonance. The results show that some of the parameters, especially the velocity of moving mass and external excitation, affect the local bifurcation significantly. Therefore, these parameters play important roles in the system stability.
Perturbed bifurcations in the BCS gap equation
DEFF Research Database (Denmark)
Spathis, P. N.; Sørensen, Mads Peter; Lazarides, Nickos
1992-01-01
. The transitions from d- or s- to mixed s- and d-wave solutions result from pitchfork bifurcations. In the case of slightly different pairing strength in the x and y directions, perturbed pitchfork bifurcations emerge, leading to a dramatic change in the physical properties of the superconducting state....
BIFURCATION IN PRESCRIBED MEAN CURVATURE PROBLEM
Institute of Scientific and Technical Information of China (English)
马力
2002-01-01
This paper discusses the existence problem in the study of some partial differential equations. The author gets some bifurcation on the prescribed mean curvature problem on the unit ball, the scalar curvature problem on the n-sphere, and some field equations. The author gives some natural conditions such that the standard bifurcation or Thom-Mather theory can be used.
Directory of Open Access Journals (Sweden)
Davidović Lazar B.
2006-01-01
inferior mesenteric artery aneurysm, the resection of aneurysm was followed by reimplantation of medial part of the artery into bifurcated Dacron graft which replaced abdominal aorta. In 5 patients, some of additional surgical procedures were performed. There were 4 reconstructive procedures of abdominal aorta and one splenectomy. The patient with ruptured hepatic artery aneurysm died during surgery due to uncontrolled hemorrhage. In other patients, there was neither morbidity nor mortality in the early postoperative period (first 30 days after surgery. Mean follow up was 1 to 5 years (mean 3.4 years. One patient died after 5 years due to myocardial infarction. CONCLUSION Although the introduction of precise diagnostic procedures (computerized tomography, magnetic resonance imaging, spiral scan make diagnosis easier, the splanchnic artery aneurysms are still difficult to detect due to their uncommon clinical presentations.
Analysis of the flow at a T-bifurcation for a ternary unit
Campero, P.; Beck, J.; Jung, A.
2014-03-01
The motivation of this research is to understand the flow behavior through a 90° T- type bifurcation, which connects a Francis turbine and the storage pump of a ternary unit, under different operating conditions (namely turbine, pump and hydraulic short-circuit operation). As a first step a CFD optimization process to define the hydraulic geometry of the bifurcation was performed. The CFD results show the complexity of the flow through the bifurcation, especially under hydraulic short-circuit operation. Therefore, it was decided to perform experimental investigations in addition to the CFD analysis, in order to get a better understanding of the flow. The aim of these studies was to investigate the flow development upstream and downstream the bifurcation, the estimation of the bifurcation loss coefficients and also to provide comprehensive data of the flow behavior for the whole operating range of the machine. In order to evaluate the development of the velocity field Stereo Particle Image Velocimetry (S-PIV) measurements at different sections upstream and downstream of the bifurcation on the main penstock and Laser Doppler Anemometrie (LDA) measurements at bifurcation inlet were performed. This paper presents the CFD results obtained for the final design for different operating conditions, the model test procedures and the model test results with special attention to: 1) The bifurcation head loss coefficients, and their extrapolation to prototype conditions, 2) S-PIV and LDA measurements. Additionally, criteria to define the minimal uniformity conditions for the velocity profiles entering the turbine are evaluated. Finally, based on the gathered flow information a better understanding to define the preferred location of a bifurcation is gained and can be applied to future projects.
Crisis bifurcations in plane Poiseuille flow.
Zammert, Stefan; Eckhardt, Bruno
2015-04-01
Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.
Voltage stability, bifurcation parameters and continuation methods
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F.L. [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
Angiographic features of unilateral nonbifurcating cervical carotid artery: A case report
Energy Technology Data Exchange (ETDEWEB)
En, Na Lae [Dept. of Radiology, Gangnam Severance Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of); Lee, Seung Koo [Dept. of Radiology, Severance Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of)
2015-08-15
Nonbifurcating cervical carotid artery is a rare anomaly of the common carotid artery (CCA), in which the branches of the external carotid artery (ECA) arise directly from the CCA or proximal internal carotid artery without bifurcation, and therefore there is no proximal main trunk of the ECA. We report a unilateral nonbifurcating cervical carotid artery of a 67-year-old woman, incidentally found during cerebral aneurismal treatment.
On the effect of AVR gain on bifurcations of subsynchronous resonance in power systems
Energy Technology Data Exchange (ETDEWEB)
Widyan, Mohammad S. [Electrical Engineering Department, The Hashemite University, 13115 Zarqa (Jordan)
2010-07-15
This paper presents the effect of the automatic voltage regulator (AVR) gain on the bifurcations of subsynchronous resonance (SSR) in power systems. The first system of the IEEE second benchmark model of SSR is chosen for numerical investigations. The dynamics of both axes damper windings of the generator and that of the power system stabilizer (PSS) are included. The bifurcation parameter is the compensation factor. Hopf bifurcation, where a pair of complex conjugate eigenvalues of the linearized model around the operating point transversally crosses from left- to right-half of the complex plane, is detected in all AVR gains. It is shown that the Hopf bifurcation is of subcritical type. The results also show that the location of the Hopf bifurcation point i.e. the stable operating point regions are affected by the value of the AVR gain. The variation of the location of the Hopf bifurcation point as function of the AVR gain for two operating conditions is obtained. Time domain simulation results based on the nonlinear dynamical mathematical model carried out at different compensation factors and AVR gains agree with that of the bifurcation analysis. (author)
"Virtual" in-vivo bench test for bifurcation stenting with "StentBoost".
Agostoni, Pierfrancesco; Verheye, Stefan; Vermeersch, Paul; Cornelis, Kristoff; Van Langenhove, Glenn
2009-04-01
"StentBoost" is a new angiographic technique that allows improved angiographic visualization of stents deployed in coronary arteries, by enhancing the X-ray focus of the region where the stent is placed. Using this technique we were able to assess the deformation and the expansion of a stent deployed to treat a bifurcation lesion between the mid-left anterior descending (LAD) artery and a big second diagonal branch, during sequential inflations of: (1) the stent per se in the LAD, (2) the ostium of the diagonal branch through the stent struts, (3) the stent again with a non compliant balloon, and (4) both branches with the kissing balloon technique. "StentBoost" guided our clinical and angiographic decision-making process and allowed us to create a "virtual" bench test of the stent deployed at the level of the bifurcation treated.
Grootenboers, M.J.J.H.
2008-01-01
The aim of this thesis was two-fold. First, - part I of the dissertation -, to explore ILuP with melphalan and hyperthermia followed by pulmonary metastasectomy in patients with resectable pulmonary metastases. Second, - part II -, to investigate the feasibility and pharmacokinetics of SPAP with gem
Hero's journey in bifurcation diagram
Monteiro, L. H. A.; Mustaro, P. N.
2012-06-01
The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films.
Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations
Indian Academy of Sciences (India)
Zaiyun Zhang; Fnag-Li Xia; Xin-Ping Li
2013-01-01
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).
Bifurcation analysis on a delayed SIS epidemic model with stage structure
Directory of Open Access Journals (Sweden)
Kejun Zhuang
2007-05-01
Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.
Stability and Hopf bifurcation in a delayed competitive web sites model
Energy Technology Data Exchange (ETDEWEB)
Xiao Min [Department of Mathematics, Southeast University, Nanjing 210096 (China): Department of Mathematics, Nanjing Xiaozhuang College, Nanjing 210017 (China); Cao Jinde [Department of Mathematics, Southeast University, Nanjing 210096 (China)]. E-mail: jdcao@seu.edu.cn
2006-04-24
The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found.
Stability and Hopf bifurcation in a delayed competitive web sites model
Xiao, Min; Cao, Jinde
2006-04-01
The delayed differential equations modeling competitive web sites, based on the Lotka Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found.
Equilibrium-torus bifurcation in nonsmooth systems
DEFF Research Database (Denmark)
Zhusubahyev, Z.T.; Mosekilde, Erik
2008-01-01
Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium...... linear approximation to our system in the neighbourhood of the border. We determine the functional relationships between the parameters of the normal form map and the actual system and illustrate how the normal form theory can predict the bifurcation behaviour along the border-collision equilibrium......-torus bifurcation curve....
EFFECTS OF CONSTANT EXCITATION ON LOCAL BIFURCATION
Institute of Scientific and Technical Information of China (English)
WU Zhi-qiang; CHEN Yu-shu
2006-01-01
The effects of the constant excitation on the local bifurcation of the periodic solutions in the 1:2 internal resonant systems were analyzed based on the singularity theory. It is shown that the constant excitation make influence only when there exist some nonlinear terms, in the oscillator with lower frequency. Besides acting as main bifurcation parameter, the constant excitation, together with coefficients of some nonlinear terms,may change the values of unfolding parameters and the type of the bifurcation. Under the non-degenerate cases, the effect of the third order terms can be neglected.
Attractivity and bifurcation for nonautonomous dynamical systems
Rasmussen, Martin
2007-01-01
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
Bifurcations of non-smooth systems
Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.
2012-12-01
Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.
Backward Bifurcation in Simple SIS Model
Institute of Scientific and Technical Information of China (English)
Zhan-wei Wang
2009-01-01
We describe and analyze a simple SIS model with treatment.In particular,we give a completely qualitative analysis by means of the theory of asymptotically autonomous system.It is found that a backward bifurcation occurs if the adequate contact rate or the capacity is small.It is also found that there exists bistable endemic equilibria.In the case of disease-induced death,it is shown that the backward bifurcation also occurs.Moreover,there is no limit cycle under some conditions,and the subcritical Hopf bifurcation occurs under another conditions.
Cellular Cell Bifurcation of Cylindrical Detonations
Institute of Scientific and Technical Information of China (English)
HAN Gui-Lai; JIANG Zong-Lin; WANG Chun; ZHANG Fan
2008-01-01
Cellular cell pattern evolution of cylindrically-diverging detonations is numerically simulated successfully by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. From the simulation, three cell bifurcation modes are observed during the evolution and referred to as concave front focusing, kinked and wrinkled wave front instability, and self-merging of cellular cells. Numerical research demonstrates that the wave front expansion resulted from detonation front diverging plays a major role in the cellular cell bifurcation, which can disturb the nonlinearly self-sustained mechanism of detonations and finally lead to cell bifurcations.
Endovascular management of giant middle cerebral artery aneurysms
Huang, Lei; Cao, Wenjie; Ge, Liang; Lu, Gang; Wan, Jun; Zhang, Lei; Gu, Weijin; Zhang, Xiaolong; Geng, Daoying
2015-01-01
Background: This article reported the experience of endovascular treatment in giant middle cerebral artery (MCA) aneurysms with parent artery occlusion or stent-assisted coiling. Material and methods: Eleven consecutive patients with giant MCA aneurysms were included. The aneurysms predominantly involved the M1 segment in two cases, bifurcation in four cases, and M2 in five cases. Four M2 fusiform aneurysms were treated with parent artery sacrifice after balloon occlusion test. The seven unru...
Mining data from CFD simulation for aneurysm and carotid bifurcation models.
Miloš, Radović; Dejan, Petrović; Nenad, Filipović
2011-01-01
Arterial geometry variability is present both within and across individuals. To analyze the influence of geometric parameters, blood density, dynamic viscosity and blood velocity on wall shear stress (WSS) distribution in the human carotid artery bifurcation and aneurysm, the computer simulations were run to generate the data pertaining to this phenomenon. In our work we evaluate two prediction models for modeling these relationships: neural network model and k-nearest neighbor model. The results revealed that both models have high prediction ability for this prediction task. The achieved results represent progress in assessment of stroke risk for a given patient data in real time. PMID:22256273
BIFURCATION OF PERIODIC ORBITS OF A THREE-DIMENSIONAL SYSTEM
Institute of Scientific and Technical Information of China (English)
LIU XUANLIANG; HAN MAOAN
2005-01-01
Consider a three-dimensional system having an invariant surface. By using bifurcation techniques and analyzing the solutions of bifurcation equations, the authors study the spacial bifurcation phenomena of a k multiple closed orbit in the invariant surface.The sufficient conditions of the existence of many closed orbits bifurcate from the k multiple closed orbit are obtained.
Bifurcation of non-negative solutions for an elliptic system
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In the paper,we consider a nonlinear elliptic system coming from the predator-prey model with diffusion.Predator growth-rate is treated as bifurcation parameter.The range of parameter is found for which there exists nontrivial solution via the theory of bifurcation from infinity,local bifurcation and global bifurcation.
Fluid dynamics in airway bifurcations: I. Primary flows.
Martonen, T B; Guan, X; Schreck, R M
2001-04-01
The subject of fluid dynamics within human airways is of great importance for the risk assessment of air pollutants (inhalation toxicology) and the targeted delivery of inhaled pharmacologic drugs (aerosol therapy). As cited herein, experimental investigations of flow patterns have been performed on airway models and casts by a number of investigators. We have simulated flow patterns in human lung bifurcations and compared the results with the experimental data of Schreck (1972). The theoretical analyses were performed using a third-party software package, FIDAP, on the Cray T90 supercomputer. This effort is part of a systematic investigation where the effects of inlet conditions, Reynolds numbers, and dimensions and orientations of airways were addressed. This article focuses on primary flows using convective motion and isovelocity contour formats to describe fluid dynamics; subsequent articles in this issue consider secondary currents (Part II) and localized conditions (Part III). The agreement between calculated and measured results, for laminar flows with either parabolic or blunt inlet conditions to the bifurcations, was very good. To our knowledge, this work is the first to present such detailed comparisons of theoretical and experimental flow patterns in airway bifurcations. The agreement suggests that the methodologies can be employed to study factors affecting airflow patterns and particle behavior in human lungs.
Delay-induced stochastic bifurcations in a bistable system under white noise
International Nuclear Information System (INIS)
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses
Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise.
Xu, Yong; Gu, Rencai; Zhang, Huiqing; Xu, Wei; Duan, Jinqiao
2011-05-01
This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing-Van der Pol oscillator. By using the stochastic averaging method, theoretically, one can obtain the stationary probability density function of amplitude for the Duffing-Van der Pol oscillator and can reveal interesting dynamics under the influence of Gaussian colored noise. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that system parameters, noise intensity, and noise correlation time, respectively, can be treated as bifurcation parameters. They also imply that the effects of multiplicative noise are rather different from that of additive noise. The results of direct numerical simulation verify the effectiveness of the theoretical analysis. Moreover, the largest Lyapunov exponent calculations indicate that P and D bifurcations have no direct connection.
Local and global bifurcations at infinity in models of glycolytic oscillations
DEFF Research Database (Denmark)
Sturis, Jeppe; Brøns, Morten
1997-01-01
We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node...... at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable...... sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models...
Delay-induced stochastic bifurcations in a bistable system under white noise.
Sun, Zhongkui; Fu, Jin; Xiao, Yuzhu; Xu, Wei
2015-08-01
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Delay-induced stochastic bifurcations in a bistable system under white noise
Energy Technology Data Exchange (ETDEWEB)
Sun, Zhongkui, E-mail: sunzk@nwpu.edu.cn; Fu, Jin; Xu, Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Xiao, Yuzhu [Department of Mathematics and Information Science, Chang' an University, Xi' an 710086 (China)
2015-08-15
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.
DNS of bifurcations in an air-filled rotating baroclinic annulus
Randriamampianina, A; Read, P L; Maubert, P; Randriamampianina, Anthony; Fruh, Wolf-Gerrit; Read, Peter L.; Maubert, Pierre
2006-01-01
Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating is presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies by Maubert and Randriamampianina, the fluid used is air rather than a liquid as used in all other previous work. This study investigated a bifurcation sequence from the axisymmetric flow to a number of complex flows. The transition sequence, on increase of the rotation rate, from the axisymmetric solution via a steady, fully-developed baroclinic wave to chaotic flow followed a variant of the classical quasi-periodic bifurcation route, starting with a subcritical Hopf and associated saddle-node bifurcation. This was followed by a sequence of two supercritical Hopf-type bifurcations, first to an amplitude vacillation, then to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and finally to a chaotic MAV\\...
Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka-Volterra System with Time Delay
Chang, Xiaoyuan; Wei, Junjie
2015-06-01
In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka-Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka-Volterra diffusion system with time delay to illustrate our conclusions.
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
Directory of Open Access Journals (Sweden)
Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Delay-induced stochastic bifurcations in a bistable system under white noise.
Sun, Zhongkui; Fu, Jin; Xiao, Yuzhu; Xu, Wei
2015-08-01
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses. PMID:26328553
BIFURCATIONS OF A CANTILEVERED PIPE CONVEYING STEADY FLUID WITH A TERMINAL NOZZLE
Institute of Scientific and Technical Information of China (English)
Xu Jian; Huang Yuying
2000-01-01
This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.
Singular analysis of two-dimensional bifurcation system
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Bifurcation properties of two-dimensional bifurcation system are studied in this paper.Universal unfolding and transition sets of the bifurcation equations are obtained.The whole parametric plane is divided into several different persistent regions according to the type of motion,and the different qualitative bifurcation diagrams in different persistent regions are given.The bifurcation properties of the two-dimensional bifurcation system are compared with its reduced one-dimensional system.It is found that the system which is reduced to one dimension has lost many bifurcation properties.
Morphological Transitions of Sliding Drops -- Dynamics and Bifurcations
Engelnkemper, Sebastian; Gurevich, Svetlana V; Thiele, Uwe
2016-01-01
We study fully three-dimensional droplets that slide down an incline employing a thin-film equation that accounts for capillarity, wettability and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to pearling-coalescence cycles) which emerges at a global instability, the related hysteresis in behavior and a period-doubling cascade. The non-trivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it ...
Numerical Study on the Bifurcation of the North Equatorial Current
Institute of Scientific and Technical Information of China (English)
LIU Yulong; WANG Qi; SONG Jun; ZHU Xiande; GONG Xiaoqing; WU Fang
2011-01-01
A 1.5-layer reduced-gravity model forced by wind stress is used to study the bifurcations of the North Equatorial Current (NEC).The authors found that after removing the Ekman drift,the modelled circulations can serve well as a proxy of the SODA circulations on the σθ=25.0kgm-3 potential density surface based on available long-term reanalysis wind stress data.The modelled results show that the location of the western boundary bifurcation of the NEC depends on both zonal averaged and local zero wind stress curl latitude.The effects of the anomalous wind stress curl added in different areas are also investigated and it is found that they can change the strength of the Mindanao Eddy (ME),and then influence the interior pathway.
Fluid dynamics in airway bifurcations: III. Localized flow conditions.
Martonen, T B; Guan, X; Schreck, R M
2001-04-01
Localized flow conditions (e.g., backflows) in transition regions between parent and daughter airways of bifurcations were investigated using a computational fluid dynamics software code (FIDAP) with a Cray T90 supercomputer. The configurations of the bifurcations were based on Schreck s (1972) laboratory models. The flow intensities and spatial regions of reversed motion were simulated for different conditions. The effects of inlet velocity profiles, Reynolds numbers, and dimensions and orientations of airways were addressed. The computational results showed that backflow was increased for parabolic inlet conditions, larger Reynolds numbers, and larger daughter-to-parent diameter ratios. This article is the third in a systematic series addressed in this issue; the first addressed primary velocity patterns and the second discussed secondary currents.
BIFURCATIONS AND CHAOS CONTROL IN TCP-RED SYSTEM
Institute of Scientific and Technical Information of China (English)
Liu Fang
2006-01-01
Objective Analyzing the nonlinear dynamics of the TCP-RED congestion control system is of great importance. This study will help investigate the loss of stability in Internet and design a proper method for controlling bifurcation and chaos in such system. Methods Based on bifurcation diagram, the effect of parameter on system performance is discussed. By using the state feedback and parameter variation strategy, a simple real time control method is proposed to modify the existing RED scheme. Results With our control method, the parametric sensitivity of RED mechanism is attenuated. Moreover, a sufficient condition on the robust stability of the system is also derived to adjust the parameters in TCP-RED system. Conclusion The proposed method has the advantages of simple implementation and unnecessary knowledge of the exact system.
On local bifurcations in neural field models with transmission delays.
van Gils, S A; Janssens, S G; Kuznetsov, Yu A; Visser, S
2013-03-01
Neural field models with transmission delays may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions the associated equilibrium may destabilise in a Hopf bifurcation. Furthermore, two Hopf curves may intersect in a double Hopf point in a two-dimensional parameter space. We provide general formulas for the corresponding critical normal form coefficients, evaluate these numerically and interpret the results. PMID:23192328
Bifurcation analysis of fan casing under rotating air flow excitation
Institute of Scientific and Technical Information of China (English)
温登哲; 陈予恕
2014-01-01
A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly’s shell theory and Hamilton’s principle, the dynamic equations are established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.
Torus bifurcations in multilevel converter systems
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
This paper considers the processes of torus formation and reconstruction through smooth and nonsmooth bifurcations in a pulse-width modulated DC/DC converter with multilevel control. When operating in a regime of high corrector gain, converters of this type can generate structures of stable tori....... The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company....
Cavitated Bifurcation for Incompressible Hyperelastic Material
Institute of Scientific and Technical Information of China (English)
任九生; 程昌钧
2002-01-01
The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison.And the growth of a pre-existing micro-void is also observed.
Retinal Artery Occlusion Treatment with Hyperbaric Oxygen
Directory of Open Access Journals (Sweden)
Harun Cakmak
2016-01-01
Full Text Available Retinal artery occlusion is one of the vision-threating emergency situations in ophthalmology. In this paper, a case of retinal artery occlusion is presented. Fifty seven year- old female patient presented with a sudden onset visual loss in her left eye. Best corrected visual acuity (BCVA levels were 1.0 and 0.7 in the right and left eye, respectiveley. Dilated fundus examination revealed no pathological finding in the right eye. Whereas calcified plaque was seen in upper arquat artery bifurcation in the left eye. Pallorness with retinal edema was seen in this arterial trace. Retinal artery occlusion was diagnosed and patient was referred for hyperbaric oxygen therapy. After a total of 20 sessions of hyperbaric oxygen therapy, the calcified plaques disappeared and her BCVA increased to 20/20. Hyperbaric oxygen treatment is vision-saving method which should be considered in retinal artery occlusion.
Modeling of blood flow in arterial trees.
Anor, Tomer; Grinberg, Leopold; Baek, Hyoungsu; Madsen, Joseph R; Jayaraman, Mahesh V; Karniadakis, George E
2010-01-01
Advances in computational methods and medical imaging techniques have enabled accurate simulations of subject-specific blood flows at the level of individual blood cell and in complex arterial networks. While in the past, we were limited to simulations with one arterial bifurcation, the current state-of-the-art is simulations of arterial networks consisting of hundreds of arteries. In this paper, we review the advances in methods for vascular flow simulations in large arterial trees. We discuss alternative approaches and validity of various assumptions often made to simplify the modeling. To highlight the similarities and discrepancies of data computed with different models, computationally intensive three-dimensional (3D) and inexpensive one-dimensional (1D) flow simulations in very large arterial networks are employed. Finally, we discuss the possibilities, challenges, and limitations of the computational methods for predicting outcomes of therapeutic interventions for individual patients. PMID:20836052
Huang, Er-Wen; Peng, Long-Yun; Zheng, Jin-Xiang; Wang, Dan; Tan, Xiao-Hong; Yang, Zhong-Yi; Li, Xue-Mei; Wu, Qiu-Ping; Tang, Shuang-Bo; Luo, Bin; Quan, Li; Liu, Shui-Ping; Liu, Xiao-Shan; Li, Zhao-Hui; Shi, He; Lv, Guo-Li; Zhao, Jian; Liu, Chao; Cheng, Jian-Ding
2016-05-01
A large-scale meta-analysis of 14 genome-wide association studies has identified and replicated a series of susceptibility polymorphisms for coronary artery disease (CAD) in European ancestry populations, but evidences for the associations of these loci with CAD in other ethnicities remain lacking. Herein we investigated the associations between ten (rs579459, rs12413409, rs964184, rs4773144, rs2895811, rs3825807, rs216172, rs12936587, rs46522 and rs3798220) of these loci and CAD in Southern Han Chinese (CHS). Genotyping was performed in 1716 CAD patients and 1572 controls using mass spectrography. Both allelic and genotypic associations of rs964184, rs2895811 and rs3798220 with CAD were significant, regardless of adjustment for covariates of gender, age, hypertension, type 2 diabetes, blood lipid profiles and smoking. Significant association of rs12413409 was initially not observed, but after the adjustment for the covariates, both allelic and genotypic associations were identified as significant. Neither allelic nor genotypic association of the other six polymorphisms with CAD was significant regardless of the adjustment. Our results indicated that four loci of the total 10 were associated with CAD in CHS. Therefore, some of the CAD-related loci in European ancestry populations are indeed susceptibility loci for the risk of CAD in Han Chinese. PMID:26740236
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The bidirectional associative memory (BAM) neural network with four neurons and two delays is considered in the present paper.A linear stability analysis for the trivial equilibrium is firstly employed to provide a possible critical point at which a zero and a pair of pure imaginary eigenvalues occur in the corresponding characteristic equation.A fold-Hopf bifurcation is proved to happen at this critical point by the nonlinear analysis.The coupling strength and the delay are considered as bifurcation parameters to investigate the dynamical behaviors derived from the fold-Hopf bifurcation.Various dynamical behaviours are qualitatively classified in the neighbourhood of the fold-Hopf bifurcation point by using the center manifold reduction (CMR) together with the normal form.The bifurcating periodic solutions are expressed analytically in an approximate form.The validity of the results is shown by their consistency with the numerical simulation.
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E. V. Nikolaeva
2015-01-01
Full Text Available Pulmonary arterial hypertension (PAH associated with systemic connective tissue diseases (SCTD is a poor prognostic manifestation of the latter that result in death if untreated. The invasive determination of hemodynamic parameters is prominent in diagnosing the disease and determining its treatment policy and prognosis.Objective: to analyze the results of catheterization in PAH-SCTD patients admitted to the V.A. Nasonova Research Institute of Rheumatology.Subjects and methods. The investigation included 59 patients admitted to the V.A. Nasonova Research Institute of Rheumatology from September 2009 to September 2014. PAH was diagnosed in accordance with the conventional guidelines. All the patients underwent right heart and pulmonary artery (PA catheterization at the diagnosis and over time during treatment.Results and discussion. All the patients included in the trial met the pre-capillary pulmonary hypertension (PH criteria: mean pulmonary artery pressure (MPAP ≥25 mm Hg; and PA wedge pressure (PAWP <15 mm Hg. The exclusion of other causes of PH (pulmonary fibrosis, left heart disease, and thromboembolism, as well as a high transpulmonary pressure gradient >15 mm Hg and pulmonary vascular resistance (PVR >3 Wood units could diagnose PAH in all our patients. There was a statistically highly significant association between pathological hemodynamic changes and functional class (FC. FC was found to be most closely correlated with right atrial pressure (RAP, cardiac output (CO, PVR, and cardiac index (CI. Among the most common manifestations of heart failure, only the presence of peripheral edemas was associated with worse hemodynamic parameters in PAH. It should be noted that out of two biomarkers (N-terminal pro-brain natriuretic peptide and uric acid, the former is largely related to the magnitude of changes in hemodynamic factors. The critical values of hemodynamic parameters were due to extreme edema – anasarca (RAP >17 mm Hg
Stolzenburg, Nicola; Breinl, Janni; Bienek, Stephanie; Jaguszewski, Milosz; Löchel, Melanie; Taupitz, Matthias; Speck, Ulrich; Wagner, Susanne; Schnorr, Jörg
2016-01-01
Purpose Beyond antiproliferative properties, paclitaxel exhibits anti-inflammatory activity, which might be beneficial in the local treatment of nonocclusive coronary artery disease. Paclitaxel release and tissue concentrations after paclitaxel-coated balloon treatment using different pressures have not been investigated so far. The aim of the study was to investigate in an atherosclerotic rabbit model whether drug transfer from paclitaxel-coated balloons into the vessel wall is affected by t...
Energy Technology Data Exchange (ETDEWEB)
Hajihosseini, Amirhossein, E-mail: hajihosseini@khayam.ut.ac.ir [School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746 (Iran, Islamic Republic of); Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); Maleki, Farzaneh, E-mail: farzanmaleki83@khayam.ut.ac.ir [School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746 (Iran, Islamic Republic of); Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); Rokni Lamooki, Gholam Reza, E-mail: rokni@khayam.ut.ac.ir [School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746 (Iran, Islamic Republic of); Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of)
2011-11-15
Highlights: > We construct a recurrent neural network by generalizing a specific n-neuron network. > Several codimension 1 and 2 bifurcations take place in the newly constructed network. > The newly constructed network has higher capabilities to learn periodic signals. > The normal form theorem is applied to investigate dynamics of the network. > A series of bifurcation diagrams is given to support theoretical results. - Abstract: A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov-Takens, pitchfork-Hopf and Hopf-Hopf codimension two, and the degenerate Bogdanov-Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Köpf, Michael H
2014-10-07
© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.
Directory of Open Access Journals (Sweden)
Regine Schmidt
2013-01-01
Full Text Available Contrast-enhanced first-pass magnetic resonance imaging (MRI in combination with a tracer kinetic model, for example, MMID4, can be used to determine myocardial blood flow (MBF and myocardial perfusion reserve (MPR. Typically, the arterial input function (AIF required for this methodology is estimated from the left ventricle (LV. Dispersion of the contrast agent bolus might occur between the LV and the myocardial tissue. Negligence of bolus dispersion could cause an error in MBF determination. The aim of this study was to investigate the influence of bolus dispersion in a simplified coronary bifurcation geometry including one healthy and one stenotic branch on the quantification of MBF and MPR. Computational fluid dynamics (CFD simulations were combined with MMID4. Different inlet boundary conditions describing pulsatile and constant flows for rest and hyperemia and differing outflow conditions have been investigated. In the bifurcation region, the increase of the dispersion was smaller than inside the straight vessels. A systematic underestimation of MBF values up to −16.1% for pulsatile flow and an overestimation of MPR up to 7.5% were found. It was shown that, under the conditions considered in this study, bolus dispersion can significantly influence the results of quantitative myocardial MR-perfusion measurements.
Reverse bifurcation and fractal of the compound logistic map
Wang, Xingyuan; Liang, Qingyong
2008-07-01
The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.
Affordance-controlled bifurcations of action patterns in martial arts.
Hristovski, Robert; Davids, Keith; Araújo, Duarte
2006-10-01
Effects of participant-target distance and perceived handstriking efficiency on emergent behavior in the martial art of boxing were investigated, revealing affordance-controlled nonlinear dynamical effects (i.e. bifurcations) within the participant--target system. Results established the existence of critical values of scaled distances for emergence of first time excitations and annihilations of a diverse range of boxing actions i.e. on the appearance and dissolution of jabs, hooks and uppercuts. Reasons for the action diversity were twofold: (a) topological discontinuous changes (bifurcations) in the number of possible handstrikes, i.e. motor solutions to the hitting task; (b) fine modification of probabilities of emergence of striking patterns. Exploitation of a 'strikeability' affordance available in scaled distance-to-target information by boxers led to a diversity of emergent actions through a cascade of bifurcations in the task perceptual-motor work space. Data suggested that perceived efficiency (E) of an action changed as a function of scaled distance (D) and was correlated with the probability of occurrence of action patterns (P), exhibiting the following dependence P = P(E(D)). The implication is that probability of occurrence (P) depends on efficiency (E), which in turn depends on scaled distance (D) to the target. Accordingly, scaled distance-dependent perceived efficiency seems a viable candidate for a contextual (control) parameter to describe the nonlinear dynamics of striking actions in boxing.
Ternary choices in repeated games and border collision bifurcations
International Nuclear Information System (INIS)
Highlights: ► We extend a model of binary choices with externalities to include more alternatives. ► Introducing one more option affects the complexity of the dynamics. ► We find bifurcation structures which where impossible to observe in binary choices. ► A ternary choice cannot simply be considered as a binary choice plus one. - Abstract: Several recent contributions formalize and analyze binary choices games with externalities as those described by Schelling. Nevertheless, in the real world choices are not always binary, and players have often to decide among more than two alternatives. These kinds of interactions are examined in game theory where, starting from the well known rock-paper-scissor game, several other kinds of strategic interactions involving more than two choices are examined. In this paper we investigate how the dynamics evolve introducing one more option in binary choice games with externalities. The dynamics we obtain are always in a stable regime, that is, the structurally stable dynamics are only attracting cycles, but of any possible positive integer as period. We show that, depending on the structure of the game, the dynamics can be quite different from those existing when considering binary choices. The bifurcation structure, due to border collisions, is explained, showing the existence of so-called big-bang bifurcation points.
Parameterized center manifold for unfolding bifurcations with an eigenvalue +1 in n-dimensional maps
Wen, Guilin; Yin, Shan; Xu, Huidong; Zhang, Sijin; Lv, Zengyao
2016-10-01
For the fold bifurcation with an eigenvalue +1, there are three types of potential solutions from saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation. In the existing analysis methods for high maps, there is a problem that for the fold bifurcation, saddle-node bifurcation and transcritical bifurcation cannot be distinguished by the center manifold without bifurcation parameter. In this paper, a parameterized center manifold has been derived to unfold the solutions of the fold bifurcation with an eigenvalue +1, which is used to reduce a general n-dimensional map to one-dimensional map. On the basis of the reduced map, the conditions of the fold bifurcations including saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation are established for general maps, respectively. We show the applications of the proposed bifurcation conditions by three four-dimensional map examples to distinguish saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation.
Xu, Jinhu; Zhou, Yicang
2016-04-01
A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory. Numerical simulations are done to explore the rich dynamics, including stability switches, Hopf bifurcations, and chaotic oscillations. PMID:27105992
Directory of Open Access Journals (Sweden)
Yan Zhang
2014-01-01
Full Text Available We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and nonhomogeneous periodic solutions of this particular system. In particular, we also prove that the spatial homogeneous periodic solutions bifurcating from the smallest Hopf bifurcation point of the system are always unstable. This together with the instability results of the spatially nonhomogeneous periodic solutions by Yi et al., 2009, indicates that, in this model, all the oscillatory patterns from Hopf bifurcations are unstable.
Lee, Yunghwan; Min, Hyung Ki; Yoon, Sang Pil
2013-01-01
We found multiple aneurysms in the intracranial arteries and abdominal aorta of an 87-year-old Korean female cadaver, whose cause of death was reported as "cholangiocarcinoma." An abdominal aortic aneurysm was observed in the infrarenal aorta, where the inferior mesenteric artery arose. The intracranial aneurysms were found in the A3 segment of the anterior cerebral artery and at the bifurcation of the middle cerebral artery. This case provides an example of the very rare association of perip...
Split Right Coronary Artery Its Definition and Its Territory
Sawaya, Fadi J.; Sawaya, Jaber I.; Angelini, Paolo
2008-01-01
We report here, for perhaps the 1st time in the English-language literature, the extent of the territory fed by the anterior bifurcation of the (anomalous) split right coronary artery (RCA). A 64-year-old man presented with an occlusion of the anterior bifurcation of a split RCA—which resulted in an infarct that involved both the inferoseptal left ventricular wall and the anterior right ventricular free wall. Split RCA is the same anomaly as the improperly named “double right coronary artery....
Directory of Open Access Journals (Sweden)
Chi-Lun Huang
Full Text Available OBJECTIVE: The clinical implication of the coronary artery calcium score (CS is well demonstrated. However, little is known about the association between lower extremity arterial calcification and clinical outcomes. METHODS AND RESULTS: Eighty-two patients with symptomatic peripheral artery disease (age 61.0±12.4 years were followed for 21±11 months. CSs, ranging from the common iliac artery bifurcation to the ankle area, were analyzed through noncontrast multidetector computed tomography images retrospectively. The primary endpoints of this study were amputation and mortality. Old age, diabetes, hyperlipidemia, and end-stage renal disease were associated with higher CSs. Patients with more advanced Fontaine stages also tended to have significantly higher CSs (p = 0.03. During the follow-up period (21±11 months, 29 (35% patients underwent amputation, and 24 (29% patients died. Among the patients who underwent amputation, there were no significant differences in CSs between the amputated legs and the non-amputated legs. In the Cox proportional hazard model with CS divided into quartiles, patients with CS in the highest quartile had a 2.88-fold (95% confidence interval [CI] 1.18-12.72, p = 0.03 and a 5.16-fold (95% CI 1.13-21.61, p = 0.04 higher risk for amputation and all-cause mortality, respectively, than those with CS in the lowest quartile. These predictive effects remained after conventional risk factor adjustment. CONCLUSION: Lower extremity arterial CSs are associated with disease severity and outcomes, including amputation and all-cause mortality, in patients with symptomatic peripheral artery disease. However, the independent predictive value needs further investigation in large scale, prospective studies.
Hyakutake, Toru; Nagai, Shinya
2015-01-01
We constructed three-dimensional microvascular bifurcation models using a parent vessel of diameter 10μm and investigated the flow behavior of the red blood cells (RBCs) through bifurcations. We considered symmetric and asymmetric model types. Two cases of equal daughter vessel diameter were employed for the asymmetric models, where the first was 10μm, which is the same as the parent vessel and the second was 7.94μm, which satisfies Murray's law. Simulated blood flow was computed using the lattice Boltzmann method in conjunction with the immersed boundary method for incorporating fluid-membrane interactions between the flow field and deformable RBCs. First, we investigated the flow behavior of a single RBC through microvascular bifurcations. In the case of the symmetric bifurcation, the turning point of the fractional plasma flow wherein the RBC flow changed from one daughter vessel to the other was 0.50. This turning point was however different for asymmetric bifurcations. Additionally, we varied the initial offset of RBCs from the centerline of the parent vessel. The simulation results indicated that the RBCs preferentially flow through the branch of a larger flow ratio. Next, we investigated the distribution characteristics of multiple RBCs. Simulations indicated that the results of the symmetric model were similar to those predicted by a previously published empirical model. On the other hand, results of asymmetric models deviated from those of the symmetric and empirical models. These results suggest that the distribution of RBCs varies according to the bifurcation angle and daughter vessel diameter in a microvascular bifurcation of the size considered.
Bifurcations of Tumor-Immune Competition Systems with Delay
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Ping Bi
2014-01-01
Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.
Bulusu, Kartik V; Plesniak, Michael W
2016-01-01
The arterial network in the human vasculature comprises of ubiquitously present blood vessels with complex geometries (branches, curvatures and tortuosity). Secondary flow structures are vortical flow patterns that occur in curved arteries due to the combined action of centrifugal forces, adverse pressure gradients and inflow characteristics. Such flow morphologies are greatly affected by pulsatility and multiple harmonics of physiological inflow conditions and vary greatly in size-strength-shape characteristics compared to non-physiological (steady and oscillatory) flows (1 - 7). Secondary flow structures may ultimately influence the wall shear stress and exposure time of blood-borne particles toward progression of atherosclerosis, restenosis, sensitization of platelets and thrombosis (4 - 6, 8 - 13). Therefore, the ability to detect and characterize these structures under laboratory-controlled conditions is precursor to further clinical investigations. A common surgical treatment to atherosclerosis is stent implantation, to open up stenosed arteries for unobstructed blood flow. But the concomitant flow perturbations due to stent installations result in multi-scale secondary flow morphologies (4 - 6). Progressively higher order complexities such as asymmetry and loss in coherence can be induced by ensuing stent failures vis-à-vis those under unperturbed flows (5). These stent failures have been classified as "Types I-to-IV" based on failure considerations and clinical severity (14). This study presents a protocol for the experimental investigation of the complex secondary flow structures due to complete transverse stent fracture and linear displacement of fractured parts ("Type IV") in a curved artery model. The experimental method involves the implementation of particle image velocimetry (2C-2D PIV) techniques with an archetypal carotid artery inflow waveform, a refractive index matched blood-analog working fluid for phase-averaged measurements (15 - 18
DEFF Research Database (Denmark)
Johansson, Helle Wulf; Hay-Schmidt, Anders; Poulsen, Asser Nyander;
2009-01-01
arteries using reverse transcription polymerase chain reaction (RT-PCR) and quantitative real-time PCR. Western blotting was used to detect immunoreactivity for the porcine BK(Ca) channel alpha-subunit and beta-subunit proteins. The BK(Ca) channel alpha-subunit RNA and protein distribution patterns were...... visualized using in situ hybridization and immunofluorescence studies, respectively. The study verified that the BK(Ca) channel alpha-subunit is located to smooth muscle cells of porcine basilar and middle cerebral arteries. The mRNA transcript for beta1-, beta2- and beta4-subunit were shown by RT-PCR...... in porcine basilar and middle cerebral arteries. However, at the protein level, only, the beta1-subunit protein was found by western blotting....
Directory of Open Access Journals (Sweden)
Hunor Santha
2012-01-01
Full Text Available This paper describes a three-layer head phantom with artificial pulsating arteries at five different depths (1.2 mm, 3.7 mm, 6.8 mm, 9.6 mm and 11.8 mm. The structure enables formation of spatially and temporally varying tissue properties similar to those of living tissues. In our experiment, pressure pulses were generated in the arteries by an electronically controlled pump. The physical and optical parameters of the layers and the liquid in the artificial arteries were similar to those of real tissues and blood. The amplitude of the pulsating component of the light returning from the phantom tissues was measured at each artery depth mentioned above. The build-up of the in-house-developed pulse oximeter used for performing the measurements and the physical layout of the measuring head are described. The radiant flux generated by the LED on the measuring head was measured to be 1.8 mW at 910 nm. The backscattered radiant flux was measured, and found to be 0.46 nW (0.26 ppm, 0.55 nW (0.31 ppm, and 0.18 nW (0.10 ppm for the 1.2 mm, 3.7 mm and 6.8 mm arteries, respectively. In the case of the 9.6 mm and 11.8 mm arteries, useful measurement data were not obtained owing to weak signals. We simulated the phantom with the arteries at the above-mentioned five depths and at two additional ones (2.5 mm and 5.3 mm in depth using the Monte Carlo method. The measurement results were verified by the simulation results. We concluded that in case of 11 mm source-detector separation the arteries at a depth of about 2.5 mm generate the strongest pulse oximeter signal level in a tissue system comprising three layers of thicknesses: 1.5 mm (skin, 5.0 mm (skull, and > 50 mm (brain.
Emergence of Network Bifurcation Triggered by Entanglement
Yong, Xi; Gao, Xun; Li, Angsheng
2016-01-01
In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the anti-symmetric Lotka-Volterra (ALV) equations. In this work, we prove the existence of a novel bifurcation mechanism for the ALV equations, where the equilibrium state can be drastically changed by flipping the stability of a pair of fixed points. As an application, we focus on the implications of the bifurcation mechanism for evolutionary networks; we found that the bifurcation point can be determined quantitatively by the quantum entanglement in the microscopic interactions. The equilibrium state can be critically changed from one type of global demographic condensation to another state that supports global cooperation for homogeneous networks. In other words, our results indicate that there exist a class of many-body systems where the macroscopic properties are, to some ...
Stochastic bifurcations in a prototypical thermoacoustic system.
Gopalakrishnan, E A; Tony, J; Sreelekha, E; Sujith, R I
2016-08-01
We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.
Stochastic bifurcations in a prototypical thermoacoustic system
Gopalakrishnan, E. A.; Tony, J.; Sreelekha, E.; Sujith, R. I.
2016-08-01
We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.
Crisis bifurcations in plane Poiseuille flow
Zammert, Stefan
2015-01-01
Direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace reveal several interior and exterior crisis bifurcations. They appear in the upper branch that emerges in a saddle-node bifurcation near $Re_{SN}=641$ and then undergoes several bifurcations into a chaotic attractor. Near $Re_{XC}=785.95$ the attractor collides with the lower-branch state and turns into a chaotic saddle in a exterior crisis, with a characteristic $(Re-Re_{XC})^{-\\delta}$ variation in lifetimes. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. They contribute to increasing the complexity of the dynamics and to a more dense coverage of state space. The exterior crisis marks the onset of transient turbulence in this subspace of plane Poiseuille flow.
International Nuclear Information System (INIS)
An aggressive mediastinal fibrosis was found in a 42-year-old female, suffering from dysphagia, stabbing pain in the chest, and an unclear weight loss. In this case, the rare combination of esophageal involvement, bronchial narrowing, and pulmonary artery obstruction could easily be demonstrated with a barium study and a helical CT examination including three-dimensional reconstructions. (orig.)
Periodic orbits near a bifurcating slow manifold
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2015-01-01
This paper studies a class of $1\\frac12$-degree-of-freedom Hamiltonian systems with a slowly varying phase that unfolds a Hamiltonian pitchfork bifurcation. The main result of the paper is that there exists an order of $\\ln^2\\epsilon^{-1}$-many periodic orbits that all stay within an $\\mathcal O......(\\epsilon^{1/3})$-distance from the union of the normally elliptic slow manifolds that occur as a result of the bifurcation. Here $\\epsilon\\ll 1$ measures the time scale separation. These periodic orbits are predominantly unstable. The proof is based on averaging of two blowup systems, allowing one to estimate...
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the B_{x}-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
CAVITATION BIFURCATION FOR COMPRESSIBLE ANISOTROPIC HYPERELASTIC MATERIALS
Institute of Scientific and Technical Information of China (English)
ChengChangjun; RenJiusheng
2004-01-01
The effect of material anisotropy on the bifurcation for void tormation in anisotropic compressible hyperelastic materials is examined. Numerical solutions are obtained in an anisotropic sphere, whose material is transversely isotropic in the radial direction. It is shown that the bifurcation may occur either to the right or to the left, depending on the degree of material anisotropy. The deformation and stress contribution in the sphere before cavitation are different from those after cavitation. The stability of solutions is discussed through a comparison of energy.
Institute of Scientific and Technical Information of China (English)
陈予恕; 徐鉴
1996-01-01
The bifurcation of the second-order approximate solutions of nonlinear parametrically excited systems possessing generalized van der Pol’s dampings and quintic Duffing’s nonlinearities subjected to a primary parametric resonance is investigated. Using singularity theory with Z2-symmetry, bifurcations of the solutions are universally classified in a topologically equivalent sense for Z2-codimension>3. The question of whether the approximate solutions from the classical perturbation methods can be topologically equivalent in describing the periodic responses and the bifurcations of the original systems is made clear. The numerical results indicate that the vibration characteristic may suddenly disappear in the range of Z2-codimension>4.
Yu, Jinchen; Peng, Mingshu
2016-10-01
In this paper, a Kaldor-Kalecki model of business cycle with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the positive equilibrium is investigated. It is found that there exist Hopf bifurcations when the discrete time delay passes a sequence of critical values. By applying the method of multiple scales, the explicit formulae which determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate our main results.
Nomura, Yasuyuki; Saito, Satoshi; Ishiwata, Ryosuke; Sugiyama, Yuki
2016-01-01
A dissipative system with asymmetric interaction, the optimal velocity model, shows a Hopf bifurcation concerned with the transition from a homogeneous motion to the formation of a moving cluster, such as the emergence of a traffic jam. We investigate the properties of Hopf bifurcation depending on the particle density, using the dynamical system for the traveling cluster solution of the continuum system derived from the original discrete system of particles. The Hopf bifurcation is revealed as a subcritical one, and the property explains well the specific phenomena in highway traffic: the metastability of jamming transition and the hysteresis effect in the relation of car density and flow rate. PMID:26871081
Splitting rivers at their seams: bifurcations and avulsion
Kleinhans, M.G.; Ferguson, R.I.; Lane, S.N.; Hardy, R.J.
2012-01-01
River bifurcations are critical but poorly understood elements of many geomorphological systems. They are integralelements of alluvial fans, braided rivers, fluvial lowland plains, and deltas and control the partitioning of water and sediment throughthese systems. Bifurcations are commonly unstable
Codimension-2 bifurcations of the Kaldor model of business cycle
International Nuclear Information System (INIS)
Research highlights: → The conditions are given such that the characteristic equation may have purely imaginary roots and double zero roots. → Purely imaginary roots lead us to study Hopf and Bautin bifurcations and to calculate the first and second Lyapunov coefficients. → Double zero roots lead us to study Bogdanov-Takens (BT) bifurcation. → Bifurcation diagrams for Bautin and BT bifurcations are obtained by using the normal form theory. - Abstract: In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov-Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.
Directory of Open Access Journals (Sweden)
Alex Lederman
2009-09-01
Full Text Available Treating narrow arteries and their bifurcations is a major challenge to the endovascular surgeon. We describe a new endovascular technique that was used to treat a narrow aorta and that may also be used to preserve other bifurcations. Using three straight stents may enable the endovascular surgeon to treat bifurcation while maintaining flow to both distal arteries.O tratamento de artérias de pequeno calibre e suas bifurcações é um grande desafio para o cirurgião endovascular. Descrevemos uma nova técnica endovascular que foi usada no tratamento de uma aorta de pequeno calibre e que também pode ser usada para preservar outras bifurcações. O uso de três stents retos pode permitir ao cirurgião endovascular o tratamento de bifurcação mantendo o fluxo em ambas as artérias distais.
Bifurcation Analysis of a Discrete Logistic System with Feedback Control
Institute of Scientific and Technical Information of China (English)
WU Dai-yong
2015-01-01
The paper studies the dynamical behaviors of a discrete Logistic system with feedback control. The system undergoes Flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors of the system, such as the period-doubling bifurcation in periods 2, 4, 8 and 16, and quasi-periodic orbits and chaotic sets.
Delay-induced multistability near a global bifurcation
Hizanidis, J.; Aust, R.; Schoell, E.
2007-01-01
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit cycles are found in accordance with Shilnikov's theorems.
Two degenerate boundary equilibrium bifurcations in planar Filippov systems
Dercole, F.; Della Rossa, F.; Colombo, A.; Kuznetsov, Yuri
2011-01-01
We contribute to the analysis of codimension-two bifurcations in discontinuous systems by studying all equilibrium bifurcations of 2D Filippov systems that involve a sliding limit cycle. There are only two such local bifurcations: (1) a degenerate boundary focus, which we call the homoclinic boundar
NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper we consider the numerical solution of some delay differential equations undergoing a Hopf bifurcation. We prove that if the delay differential equations have a Hopf bifurcation point atλ=λ*, then the numerical solution of the equation also has a Hopf bifurcation point atλh =λ* + O(h).
CLASSIFICATION OF BIFURCATIONS FOR NONLINEAR DYNAMICAL PROBLEMS WITH CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
吴志强; 陈予恕
2002-01-01
Bifurcation of periodic solutions widely existed in nonlinear dynamical systems isa kind of constrained one in intrinsic quality because its amplitude is always non-negative.Classification of the bifurcations with the type of constraint was discussed. All its six typesof transition sets are derived, in which three types are newly found and a method isproposed for analyzing the constrained bifurcation.
Chaos and reverse bifurcation in a RCL circuit
Cascais, J.; Dilão, R.; da Costa, A. Noronha
1983-01-01
The bifurcation diagram and attractor of a driven non-linear oscillator are directly obtained. The system exhibits not only period doubling, chaotic band merging and noise-free windows like the logistic map, but also reverse flip bifurcations, i.e. period halving. A negative schwartzian derivative map is found also possessing reverse bifurcations.
The Bifurcations of Traveling Wave Solutions of the Kundu Equation
Yating Yi; Zhengrong Liu
2013-01-01
We use the bifurcation method of dynamical systems to study the bifurcations of traveling wave solutions for the Kundu equation. Various explicit traveling wave solutions and their bifurcations are obtained. Via some special phase orbits, we obtain some new explicit traveling wave solutions. Our work extends some previous results.
Bifurcations of rotating waves in rotating spherical shell convection.
Feudel, F; Tuckerman, L S; Gellert, M; Seehafer, N
2015-11-01
The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Bénard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered.
The symmetry groups of bifurcations of integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Orlova, E I [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2014-11-30
Two-dimensional atoms are investigated; these are used to code bifurcations of the Liouville foliations of nondegenerate integrable Hamiltonian systems. To be precise, the symmetry groups of atoms with complexity at most 3 are under study. Atoms with symmetry group Z{sub p}⊕Z{sub q} are considered. It is proved that Z{sub p}⊕Z{sub q} is the symmetry group of a toric atom. The symmetry groups of all nonorientable atoms with complexity at most 3 are calculated. The concept of a geodesic atom is introduced. Bibliography: 9 titles.
Equilibrium points and bifurcation control of a chaotic system
Institute of Scientific and Technical Information of China (English)
Liang Cui-Xiang; Tang Jia-Shi
2008-01-01
Based on the Routh-Hurwitz criterion,this paper investigates the stability of a new chaotic system.State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle.Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation.Certain nP periodic orbits can be stabilized by parameter adjustment.Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
The recognition of equivariant bifurcation problems
Institute of Scientific and Technical Information of China (English)
李养成
1996-01-01
The orbit of an equivariant bifurcation problem with multiparameter is characterized under the action of the group of unipotent equivalences. When the unipotent tangent space is invariant under unipotent equivalences, the recognition problem can be solved by just using linear algebra. Sufficient conditions for a subspace to be intrinsic subspace under unipotent equivalences are given.
HOMOCLINIC TWIST BIFURCATIONS WITH Z(2) SYMMETRY
ARONSON, DG; VANGILS, SA; KRUPA, M
1994-01-01
We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two-parameter family of Z2 equivariant ODEs in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Bifurcation structure of an optical ring cavity
DEFF Research Database (Denmark)
Kubstrup, C.; Mosekilde, Erik
1996-01-01
One- and two-dimensional continuation techniques are applied to determine the basic bifurcation structure for an optical ring cavity with a nonlinear absorbing element (the Ikeda Map). By virtue of the periodic structure of the map, families of similar solutions develop in parameter space. Within...
Bifurcations in dynamical systems with parametric excitation
Fatimah, Siti
2002-01-01
This thesis is a collection of studies on coupled nonconservative oscillator systems which contain an oscillator with parametric excitation. The emphasis this study will, on the one hand, be on the bifurcations of the simple solutions such as fixed points and periodic orbits, and on the other hand o
Bifurcation structure of successive torus doubling
Energy Technology Data Exchange (ETDEWEB)
Sekikawa, Munehisa [Department of Information Science, Faculty of Engineering, Utsunomiya University (Japan)]. E-mail: muse@aihara.jst.go.jp; Inaba, Naohiko [Department of Information Science, Faculty of Engineering, Utsunomiya University (Japan)]. E-mail: inaba@is.utsunomiya-u.ac.jp; Yoshinaga, Tetsuya [Department of Radiologic Science and Engineering, School of Health Sciences, The University of Tokushima (Japan)]. E-mail: yosinaga@medsci.tokushima-u.ac.jp; Tsubouchi, Takashi [Institute of Engineering Mechanics and Systems, University of Tsukuba (Japan)]. E-mail: tsubo@esys.tsukuba.ac.jp
2006-01-02
The authors discuss the 'embryology' of successive torus doubling via the bifurcation theory, and assert that the coupled map of a logistic map and a circle map has a structure capable of generating infinite number of torus doublings.
Proposition of an outflow boundary approach for carotid artery stenosis CFD simulation.
Zhang, Yu; Furusawa, Toyoki; Sia, Sheau Fung; Umezu, Mitsuo; Qian, Yi
2013-01-01
The purpose of this study was to propose an innovative approach of setting outlet boundary conditions for the computational fluid dynamics (CFD) simulation of human common carotid arteries (CCAs) bifurcation based on the concept of energy loss minimisation at flow bifurcation. Comparisons between this new approach and previously reported boundary conditions were also made. The results showed that CFD simulation based on the proposed boundary conditions gave an accurate prediction of the critical stenosis ratio of carotid arteries (at around 65%). Other boundary conditions, such as the constant external pressure (P = 0) and constant outflow ratio, either overestimated or underestimated the critical stenosis ratio of carotid arteries. The patient-specific simulation results furthermore indicated that the calculated internal carotid artery flow ratio at CCA bifurcation (61%) coincided with the result obtained by clinical measurements through the use of Colour Doppler ultrasound. PMID:22288780
International Nuclear Information System (INIS)
Full text: Introduction: Yttrium-90 (Y-90) microsphere radioembolization is increasingly used for the treatment of unresectable hepatocellular carcinoma and liver metastasis. Objectives and tasks: We aim to present the upper abdominal wall skin involvement detected during routine pre-therapy Technetium-99m-macroaggregated albumin (Tc-99m-MAA) on SPECT/CT due to patent hepatic falciform artery and the precautions to avoid this potential complication. Material and methods: 38-year-old male with colon cancer and multiple liver metastasis was evaluated prior to radioembolization and Tc-99 MAA was slowly hand injected at the bifurcation of the proper hepatic artery. Then, the SPECT/CT scan was performed in order to investigate the systemic shunt or gastric involvement. Results: On SPECT/CT scan, involvement of the upper abdominal wall through falciform ligament was seen. Re-evaluation of the hepatic angiogram identified a patent hepatic falciform artery arising from the left hepatic artery. Y-90 microspheres were slowly hand injected to the left hepatic artery superselectively and no extra-hepatic activity was seen on SPECT/CT scan. Conclusion: Upper abdominal pain and dermatitis are uncommon findings after radioembolization and may occur due to inadvertent delivery of Y-90 microspheres into patent hepatic falciform artery. To prevent these complications, either patent hepatic falciform artery must be embolized by coil or Y-90 injection must be performed superselectively
BIFURCATION OF A SHAFT WITH HYSTERETIC-TYPE INTERNAL FRICTION FORCE OF MATERIAL
Institute of Scientific and Technical Information of China (English)
丁千; 陈予恕
2003-01-01
The bifurcation of a shaft with hysteretic internal friction of material was analysed. Firstly, the differential motion equation in complex form was deduced using Hamilton principle. Then averaged equations in primary resonances were obtained using the averaging method. The stability of steady-state responses was also determined. Lastly, the bifurcations of both normal motion (synchronous whirl) and self-excited motion (nonsynchronous whirl) were investigated using the method of singularity. The study shows that by a rather large disturbance, the stability of the shaft can be lost through Hopf bifurcation in case the stability condition is not satisfied. The averaged self-excited response appears as a type of unsymmetrical bifurcation with high orders of co-dimension. The second Hopf bifurcation, which corresponds to double amplitude-modulated response, can occur as the speed of the shaft increases. Balancing the shaft carefully to decrease its unbalance level and increasing the external damping are two effective methods to avoid the appearance of the self-sustained whirl induced by the hysteretic internal friction of material.
Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction
Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi
This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; Curzen, Nicholas P;
2011-01-01
Background— Controversy persists regarding the correct strategy for bifurcation lesions. Therefore, we combined the patient-level data from 2 large trials with similar methodology: the NORDIC Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study (BBC ONE). Methods and Results.......001). Procedure duration, contrast, and x-ray dose favored the simple approach. Subgroup analysis revealed similar composite end point results for true bifurcations (n=657, simple 9.2% versus complex 17.3%; hazard ratio 1.90 [95% confidence interval 1.22 to 2.94], P=0.004), wide-angled bifurcations >60 to 70° (n.......57). Conclusions— For bifurcation lesions, a provisional single-stent approach is superior to systematic dual stenting techniques in terms of safety and efficacy. A complex approach does not appear to be beneficial in more anatomically complicated lesions....
Complex Dynamics Caused by Torus Bifurcation in Power Systems
Institute of Scientific and Technical Information of China (English)
YU Xiaodan; JIA Hongjie; DONG Cun
2006-01-01
Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjuployed to reveal the relationship between torus bifurcation and some complex dynamics.Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system.Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence.It is also found that chaos has close relationship with various instability scenarios of power systems.Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.
BIFURCATION ANALYSIS OF EQUILIBRIUM POINT IN TWO NODE POWER SYSTEM
Directory of Open Access Journals (Sweden)
Halima Aloui
2014-01-01
Full Text Available This study presents a study of bifurcation in a dynamic power system model. It becomes one of the major precautions for electricity suppliers and these systems must maintain a steady state in the neighborhood of the operating points. We study in this study the dynamic stability of two node power systems theory and the stability of limit cycles emerging from a subcritical or supercritical Hopf bifurcation by computing the first Lyapunov coefficient. The MATCONT package of MATLAB was used for this study and detailed numerical simulations presented to illustrate the types of dynamic behavior. Results have proved the analyses for the model exhibit dynamical bifurcations, including Hopf bifurcations, Limit point bifurcations, Zero Hopf bifurcations and Bagdanov-taknes bifurcations.
Directory of Open Access Journals (Sweden)
Qunhong Li
2015-01-01
Full Text Available This paper investigates the codimension-two grazing bifurcations of a three-degree-of-freedom vibroimpact system with symmetrical rigid stops since little research can be found on this important issue. The criterion for existence of double grazing periodic motion is presented. Using the classical discontinuity mapping method, the Poincaré mapping of double grazing periodic motion is obtained. Based on it, the sufficient condition of codimension-two bifurcation of double grazing periodic motion is formulated, which is simplified further using the Jacobian matrix of smooth Poincaré mapping. At the end, the existence regions of different types of periodic-impact motions in the vicinity of the codimension-two grazing bifurcation point are displayed numerically by unfolding diagram and phase diagrams.
Cortese, Bernardo; Piraino, Davide; Buccheri, Dario; Alfonso, Fernando
2016-10-01
Bifurcation lesion management still represents a challenge for interventional cardiologists and currently there is a number of different approaches/techniques involving coronary stents. The use of a drug-coated balloon for native coronary vessel management is emerging as an alternative treatment, although in selected patient populations only. In particular, this technology has been tested for the treatment of bifurcations, both for the main vessel and the side branches. Several studies have evaluated this treatment as an alternative or as a therapeutic option complementary to stents, with conflicting and debatable results. However, the perspective of leaving lower metallic burden in this type of lesions is highly appealing and should be deeply investigated. We review here the currently available scientific data and future perspectives on drug-coated balloon use for bifurcation lesions. PMID:27390995
Hopf bifurcation in a diffusive Lotka-Volterra type system with nonlocal delay effect
Guo, Shangjiang; Yan, Shuling
2016-01-01
The dynamics of a diffusive Lotka-Volterra type model for two species with nonlocal delay effect and Dirichlet boundary conditions is investigated in this paper. The existence and multiplicity of spatially nonhomogeneous steady-state solutions are obtained by means of Lyapunov-Schmidt reduction. The stability of spatially nonhomogeneous steady-state solutions and the existence of Hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic orbits are derived. Finally, our theoretical results are illustrated by a model with homogeneous kernels and one-dimensional spatial domain.
Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model
Ren, Jingli; Yu, Liping
2016-07-01
In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.
Tate, Quinn; Kim, Seong-Eun; Treiman, Gerald; Parker, Dennis L.; Hadley, J. Rock
2012-01-01
The purpose of this work was to design and construct a multi-channel receive-only RF coil for 3 Tesla magnetic resonance imaging of the human carotid artery and bifurcation with optimized signal to noise ratio in the carotid vessels along the full extent of the neck. A neck phantom designed to match the anatomy of a subject with a neck representing the body habitus often seen in subjects with carotid arterial disease, was constructed. Sixteen circular coil elements were arranged on a semi-rig...
Stochastic D-bifurcation for a damped sine-Gordon equation with noise
Energy Technology Data Exchange (ETDEWEB)
Huang, Qiongwei; Xue, Changfeng, E-mail: cfxue@163.com [Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng 224051 (China); Tang, Jiashi [College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082 (China)
2015-04-15
We investigate the stochastic bifurcation of a damped sine-Gordon equation with Dirichlet boundary conditions under the influence of multiplicative Gaussian white noise. Introducing a slow time scale, we derive the amplitude equations near the trivial solution by multiscale analysis. And the stationary probability density functions are formulated analytically using the stochastic averaging of energy envelope. The numerical calculations show that the system undergoes a stochastic D-bifurcation of energy envelope from a delta measure to new stationary measures when the control parameter crosses a critical point.
Normal form analysis of multiple bifurcations in incompletely mixed chemical reactors
Puhl, Andreas; Nicolis, Grégoire
1987-07-01
Using the theory of normal forms, we investigate the effects of mixing in a continuous flow stirred tank reactor (CSTR) for a reaction model exhibiting oscillatory behavior in the vicinity of a degenerated bifurcation point (here, a Takens-Bogdanov point). In addition we show without specification of a particular reaction system that, as long as reaction rates remain much slower than the inverse mixing time, incomplete mixing introduces a new bifurcation parameter for nonpremixed feeding conditions, whereas premixed feeding conditions merely lead to a renormalization of flow rate.
Quelques problèmes de stabilité et de bifurcation des solides visqueux
ABED-MERAIM, Farid
1999-01-01
This PhD thesis is composed essentially of two main parts, of unequal sizes, which are summarized as follows: Part I: It is concerned with stability and bifurcation issues relating to strain-rate-independent solids and structures (i.e., elastic or elasto-plastic). A thorough and comprehensive review of the various investigations in this field allowed us to propose an original and compact presentation of the theory of stability and bifurcation. An illustration of this theory is then shown thro...
Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without ilnikov Orbits
Directory of Open Access Journals (Sweden)
Na Li
2015-01-01
Full Text Available This paper mainly investigates the dynamical behaviors of a chaotic system without ilnikov orbits by the normal form theory. Both the stability of the equilibria and the existence of local Hopf bifurcation are proved in view of analyzing the associated characteristic equation. Meanwhile, the direction and the period of bifurcating periodic solutions are determined. Regarding the delay as a parameter, we discuss the effect of time delay on the dynamics of chaotic system with delayed feedback control. Finally, numerical simulations indicate that chaotic oscillation is converted into a steady state when the delay passes through a certain critical value.
Jiang, Heping; Jiang, Jiao; Song, Yongli
In this paper, we firstly employ the normal form theory of delayed differential equations according to Faria and Magalhães to derive the normal form of saddle-node-Hopf bifurcation for the general retarded functional differential equations. Then, the dynamical behaviors of a Leslie-Gower predator-prey model with time delay and nonmonotonic functional response are considered. Specially, the dynamical classification near the saddle-node-Hopf bifurcation point is investigated by using the normal form and the center manifold approaches. Finally, the numerical simulations are employed to support the theoretical results.
Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips
Institute of Scientific and Technical Information of China (English)
SHUI; Shuliang; ZHU; Deming
2005-01-01
Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.
Significance of the resting angles of hair-cell bundles for Hopf bifurcation criticality
Kim, Kyung-Joong; Ahn, Kang-Hun
2016-08-01
We investigate the significance of the inclined angle of a hair bundle at equilibrium. We find that, while the angle gives a geometrical conversion factor between the bundle deflection and the ion channel displacement, it also controls the dynamics of the bundle. We show that a Hopf bifurcation, which enhances sensitivity, can be driven by the geometrical factor. However, existing experimental data indicate that mammalian auditory hair-cell bundles are located far away from the Hopf bifurcation point, suggesting that the high sensitivity of mammalian hearing might come from other mechanisms.
Institute of Scientific and Technical Information of China (English)
Nan Zhang; Tong Qiu; Bingzhen Chen
2015-01-01
The major difficulty in achieving good performance of industrial polymerization reactors lies in the lack of under-standing of their nonlinear dynamics and the lack of wel-developed techniques for the control of nonlinear pro-cesses, which are usually accompanied with bifurcation phenomenon. This work aims at investigating the nonlinear behavior of the parameterized nonlinear system of vinyl acetate polymerization and further modifying the bifurcation characteristics of this process via a washout filter-aid control er, with all the original steady state equilibria preserved. Advantages and possible extensions of the proposed methodology are discussed to provide scientific guide for further controller design and operation improvement.
Directory of Open Access Journals (Sweden)
Sareh Sepahvand Hossein Beigi
2015-09-01
Full Text Available Background: Coronary Artery Disease (CAD is an important disease where the arteries and vessels supplying oxygen and nutrients to the heart are narrowed or blocked. Early diagnosis and recognition of CAD leads to its complete treatment. Drug therapy, angiography, coronary angioplasty, and in advanced cases, coronary artery bypass surgery restore the normal flow of blood to the heart muscle. Objectives: The present study aimed to identify the association between rs4977574 polymorphism in ANRIL gene and CAD in Iranian patients. Materials and Methods: Blood samples were collected from 100 subjects with positive angiography (case group and 93 ones with negative angiography (control group. Using Taq Man Real Time PCR, the extracted DNAs from the patients and controls were genotyped for rs4977574 polymorphism in ANRIL gene (applied biosystem, USA. Then, the genotypes and clinical parameters were compared by the SPSS statistical software, version 18 (Chicago, USA. The results were compared by one-way ANOVA, simple T-test, and Chi-square test and were presented as mean ± Standard Deviation (SD. P values < 0.05 were considered as statistically significant. Results: The results showed a significant relationship between CAD and Diastolic Blood Pressure (DBP, Body Mass Index (BMI, uric acid, Low Density Lipoprotein (LDL, cholesterol, and triglyceride. However, no significant association was observed between rs4977574 polymorphism and biochemical characteristics in the two groups. Allele frequency was AA = 22%, AG = 44%, and GG = 34% in the case group and AA = 17%, AG = 44%, and GG = 32% in the control group. Conclusions: The present study examined the association between rs4977574 polymorphism in ANRIL gene and CAD in a population of Iranian patients. The study findings revealed no direct relationship between rs4977574 polymorphism and the disease in Iranian population.
Chen, Kuen-Bao; Chen, Kuan-Chung; Chang, Ya-Lin; Chang, Kun-Lung; Chang, Pei-Chun; Chang, Tung-Ti; Chen, Yu-Chian
2016-01-01
Coronary artery disease (CAD) is the most common cause of heart attack and the leading cause of mortality in the world. It is associated with mitochondrial dysfunction and increased level of reactive oxygen species production. According to the Ottawa Heart Genomics Study genome-wide association study, a recent research identified that Q688 spastic paraplegia 7 (SPG7) variant is associated with CAD as it bypasses the regulation of tyrosine phosphorylation of AFG3L2 and enhances the processing and maturation of SPG7 protein. This study aims to identify potential compounds isolated from Traditional Chinese Medicines (TCMs) as potential lead compounds for paraplegin (SPG7) inhibitors. For the crystallographic structure of paraplegin, the disordered disposition of key amino acids in the binding site was predicted using the PONDR-Fit protocol before virtual screening. The TCM compounds saussureamine C and 3-(2-carboxyphenyl)-4(3H)-quinazolinone, have potential binding affinities with stable H-bonds and hydrophobic contacts with key residues of paraplegin. A molecular dynamics simulation was performed to validate the stability of the interactions between each candidate and paraplegin under dynamic conditions. Hence, we propose these compounds as potential candidates as lead drug from the compounds isolated from TCM for further study in drug development process with paraplegin protein for coronary artery disease. PMID:27164068
Moohebati, Mohsen; Kabirirad, Vahid; Ghayour-Mobarhan, Majid; Esmaily, Habibollah; Tavallaie, Shima; Akhavan Rezayat, Amir; Pourghadamyari, Hossein; Sahebkar, Amirhossein
2014-01-01
It has been suggested that antioxidized low-density lipoprotein (anti-oxLDL) antibodies play a role in the pathogenesis of atherosclerosis. The aim of this study was to measure serum ox-LDL IgG levels in 31 patients with angiographically defined coronary artery disease (CAD) (≥50% stenosis in at least one major coronary artery; CAD(+) group) and compare these levels with those of 32 subjects with coronary stenosis (CAD(-) group) and 24 healthy age- and sex-matched controls using ELISA. We did not find any significant difference between CAD(+), CAD(-), and control groups in regard to oxLDL IgG levels (P = 0.83). Serum oxLDL IgG levels did not differ between 1VD (one vessel disease), 2VD (2 vessels disease), and 3VD (3 vessels disease) subgroups of CAD(+) patients (P = 0.20). Serum anti-oxLDL titers were only significantly correlated with LDL-C in the CAD(+) group (P cardiovascular risk factors was associated with serum ox-LDL IgG levels. The present results suggest that serum levels of ox-LDL IgG are neither associated with the presence and severity of CAD nor with the conventional cardiovascular risk factors.
Renal Arterial Network Structure by Computed Tomography, and Nephron-Arterial Interactions
DEFF Research Database (Denmark)
2015-01-01
Our goal is to predict interactions that develop among nephrons and between nephrons and the arterial network that supports them. We have developed a computationally simple but physiologically-based mathematical model of the kidney vascular tree to study renal autoregulation in ensembles of inter......Our goal is to predict interactions that develop among nephrons and between nephrons and the arterial network that supports them. We have developed a computationally simple but physiologically-based mathematical model of the kidney vascular tree to study renal autoregulation in ensembles...... of interacting nephrons not directly available for experimentation. The study combines computed tomography (CT) of a renal vascular cast at 2 micrometer resolution with simulation. The CT scan showed a bifurcating branching structure with as many as 7 bifurcations between arcuate arteries and the renal surface......, with afferent arterioles originating from all arterial structures, including arcuate arteries. The modeling component has 2 novel features: a probability based vascular tree based on the data from the CT images, and a network of arteries supplying several simple whole nephron models coupled electrotonically...
Influence of noise and near-resonant perturbations on bifurcations in Josephson junctions
DEFF Research Database (Denmark)
Svensmark, Henrik; Hansen, Jørn Bindslev; Pedersen, Niels Falsig
1987-01-01
The stabilization of a nonlinear system against period-doubling bifurcations by means of a periodic perturbation has been investigated. With the Josephson junction as a model system, both numerical simulations (including noise) and measurements on Josephson tunnel junctions have been performed...
Directory of Open Access Journals (Sweden)
Michal Marszal
2014-01-01
Full Text Available This paper investigates dynamics of double pendulum subjected to vertical parametric kinematic excitation. It includes detailed bifurcation diagrams in two-parameter space (excitation’s frequency and amplitude for both oscillations and rotations in the domain of periodic solutions.
Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation
Institute of Scientific and Technical Information of China (English)
MA Zhi-Min; SUN Yu-Huai; LIU Fu-Sheng
2013-01-01
In this paper,the generalized Boussinesq wave equation utt-uxx + a(um)xx + bu =0 is investigated by using the bifurcation theory and the method of phase portraits analysis.Under the different parameter conditions,the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained.
REMARKS ON BIFURCATIONS OF u″ + μu- uk = 0 (4 ≤ k ∈ Z+)
Institute of Scientific and Technical Information of China (English)
李常品
2001-01-01
In this paper, we investigate the bifurcations of one class of steady-state reaction-diffusion equations of the form u" +μu-uκ =0, subject to u(0)=u(π)=0, where μ is a parameter, 4≤k∈Z+.Using the singularity theory based on the Liapunov-Schmidt reduction, some satisfactory results are obtained.
An Incidental Finding of the Thyroidea Ima Artery:-A Case Report Study
Directory of Open Access Journals (Sweden)
Lalit C. Ratanpara
2015-12-01
Full Text Available We are here reporting a case of an incidental finding of the thyroidea ima artery emerging from the brachiocephalic trunk with a typical inferior thyroid vessels on both sides emerging from the thyrocervical trunk. The thyroidea ima artery entered the thyroid gland near to anterior surface of right lobe of thyroid gland. It arose from the brachiocephalic artery proximal to its bifurcation.
Lee, Seung-Jun; Park, Sung-Ha
2013-01-01
Arterial ageing is characterized by age associated degeneration and sclerosis of the media layer of the large arteries. However, besides ageing, clinical conditions, which enhance oxidative stress and inflammation act to accelerate the degree of arterial ageing. In this review, we summarized the pathophysiology and contributing factors that accelerate arterial ageing. Among them, we focused on hypertension, the renin-angiotensin-aldosterone system and vascular inflammation which are modifiabl...
Multiparametric bifurcations of an epidemiological model with strong Allee effect.
Cai, Linlin; Chen, Guoting; Xiao, Dongmei
2013-08-01
In this paper we completely study bifurcations of an epidemic model with five parameters introduced by Hilker et al. (Am Nat 173:72-88, 2009), which describes the joint interplay of a strong Allee effect and infectious diseases in a single population. Existence of multiple positive equilibria and all kinds of bifurcation are examined as well as related dynamical behavior. It is shown that the model undergoes a series of bifurcations such as saddle-node bifurcation, pitchfork bifurcation, Bogdanov-Takens bifurcation, degenerate Hopf bifurcation of codimension two and degenerate elliptic type Bogdanov-Takens bifurcation of codimension three. Respective bifurcation surfaces in five-dimensional parameter spaces and related dynamical behavior are obtained. These theoretical conclusions confirm their numerical simulations and conjectures by Hilker et al., and reveal some new bifurcation phenomena which are not observed in Hilker et al. (Am Nat 173:72-88, 2009). The rich and complicated dynamics exhibit that the model is very sensitive to parameter perturbations, which has important implications for disease control of endangered species.
Bifurcations and safe regions in open Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Barrio, R; Serrano, S [GME, Dpto Matematica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Blesa, F [GME, Dpto Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es, E-mail: fblesa@unizar.es, E-mail: sserrano@unizar.es
2009-05-15
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Henon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Bifurcations and safe regions in open Hamiltonians
Barrio, R.; Blesa, F.; Serrano, S.
2009-05-01
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
International Nuclear Information System (INIS)
The coexistence of a resting condition and period-1 firing near a subcritical Hopf bifurcation point, lying between the monostable resting condition and period-1 firing, is often observed in neurons of the central nervous systems. Near such a bifurcation point in the Morris—Lecar (ML) model, the attraction domain of the resting condition decreases while that of the coexisting period-1 firing increases as the bifurcation parameter value increases. With the increase of the coupling strength, and parameter and initial value dependent synchronization transition processes from non-synchronization to compete synchronization are simulated in two coupled ML neurons with coexisting behaviors: one neuron chosen as the resting condition and the other the coexisting period-1 firing. The complete synchronization is either a resting condition or period-1 firing dependent on the initial values of period-1 firing when the bifurcation parameter value is small or middle and is period-1 firing when the parameter value is large. As the bifurcation parameter value increases, the probability of the initial values of a period-1 firing neuron that lead to complete synchronization of period-1 firing increases, while that leading to complete synchronization of the resting condition decreases. It shows that the attraction domain of a coexisting behavior is larger, the probability of initial values leading to complete synchronization of this behavior is higher. The bifurcations of the coupled system are investigated and discussed. The results reveal the complex dynamics of synchronization behaviors of the coupled system composed of neurons with the coexisting resting condition and period-1 firing, and are helpful to further identify the dynamics of the spatiotemporal behaviors of the central nervous system. (general)
Dynamics of Surfactant Liquid Plugs at Bifurcating Lung Airway Models
Tavana, Hossein
2013-11-01
A surfactant liquid plug forms in the trachea during surfactant replacement therapy (SRT) of premature babies. Under air pressure, the plug propagates downstream and continuously divides into smaller daughter plugs at continuously branching lung airways. Propagating plugs deposit a thin film on airway walls to reduce surface tension and facilitate breathing. The effectiveness of SRT greatly depends on the final distribution of instilled surfactant within airways. To understand this process, we investigate dynamics of splitting of surfactant plugs in engineered bifurcating airway models. A liquid plug is instilled in the parent tube to propagate and split at the bifurcation. A split ratio, R, is defined as the ratio of daughter plug lengths in the top and bottom daughter airway tubes and studied as a function of the 3D orientation of airways and different flow conditions. For a given Capillary number (Ca), orienting airways farther away from a horizontal position reduced R due to the flow of a larger volume into the gravitationally favored daughter airway. At each orientation, R increased with 0.0005 surfactant distribution in airways and develop effective SRT strategies.
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
Directory of Open Access Journals (Sweden)
Wen-Qing Zhang
2013-01-01
Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.
Nadeem, S.; Ijaz, S.
2016-07-01
In this paper hemodynamics of stenosis are discussed to predict effect of atherosclerosis by means of mathematical models in the presence of uniform transverse magnetic field. The analysis is carried out using silver and copper nanoparticles as a drug carrier. Exact solution for the fluid temperature, velocity, axial induced magnetic field and current density distribution are obtained under mild stenosis approximation. The results indicate that with an increase in the concentration of nanoparticle hemodynamics effects of stenosis reduces throughout the inclined composite stenosed arteries. The considered analysis also summarizes that the drug silver nanoparticles is more efficient to reduce hemodynamics of stenosis when compare to the drug copper nanoparticle. In future this model could be helpful to predict important properties in some biomedical applications.
ANGIOGRAPHIC PROFILE OF LEFT MAIN CORONARY ARTERY (LMCA STENOSIS
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Malladi Srinivasa
2015-02-01
Full Text Available Among patients with coronary artery disease, left coronary artery (LMCA stenosis is the dangerous form of coronary arterial involvement, associated with increased mortality and morbidity unless immediate intervention is done. The gold standard treatment for left main coronary artery (LMCA stenosis is the emergency coronary artery bypass grafting to its branches, left anterior descending artery (LAD, and left circumflex artery (LCX. Of percutaneous intervention in the form of angioplasty and stenting of left main coronary artery are increasingly done. The anatomy and the site of stenosi s in the left main coronary artery determine the management option. In this context, the involvement of left main coronary artery and its anatomical pattern are important in deciding management options. AIM: To study the angiographic profile of significant Left main coronary artery (LMCA stenosis among the patients who underwent coronary angiography. METHODS: A total of 1911 cases of significant coronary arterial disease, who underwent coronary angiography a t King George Hospital, Visakhapatnam were studied in the present study and their coronary angiograms were analysed with respect to the pattern of involvement. RESULTS: of the 1911 cases of coronary artery disease, 118 patients have left main coronary arte ry disease. M/F ratio is 93/25. Of them 68.4% are hypertensive, 41.5 % are diabetics, 34.7% are smokers. Mean age of presentation was 59 yrs. Isolated LMCA involvement is seen in 5, associated with single vessel disease in 9, double vessel disease in 12 an d triple vessel diseases in 93. Ostio - proximal involvement is seen in 21, mid segment involvement in 13, distal – bifurcation involvement in 93 and total occlusion of LMCA in 1 case. CONCLUSION: Significant LMCA involvement is seen in 6.1%. In majority of c ases, it is associated with triple vessel disease and distal bifurcation is the commonest site involved.
Classification of solitary wave bifurcations in generalized nonlinear Schr\\"odinger equations
Yang, Jianke
2012-01-01
Bifurcations of solitary waves are classified for the generalized nonlinear Schr\\"odinger equations with arbitrary nonlinearities and external potentials in arbitrary spatial dimensions. Analytical conditions are derived for three major types of solitary wave bifurcations, namely saddle-node bifurcations, pitchfork bifurcations and transcritical bifurcations. Shapes of power diagrams near these bifurcations are also obtained. It is shown that for pitchfork and transcritical bifurcations, their power diagrams look differently from their familiar solution-bifurcation diagrams. Numerical examples for these three types of bifurcations are given as well. Of these numerical examples, one shows a transcritical bifurcation, which is the first report of transcritical bifurcations in the generalized nonlinear Schr\\"odinger equations. Another shows a power loop phenomenon which contains several saddle-node bifurcations, and a third example shows double pitchfork bifurcations. These numerical examples are in good agreeme...
Simplest Normal Forms of Generalized Neimark-Sacker Bifurcation
Institute of Scientific and Technical Information of China (English)
DING Yumei; ZHANG Qichang
2009-01-01
The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simpli-fied. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conven-tional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest nor-mal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
By taking average over the curvature, the temperature and its gradient, the solute con-centration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidifi-cation, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysisof the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equationsshows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition vades with differ-ent thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradientscope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifur-cation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realizedthrough supercritical inverse bifurcation in the rapid solidification area.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.;
2001-01-01
One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...... behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability....
Defining universality classes for three different local bifurcations
Leonel, Edson D.
2016-10-01
The convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents α, β and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent δ. The four exponents α, β, z and δ can be used to defined classes of universality for the local bifurcations of fixed points in differential equations.
Global Bifurcation of a Novel Computer Virus Propagation Model
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.
Characterization of static bifurcations for n-dimensional flows in the frequency domain
Institute of Scientific and Technical Information of China (English)
Li ZENG; Yi ZHAO
2006-01-01
In this paper n-dimensional flows (described by continuous-time system) with static bifurcations are considered with the aim of classification of different elementary bifurcations using the frequency domain formalism. Based on frequency domain approach, we prove some criterions for the saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation, and give an example to illustrate the efficiency of the result obtained.
Patterns of disease distribution of lower extremity peripheral arterial disease.
Chen, Qian; Shi, Yang; Wang, Yutang; Li, Xiaoying
2015-03-01
Peripheral arterial disease (PAD) is a common manifestation of atherosclerosis that is associated with an increased risk of mortality and cardiovascular (CV) events. Peripheral arterial disease involves the arteries distal to the aortic bifurcation in a nonuniform manner. Studies have shown that symptoms and prognosis of patients with PAD vary according to the location and size of the affected artery. Several modalities have been used to identify the location of PAD, including noninvasive evaluations and invasive procedures. Peripheral arterial disease has a risk factor profile similar to that associated with coronary artery disease (ie, age, gender, diabetes, smoking, hypertension, and hyperlipidemia). Many studies have shown that the distribution, extent, and progression of PAD are influenced by CV risk factors but the findings are not consistent. Management strategies for PAD are different for proximal and distal PAD. The objective of this review is to discuss the patterns of diseases distribution in patients with PAD.
Singularly perturbed bifurcation subsystem and its application in power systems
Institute of Scientific and Technical Information of China (English)
An Yichun; Zhang Qingling; Zhu Yukun; Zhang Yan
2008-01-01
The singularly perturbed bifurcation subsystem is described,and the test conditions of subsystem persistence are deduced.By use of fast and slow reduced subsystem model,the result does not require performing nonlinear transformation.Moreover,it is shown and proved that the persistence of the periodic orbits for Hopf bifurcation in the reduced model through center manifold.Van der Pol oscillator circuit is given to illustrate the persistence of bifurcation subsystems with the full dynamic system.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Hopf bifurcation in the Clarida, Gali, and Gertler model
Barnett, William A.; Eryilmaz, Unal
2012-01-01
We explore bifurcation phenomena in the open-economy New Keynesian model developed by Clarida, Gali and Gertler (2002). We find that the open economy framework can bring about more complex dynamics, along with a wider variety of qualitative behaviors and policy responses. Introducing parameters related to the open economy structure affects the values of bifurcation parameters and changes the location of bifurcation boundaries. As a result, the stratification of the confidence region, as previ...
Identification of Bifurcations from Observations of Noisy Biological Oscillators
Salvi, Joshua D; Hudspeth, A J
2016-01-01
Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise.
International Nuclear Information System (INIS)
Variation of the branches of the external carotid artery (ECA) is well known, but it is extremely rare for the occipital artery (OA) to arise from the internal carotid artery (ICA). A 87-year-old man was found to have this anatomical variation on the right side by threedimensional computed tomography angiography for vascular mapping of the carotid arteries before superselective intra-arterial catheterization for advanced tongue cancer. Imaging showed the OA arose from the anterior aspect of the right ICA with the origin located 8.8 mm distal from the carotid bifurcation. The inner diameter of the origin of the OA was 2.1 mm and the angle between the OA and the ICA was 62 degrees. It is important to recognize this anatomic variation of the branches of the ECA before head and neck microsurgical reconstruction or superselective intra-arterial chemotherapy for oral cancer
Periodic solutions and flip bifurcation in a linear impulsive system
Institute of Scientific and Technical Information of China (English)
Jiang Gui-Rong; Yang Qi-Gui
2008-01-01
In this paper,the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically.The existence and the stability of period-one solution are discussed by using a discrete map.The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem.The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters.Moreover,the periodic solutions,the bifurcation diagram,and the chaotic attractor,which show their consistence with the theoretical analyses,are given in an example.中图分类:O547
Bifurcations in two coupled Rössler systems
DEFF Research Database (Denmark)
Rasmussen, J; Mosekilde, Erik; Reick, C.
1996-01-01
The paper presents a detailed bifurcation analysis of two symmetrically coupled Rössler systems. The symmetry in the coupling does not allow any one direction to become preferred, and the coupled system is therefore an example of a dissipative system that cannot be considered as effectively one......-dimensional. The results are presented in terms of one- and two-parmeter bifurcation diagrams. A particularly interesting finding is the replacement of some of the period-doubling bifurcations by torus bifurcations. By virtue of this replacement, instead of a Feigenbaum transition to chaos a transition via torus...
Hopf bifurcation for tumor-immune competition systems with delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available In this article, a immune response system with delay is considered, which consists of two-dimensional nonlinear differential equations. The main purpose of this paper is to explore the Hopf bifurcation of a immune response system with delay. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solution are also given. Especially, the conditions of the global existence of periodic solutions bifurcating from Hopf bifurcations are given. Numerical simulations are carried out to illustrate the the theoretical analysis and the obtained results.
High-codimensional static bifurcations of strongly nonlinear oscillator
Institute of Scientific and Technical Information of China (English)
Zhang Qi-Chang; Wang Wei; Liu Fu-Hao
2008-01-01
The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied.We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form.To discuss the static bifurcation,the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory.The transition set and bifurcation diagrams for the singularity are presented,while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
Oscillatory Activities in Regulatory Biological Networks and Hopf Bifurcation
Institute of Scientific and Technical Information of China (English)
YAN Shi-Wei; WANG Qi; XIE Bai-Song; ZHANG Feng-Shou
2007-01-01
Exploiting the nonlinear dynamics in the negative feedback loop, we propose a statistical signal-response model to describe the different oscillatory behaviour in a biological network motif. By choosing the delay as a bifurcation parameter, we discuss the existence of Hopf bifurcation and the stability of the periodic solutions of model equations with the centre manifold theorem and the normal form theory. It is shown that a periodic solution is born in a Hopf bifurcation beyond a critical time delay, and thus the bifurcation phenomenon may be important to elucidate the mechanism of oscillatory activities in regulatory biological networks.
Neary, Joseph M; Gould, Daniel H; Garry, Franklyn B; Knight, Anthony P; Dargatz, David A; Holt, Timothy N
2013-03-01
Producer reports from ranches over 2,438 meters in southwest Colorado suggest that the mortality of preweaned beef calves may be substantially higher than the national average despite the selection of low pulmonary pressure herd sires for over 20 years. Diagnostic investigations of this death loss problem have been limited due to the extensive mountainous terrain over which these calves are grazed with their dams. The objective of the current study was to determine the causes of calf mortality on 5 high-altitude ranches in Colorado that have been selectively breeding sires with low pulmonary pressure (branding (6 weeks of age) in the spring to weaning in the fall (7 months of age). Clinical signs were recorded, and blood samples were taken from sick calves. Postmortem examinations were performed, and select tissue samples were submitted for aerobic culture and/or histopathology. On the principal study ranch, 9.6% (59/612) of the calves that were branded in the spring either died or were presumed dead by weaning in the fall. In total, 28 necropsies were performed: 14 calves (50%) had lesions consistent with pulmonary hypertension and right-sided heart failure, and 14 calves (50%) died from bronchopneumonia. Remodeling of the pulmonary arterial system, indicative of pulmonary hypertension, was evident in the former and to varying degrees in the latter. There is a need to better characterize the additional risk factors that complicate pulmonary arterial pressure testing of herd sires as a strategy to control pulmonary hypertension. PMID:23512918
Guner, Sukriye Ilkay; Korkmaz, Fatma Demir
2015-07-01
This trial was conducted to investigate the effect of chest physiotherapy in different positions on the heart and the respiratory system after coronary artery bypass surgery. Patients are divided into two groups of 30 patients each in the study. To the patients in the first group (30 patients), percussion-vibration was performed in the 45° supine position, while slightly laterally lying and endotracheal aspiration was performed in the supine position. To the patients in the second group (30 patients), percussion-vibration was performed in the 0° supine position, while slightly laterally lying and endotracheal aspiration was performed in the supine position. The procedures are repeated two times for all patients and their means were taken. The pre- and postapplication values of patients were measured from central venous and arterial catheters and the values of patient monitors were recorded. Comparison of the two groups in terms of respiratory values did not reveal a significant difference, but chest physiotherapy with the head of the bed at 0° was determined to improve cardiac functions. Evaluation of the groups in terms of pre- and postphysiotherapy applications showed a significant increase in mixed venous oxygen saturation in both groups. Chest physiotherapy with the head of the bed elevated to 45° may be recommended in patients who carry a risk of pulmonary complications and who are candidates for chest physiotherapy at an early stage.
Kefayati, Sarah; Holdsworth, David W; Poepping, Tamie L
2014-01-01
Clinical decision-making for the treatment of patients with diseased carotid artery is mainly based on the severity of the stenosis. However, stenosis severity alone is not a sensitive indicator, and other local factors for the assessment of stroke risk are required. Flow disturbance is of particular interest due to its proven association with increased thromboembolic activities. The objective of this study was to investigate the level of turbulence intensity (TI) with regards to certain geometrical features of the plaque - namely stenosis severity, eccentricity, and ulceration. A family of eight carotid-artery bifurcation models was examined using particle image velocimetry. Results showed a marked difference in turbulence intensity among these models; increasing degree of stenosis severity resulted in increased turbulence intensity, going from 0.12 m/s for mild stenosis to 0.37 m/s for severe stenosis (with concentric geometry). Moreover, independent of stenosis severity, eccentricity led to further elevations in turbulence intensity, increasing TI by 0.05-0.10 m/s over the counterpart concentric plaque. The presence of ulceration (in a 50% eccentric plaque) produced a larger portion of moderate turbulence intensity (~0.10 m/s) compared to the non-ulcerated model, more proximal to the bifurcation apex in the post-stenotic recirculation zone. The effect of plaque eccentricity and ulceration in enhancing the downstream turbulence has potential clinical implications for a more sensitive assessment of stroke risk beyond stenosis severity alone.
The Branching Bifurcation of Adaptive Dynamics
Della Rossa, Fabio; Dercole, Fabio; Landi, Pietro
2015-06-01
We unfold the bifurcation involving the loss of evolutionary stability of an equilibrium of the canonical equation of Adaptive Dynamics (AD). The equation deterministically describes the expected long-term evolution of inheritable traits — phenotypes or strategies — of coevolving populations, in the limit of rare and small mutations. In the vicinity of a stable equilibrium of the AD canonical equation, a mutant type can invade and coexist with the present — resident — types, whereas the fittest always win far from equilibrium. After coexistence, residents and mutants effectively diversify, according to the enlarged canonical equation, only if natural selection favors outer rather than intermediate traits — the equilibrium being evolutionarily unstable, rather than stable. Though the conditions for evolutionary branching — the joint effect of resident-mutant coexistence and evolutionary instability — have been known for long, the unfolding of the bifurcation has remained a missing tile of AD, the reason being related to the nonsmoothness of the mutant invasion fitness after branching. In this paper, we develop a methodology that allows the approximation of the invasion fitness after branching in terms of the expansion of the (smooth) fitness before branching. We then derive a canonical model for the branching bifurcation and perform its unfolding around the loss of evolutionary stability. We cast our analysis in the simplest (but classical) setting of asexual, unstructured populations living in an isolated, homogeneous, and constant abiotic environment; individual traits are one-dimensional; intra- as well as inter-specific ecological interactions are described in the vicinity of a stationary regime.
Burzotta, Francesco; Cook, Brian; Iaizzo, Paul A; Singh, Jasvindar; Louvard, Yves; Latib, Azeem
2015-01-01
The Visible Heart® Laboratory is an original experimental laboratory in which harvested animal hearts are resuscitated and connected to a support machine in order to beat outside the animal body. Resuscitated animal hearts may be exposed to various types of endovascular intervention under full, multimodality inspection. This unique experimental setting allows the performance of percutaneous coronary intervention (PCI) in a setting which resembles a standard catheterisation laboratory set-up, and contemporaneously allows unique multimodality imaging. For these reasons, the performance of PCI on bifurcations in the Visible Heart® Laboratory may improve the knowledge of the dynamic stent deformations and stent-vessel wall interactions associated with the different steps of the various techniques for bifurcation stenting. Furthermore, the collected images may also serve as a novel educative resource for physicians. The performance of bifurcation stenting in the Visible Heart® Laboratory is a promising experimental setting to gain novel information regarding any existing or future PCI technique to treat coronary bifurcations.
Burzotta, Francesco; Cook, Brian; Iaizzo, Paul A; Singh, Jasvindar; Louvard, Yves; Latib, Azeem
2015-01-01
The Visible Heart® Laboratory is an original experimental laboratory in which harvested animal hearts are resuscitated and connected to a support machine in order to beat outside the animal body. Resuscitated animal hearts may be exposed to various types of endovascular intervention under full, multimodality inspection. This unique experimental setting allows the performance of percutaneous coronary intervention (PCI) in a setting which resembles a standard catheterisation laboratory set-up, and contemporaneously allows unique multimodality imaging. For these reasons, the performance of PCI on bifurcations in the Visible Heart® Laboratory may improve the knowledge of the dynamic stent deformations and stent-vessel wall interactions associated with the different steps of the various techniques for bifurcation stenting. Furthermore, the collected images may also serve as a novel educative resource for physicians. The performance of bifurcation stenting in the Visible Heart® Laboratory is a promising experimental setting to gain novel information regarding any existing or future PCI technique to treat coronary bifurcations. PMID:25983169
Brownrigg, J R W; Hinchliffe, R J; Apelqvist, J; Boyko, E J; Fitridge, R; Mills, J L; Reekers, J; Shearman, C P; Zierler, R E; Schaper, N C
2016-01-01
Non-invasive tests for the detection of peripheral artery disease (PAD) among individuals with diabetes mellitus are important to estimate the risk of amputation, ulceration, wound healing and the presence of cardiovascular disease, yet there are no consensus recommendations to support a particular diagnostic modality over another and to evaluate the performance of index non-invasive diagnostic tests against reference standard imaging techniques (magnetic resonance angiography, computed tomography angiography, digital subtraction angiography and colour duplex ultrasound) for the detection of PAD among patients with diabetes. Two reviewers independently screened potential studies for inclusion and extracted study data. Eligible studies evaluated an index test for PAD against a reference test. An assessment of methodological quality was performed using the quality assessment for diagnostic accuracy studies instrument. Of the 6629 studies identified, ten met the criteria for inclusion. In these studies, the patients had a median age of 60-74 years and a median duration of diabetes of 9-24 years. Two studies reported exclusively on patients with symptomatic (ulcerated/infected) feet, two on patients with asymptomatic (intact) feet only, and the remaining six on patients both with and without foot ulceration. Ankle brachial index (ABI) was the most widely assessed index test. Overall, the positive likelihood ratio and negative likelihood ratio (NLR) of an ABI threshold saturation of peripheral blood and Doppler wave form analyses had NLRs of 0.2 and wave form analysis may be superior to ABI for diagnosing PAD in patients with neuropathy with and without foot ulcers. There were insufficient data to support the adoption of one particular diagnostic modality over another and no comparisons existed with clinical examination. The quality of studies evaluating diagnostic techniques for the detection of PAD in individuals with diabetes is poor. Improved compliance with
On the application of Newton's and Chord methods to bifurcation problems
Directory of Open Access Journals (Sweden)
M. B. M. Elgindi
1994-01-01
Full Text Available This paper is concerned with the applications of Newton's and chord methods in the computations of the bifurcation solutions in a neighborhood of a simple bifurcation point for prescribed values of the bifurcation parameter.
Homoclinic bifurcation in Chua’s circuit
Indian Academy of Sciences (India)
S K Dana; S Chakraborty; G Ananthakrishna
2005-03-01
We report our experimental observations of the Shil’nikov-type homoclinic chaos in asymmetry-induced Chua’s oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcations. The asymmetry is introduced in the circuit by forcing a DC voltage. For a selected asymmetry, when a system parameter is controlled, we observed transition from large amplitude limit cycle to homoclinic chaos via a sequence of periodic mixed-mode oscillations interspersed by chaotic states. Moreover, we observed two intermediate bursting regimes. Experimental evidences of homoclinic chaos are verified with PSPICE simulations.
Longitudinal stent deformation during coronary bifurcation stenting.
Vijayvergiya, Rajesh; Sharma, Prafull; Gupta, Ankush; Goyal, Praveg; Panda, Prashant
2016-03-01
A distortion of implanted coronary stent along its longitudinal axis during coronary intervention is known as longitudinal stent deformation (LSD). LSD is frequently seen with newer drug eluting stents (DES), specifically with PROMUS Element stent. It is usually caused by impact of guide catheter tip, or following passage of catheters like balloon catheter, IVUS catheter, guideliner, etc. We hereby report a case of LSD during coronary bifurcation lesion intervention, using two-stents technique. Patient had acute stent thrombosis as a complication of LSD, which was successfully managed. PMID:26811144
Bifurcation Control, Manufacturing Planning and Formation Control
Institute of Scientific and Technical Information of China (English)
Wei Kang; Mumin Song; Ning Xi
2005-01-01
The paper consists of three topics on control theory and engineering applications, namely bifurcation control, manufacturing planning, and formation control. For each topic, we summarize the control problem to be addressed and some key ideas used in our recent research. Interested readers are referred to related publications for more details. Each of the three topics in this paper is technically independent from the other ones. However, all three parts together reflect the recent research activities of the first author, jointly with other researchers in different fields.
Bifurcation analysis of a preloaded Jeffcott rotor
International Nuclear Information System (INIS)
A model of two-degrees-of-freedom Jeffcott rotor system with bearing clearance subjected of an out-of-balance excitation is considered. The influence of preloading and viscous damping of the snubber ring is introduced in the mathematical description. A programme of numerical simulations is conducted to show how the preloading and viscous damping change the dynamics of the rotor system. Bifurcation diagrams and Lyapunov exponents are constructed to explore stability. It is shown that dynamics of the rotor system can be effectively controlled by varying the preloading and the damping both of the rotor and the snubber ring. In the most considered cases preloading stabilises the dynamic responses
Bifurcation analysis of a preloaded Jeffcott rotor
Energy Technology Data Exchange (ETDEWEB)
Karpenko, Evgueni V.; Pavlovskaia, Ekaterina E.; Wiercigroch, Marian E-mail: m.wiercigroch@eng.abdn.ac.uk
2003-01-01
A model of two-degrees-of-freedom Jeffcott rotor system with bearing clearance subjected of an out-of-balance excitation is considered. The influence of preloading and viscous damping of the snubber ring is introduced in the mathematical description. A programme of numerical simulations is conducted to show how the preloading and viscous damping change the dynamics of the rotor system. Bifurcation diagrams and Lyapunov exponents are constructed to explore stability. It is shown that dynamics of the rotor system can be effectively controlled by varying the preloading and the damping both of the rotor and the snubber ring. In the most considered cases preloading stabilises the dynamic responses.
Blood tracer kinetics in the arterial tree.
Directory of Open Access Journals (Sweden)
Elias Kellner
Full Text Available Evaluation of blood supply of different organs relies on labeling blood with a suitable tracer. The tracer kinetics is linear: Tracer concentration at an observation site is a linear response to an input somewhere upstream the arterial flow. The corresponding impulse response functions are currently treated empirically without incorporating the relation to the vascular morphology of an organ. In this work we address this relation for the first time. We demonstrate that the form of the response function in the entire arterial tree is reduced to that of individual vessel segments under approximation of good blood mixing at vessel bifurcations. The resulting expression simplifies significantly when the geometric scaling of the vascular tree is taken into account. This suggests a new way to access the vascular morphology in vivo using experimentally determined response functions. However, it is an ill-posed inverse problem as demonstrated by an example using measured arterial spin labeling in large brain arteries. We further analyze transport in individual vessel segments and demonstrate that experimentally accessible tracer concentration in vessel segments depends on the measurement principle. Explicit expressions for the response functions are obtained for the major middle part of the arterial tree in which the blood flow in individual vessel segments can be treated as laminar. When applied to the analysis of regional cerebral blood flow measurements for which the necessary arterial input is evaluated in the carotid arteries, present theory predicts about 20% underestimation, which is in agreement with recent experimental data.
Blood tracer kinetics in the arterial tree.
Kellner, Elias; Gall, Peter; Günther, Matthias; Reisert, Marco; Mader, Irina; Fleysher, Roman; Kiselev, Valerij G
2014-01-01
Evaluation of blood supply of different organs relies on labeling blood with a suitable tracer. The tracer kinetics is linear: Tracer concentration at an observation site is a linear response to an input somewhere upstream the arterial flow. The corresponding impulse response functions are currently treated empirically without incorporating the relation to the vascular morphology of an organ. In this work we address this relation for the first time. We demonstrate that the form of the response function in the entire arterial tree is reduced to that of individual vessel segments under approximation of good blood mixing at vessel bifurcations. The resulting expression simplifies significantly when the geometric scaling of the vascular tree is taken into account. This suggests a new way to access the vascular morphology in vivo using experimentally determined response functions. However, it is an ill-posed inverse problem as demonstrated by an example using measured arterial spin labeling in large brain arteries. We further analyze transport in individual vessel segments and demonstrate that experimentally accessible tracer concentration in vessel segments depends on the measurement principle. Explicit expressions for the response functions are obtained for the major middle part of the arterial tree in which the blood flow in individual vessel segments can be treated as laminar. When applied to the analysis of regional cerebral blood flow measurements for which the necessary arterial input is evaluated in the carotid arteries, present theory predicts about 20% underestimation, which is in agreement with recent experimental data.
Ida, K.; Kobayashi, T.; Yoshinuma, M.; Suzuki, Y.; Narushima, Y.; Evans, T. E.; Ohdachi, S.; Tsuchiya, H.; Inagaki, S.; Itoh, K.
2016-09-01
Bifurcation physics of a magnetic island was investigated using the heat pulse propagation technique produced by the modulation of electron cyclotron heating. There are two types of bifurcation phenomena observed in a large helical device (LHD) and DIII-D. One is a bifurcation of the magnetic topology between nested and stochastic fields. The nested state is characterized by the bi-directional (inward and outward) propagation of the heat pulse with slow propagation speed. The stochastic state is characterized by the fast propagation of the heat pulse with electron temperature flattening. The other bifurcation is between the magnetic island with larger thermal diffusivity and that with smaller thermal diffusivity. The damping of toroidal flow is observed at the O-point of the magnetic island both in helical plasmas and in tokamak plasmas during a mode locking phase with strong flow shears at the boundary of the magnetic island. Associated with the stochastization of the magnetic field, the abrupt damping of toroidal flow is observed in LHD. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that this flow damping is due to the change in the non-diffusive term of momentum transport.
Bifurcation and complex dynamics of a discrete-time predator-prey system
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-06-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-I type in the closed first quadrant R+2. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. It has been found that the dynamical behavior of the model is very sensitive to the parameter values and the initial conditions. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamic behaviors, including phase portraits, period-9, 10, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology.
Directory of Open Access Journals (Sweden)
Kanchan Kulkarni
2015-01-01
Full Text Available Sudden cardiac death instigated by ventricular fibrillation (VF is the largest cause of natural death in the USA. Alternans, a beat-to-beat alternation in the action potential duration, has been implicated as being proarrhythmic. The onset of alternans is mediated via a bifurcation, which may occur through either a smooth or a border-collision mechanism. The objective of this study was to characterize the mechanism of bifurcation to alternans based on experiments in isolated whole rabbit hearts. High resolution optical mapping was performed and the electrical activity was recorded from the left ventricle (LV epicardial surface of the heart. Each heart was paced using an “alternate pacing protocol,” where the basic cycle length (BCL was alternatively perturbed by ±δ. Local onset of alternans in the heart, BCLstart, was measured in the absence of perturbations (δ=0 and was defined as the BCL at which 10% of LV exhibited alternans. The influences of perturbation size were investigated at two BCLs: one prior to BCLstart (BCLprior=BCLstart+20 ms and one preceding BCLprior (BCLfar=BCLstart+40 ms. Our results demonstrate significant spatial correlation of the region exhibiting alternans with smooth bifurcation characteristics, indicating that transition to alternans in isolated rabbit hearts occurs predominantly through smooth bifurcation.
Fast-scale border collision bifurcation in SEPIC power factor pre-regulators
Institute of Scientific and Technical Information of China (English)
Liu Fang
2008-01-01
In this paper we report a kind of fast-scale instability occurring in the single-ended primary inductance converter (SEPIC) power factor pre-regulator, which is designed to operate in discontinuous conduction mode. Main results are given by exact cycle-by-cycle computer simulations as well as theoretical analysis. It is found that the instability phenomenon manifests itself as a fast-scale bifurcation at the switching period, which implies the occurrence of border collision bifurcation, or is related to the transition of the regular operating mode of the SEPIC. According to the theoretical analysis and simulation results, the effects of parameters on system stability, and the locations of the bifurcation points are confirmed. Moreover, the effects of such an instability on power factor and switching stress are also discussed. Finally, the occurrence of the asymmetric bifurcation locations is investigated. The results show that this work provides a convenient means of predicting stability boundaries which can facilitate the selection of the practical parameters.
Damped bead on a rotating circular hoop - a bifurcation zoo
Dutta, Shovan
2012-01-01
The evergreen problem of a bead on a rotating hoop shows a multitude of bifurcations when the bead moves with friction. This motion is studied for different values of the damping coefficient and rotational speeds of the hoop. Phase portraits and trajectories corresponding to all different modes of motion of the bead are presented. They illustrate the rich dynamics associated with this simple system. For some range of values of the damping coefficient and rotational speeds of the hoop, linear stability analysis of the equilibrium points is inadequate to classify their nature. A technique involving transformation of coordinates and order of magnitude arguments is presented to examine such cases. This may provide a general framework to investigate other complex systems.
Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance
Marchesiello, Antonella
2015-01-01
We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \\times Z_2$ symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.
Voll, Juliana; Campos, Rui
2016-08-01
Thirty turtle brains (Trachemys scripta elegans) were injected with latex to systematize and describe the internal carotid arteries and their main ramifications at the brain base. The internal carotid arteries had one intercarotid anastomosis. At the level of the tuber cinereum, the internal carotid artery bifurcated into its terminal branches, the rostral and the caudal branches. The rostral branch emitted the rostral choroid artery, the orbital artery, and a series of middle cerebral arteries. After giving off the last middle cerebral artery, the rostral branch continued as the rostral cerebral artery in the cerebral longitudinal fissure, and had one anastomosis with its contralateral homologous artery, the rostral communicating artery, making the first rostral closure of the cerebral arterial circle. Next, the rostral cerebral arteries anastomosed forming a rostral interhemispheric artery, making the second rostral closure of the cerebral arterial circle. The internal carotid artery, after emitting its rostral branch, continued caudally as the caudal branch. The caudal branch ran caudally along the ventral surface of the mesencephalic tegmentum, emitted the caudal cerebral artery and the mesencephalic artery, and continued caudomedially while progressively narrowing, and anastomosed with its contralateral homologous artery, forming the basilar artery. The narrower portion also emitted the trigeminal artery. The anastomosis of the caudal branches closed the cerebral arterial circle caudally. The internal carotid arteries exclusively supplied the cerebral arterial circle of the turtle. Anat Rec, 299:1090-1098, 2016. © 2016 Wiley Periodicals, Inc.
Characteristics of Period-Adding Bursting Bifurcation Without Chaos in the Chay Neuron Model
Institute of Scientific and Technical Information of China (English)
YANG Zhuo-Qin; LU Qi-Shao
2004-01-01
@@ A period-adding bursting sequence without bursting-chaos in the Chay neuron model is studied by bifurcation analysis. The genesis of each periodic bursting is separately evoked by the corresponding periodic spiking patterns through two period-doubling bifurcations, except for the period-1 bursting occurring via Hopf bifurcation. Hence,it is concluded that this period-adding bursting bifurcation without chaos has a compound bifurcation structure closely related to period-doubling bifurcations of periodic spiking in essence.
Ven, A.C. van de; Bredie, S.J.H.; Vleuten, C.J.M. van der; Holewijn, S.; Thien, Th.
2004-01-01
BACKGROUND: The aim of the current study was to investigate whether the StethoDop can serve as a valid and reproducible instrument for measuring the ankle-brachial index (ABI) and assessing venous reflux, even when used by inexperienced investigators, in comparison with the classic Doppler. METHODS:
Inversion of hematocrit partition at microfluidic bifurcations.
Shen, Zaiyi; Coupier, Gwennou; Kaoui, Badr; Polack, Benoît; Harting, Jens; Misbah, Chaouqi; Podgorski, Thomas
2016-05-01
Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit (ϕ0) partition depends strongly on RBC deformability, as long as ϕ0<20% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough ϕ0, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.
Inversion of hematocrit partition at microfluidic bifurcations
Shen, Zaiyi; Kaoui, Badr; Polack, Benoît; Harting, Jens; Misbah, Chaouqi; Podgorski, Thomas
2016-01-01
Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit ($\\phi_0$) partition depends strongly on RBC deformability, as long as $\\phi_0 <20$% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough $\\phi_0$, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical p...
Kamiyama, Kyohei; Endo, Tetsuro; Imai, Isao; Komuro, Motomasa
2016-06-01
Double covering (DC) bifurcation of a 2-torus quasi-periodic flow in a phase-locked loop circuit was experimentally investigated using an electronic circuit and via SPICE simulation; in the circuit, the input radio-frequency signal was frequency modulated by the sum of two asynchronous sinusoidal baseband signals. We observed both DC and period-doubling bifurcations of a discrete map on two Poincaré sections, which were realized by changing the sample timing from one baseband sinusoidal signal to the other. The results confirm the DC bifurcation of the original flow.
Hopf Bifurcations of a Chemostat System with Bi-parameters
Institute of Scientific and Technical Information of China (English)
李晓月; 千美华; 杨建平; 黄启昌
2004-01-01
We study a chemostat system with two parameters, S0-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the Hopf bifurcation of the chemostat system is presented.
Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions
Institute of Scientific and Technical Information of China (English)
Ran Chao WU; Jian Hua SUN
2006-01-01
Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are existence and uniqueness of 1-homoclinic orbit and 1-periodic orbit are given. Also considered is the existence of 2-homoclinic orbit and 2-periodic orbit. In additon, the corresponding bifurcation surfaces are given.
Splitting rivers at their seams: bifurcations and avulsion
Kleinhans, M.G.; Ferguson, R.I.; Lane, S.N.; Hardy, R.J.
2012-01-01
River bifurcations are critical but poorly understood elements of many geomorphological systems. They are integral elements of alluvial fans, braided rivers, fluvial lowland plains, and deltas and control the partitioning of water and sediment through these systems. Bifurcations are commonly unstabl
Identification of Bifurcations from Observations of Noisy Biological Oscillators.
Salvi, Joshua D; Ó Maoiléidigh, Dáibhid; Hudspeth, A J
2016-08-23
Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise. Using an improved mechanical-load clamp to coerce a hair bundle to traverse different bifurcations, we find that a bundle operates within at least two functional regimes. When coupled to a high-stiffness load, a bundle functions near a supercritical Hopf bifurcation, in which case it responds best to sinusoidal stimuli such as those detected by an auditory organ. When the load stiffness is low, a bundle instead resides close to a subcritical Hopf bifurcation and achieves a graded frequency response-a continuous change in the rate, but not the amplitude, of spiking in response to changes in the offset force-a behavior that is useful in a vestibular organ. The mechanical load in vivo might therefore control a hair bundle's responsiveness for effective operation in a particular receptor organ. Our results provide direct experimental evidence for the existence of distinct bifurcations associated with a noisy biological oscillator, and demonstrate a general strategy for bifurcation analysis based on observations of any noisy system.
THE UNFOLDING OF EQUIVARIANT BIFURCATION PROBLEMS WITH PARAMETERS SYMMETRY
Institute of Scientific and Technical Information of China (English)
高守平; 李养成
2004-01-01
In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcation problem with parameter symmetry factors through another is given. The corresponding results in [1]-[6] are generalized.
Identification of Bifurcations from Observations of Noisy Biological Oscillators.
Salvi, Joshua D; Ó Maoiléidigh, Dáibhid; Hudspeth, A J
2016-08-23
Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise. Using an improved mechanical-load clamp to coerce a hair bundle to traverse different bifurcations, we find that a bundle operates within at least two functional regimes. When coupled to a high-stiffness load, a bundle functions near a supercritical Hopf bifurcation, in which case it responds best to sinusoidal stimuli such as those detected by an auditory organ. When the load stiffness is low, a bundle instead resides close to a subcritical Hopf bifurcation and achieves a graded frequency response-a continuous change in the rate, but not the amplitude, of spiking in response to changes in the offset force-a behavior that is useful in a vestibular organ. The mechanical load in vivo might therefore control a hair bundle's responsiveness for effective operation in a particular receptor organ. Our results provide direct experimental evidence for the existence of distinct bifurcations associated with a noisy biological oscillator, and demonstrate a general strategy for bifurcation analysis based on observations of any noisy system. PMID:27558723
Effects of Hard Limits on Bifurcation, Chaos and Stability
Institute of Scientific and Technical Information of China (English)
Rui-qi Wang; Ji-cai Huang
2004-01-01
An SMIB model in the power systems,especially that concering the effects of hard limits on bifurcations, chaos and stability is studied.Parameter conditions for bifurcations and chaos in the absence of hard limits are compared with those in the presence of hard limits.It has been proved that hard limits can affect system stability.We find that (1)hard limits can change unstable equilibrium into stable one;(2)hard limits can change stability of limit cycles induced by Hopf bifurcation;(3)persistence of hard limits can stabilize divergent trajectory to a stable equilibrium or limit cycle;(4)Hopf bifurcation occurs before SN bifurcation,so the system collapse can be controlled before Hopf bifurcation occurs.We also find that suitable limiting values of hard limits can enlarge the feasibility region.These results are based on theoretical analysis and numerical simulations, such as condition for SNB and Hopf bifurcation,bifurcation diagram,trajectories,Lyapunov exponent,Floquet multipliers,dimension of attractor and so on.
Sediment discharge division at two tidally influenced river bifurcations
Sassi, M.G.; Hoitink, A.J.F.; Vermeulen, B.; Hidayat, H.
2013-01-01
[1] We characterize and quantify the sediment discharge division at two tidally influenced river bifurcations in response to mean flow and secondary circulation by employing a boat-mounted acoustic Doppler current profiler (ADCP), to survey transects at bifurcating branches during a semidiurnal tida
Views on the Hopf bifurcation with respect to voltage instabilities
Energy Technology Data Exchange (ETDEWEB)
Roa-Sepulveda, C.A. [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U.G. [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering
1994-12-31
This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.
Bifurcation of the femur with tibial agenesis and additional anomalies
van der Smagt, JJ; Bos, CFA; van Haeringen, A; Hogendoorn, PCW; Breuning, MH
2005-01-01
Bifurcation of the femur and tibial agenesis are rare anomalies and have been described in both the Gollop-Wolfgang Complex and the tibial agenesis-ectrodactyly syndrome. We report on two patients with bifurcation of the femur and tibial agenesis. Hand ectrodactyly was seen in one of these patients.
Magnetic navigation system assisted stenting of coronary bifurcation lesions
C. Simsek (Cihan); M. Magro (Michael); M.S. Patterson (Mark); Y. Onuma (Yosinobu); I. Ciampichetti (Isabella); S. van Weenen (Sander); R.T. van Domburg (Ron); P.W.J.C. Serruys (Patrick); H. Boersma (Eric); R.J.M. van Geuns (Robert Jan)
2011-01-01
textabstractAims: Magnetic guidewire assisted percutaneous coronary interventions (MPCI) could have certain advantages in coronary bifurcation lesions. We aimed to report the angiographic characteristics of the bifurcation lesions, as well as the procedural and clinical outcomes of the MPCI patients
Lingual and facial arteries arising from the external carotid artery in a common trunk.
Troupis, Theodore G; Dimitroulis, Dimitrios; Paraschos, Alexandros; Michalinos, Adamantios; Protogerou, Vassilis; Vlasis, Konstantinos; Troupis, George; Skandalakis, Panayiotis
2011-02-01
The present study describes analytically a rare case in which lingual and facial arteries arise together from an external carotid artery in a common trunk. Thirty anatomic dissections were performed on 15 cadavers in the macroscopic laboratory in the Department of Anatomy of the Medical School of National and Kapodistrian University of Athens. One common trunk from which originated lingual and facial arteries was found. The frequency of this morphology is measured at 6 per cent. The length of the common trunk is measured at 7.3 mm between its origin and its diversion at the facial artery and lingual artery, its diameter at 2.8 mm, its distance from carotid bifurcation at 7.9 mm, and from the superior thyroid artery at 3.3 mm. At the left side of the neck region, facial and lingual arteries arose separately. The anatomic variations of the branching pattern of the external carotid artery and the micrometric values of the vessels are especially important as a result of the numerous operations performed in the neck region that implicate various specialties such as general surgery, head and neck surgery, plastic surgery, and maxillofacial surgery.
Streamline topologies and their bifurcations for mixed convective peristaltic flow
Directory of Open Access Journals (Sweden)
Z. Asghar
2015-09-01
Full Text Available In this work our focus is on streamlines patterns and their bifurcations for mixed convective peristaltic flow of Newtonian fluid with heat transfer. The flow is considered in a two dimensional symmetric channel and the governing equations are simplified under widely taken assumptions of large wavelength and low Reynolds number in a wave frame of reference. In order to study the streamlines patterns, a system of nonlinear autonomous differential equations are established and dynamical systems approach is used to discuss the local bifurcations and their topological changes. We have discussed all types of bifurcations and their topological changes are presented graphically. We found that the vortices contract along the vertical direction whereas they expand along horizontal direction. A global bifurcations diagram is used to summarize the bifurcations. The trapping and backward flow regions are mainly affected by increasing Grashof number and constant heat source parameter in such a way that trapping region increases whereas backward flow region shrinks.
Critical bifurcation surfaces of 3D discrete dynamics
Directory of Open Access Journals (Sweden)
Michael Sonis
2000-01-01
Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
Coronary bifurcation lesions treated with simple or complex stenting
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; de Belder, Adam J;
2016-01-01
AIMS: Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data...... from two large bifurcation coronary stenting trials with similar methodology: the Nordic Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study: old, new, and evolving strategies (BBC ONE). METHODS AND RESULTS: Both multicentre randomized trials compared simple (provisional T...... groups were similar in terms of patient and lesion characteristics. Five-year mortality was lower among patients who underwent a simple strategy rather than a complex strategy [17 patients (3.8%) vs. 31 patients (7.0%); P = 0.04]. CONCLUSION: For coronary bifurcation lesions, a provisional single...
Bifurcations of emerging patterns in the presence of additive noise.
Agez, Gonzague; Clerc, Marcel G; Louvergneaux, Eric; Rojas, René G
2013-04-01
A universal description of the effects of additive noise on super- and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape.
Comments on the Bifurcation Structure of 1D Maps
DEFF Research Database (Denmark)
Belykh, V.N.; Mosekilde, Erik
1997-01-01
The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box-within-a-box struct......The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box......-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory...
Bifurcations and Stability Boundary of a Power System
Institute of Scientific and Technical Information of China (English)
Ying-hui Gao
2004-01-01
A single-axis ux decay model including an excitation control model proposed in [12,14,16] is studied. As the bifurcation parameter P m (input power to the generator) varies, the system exhibits dynamics emerging from static and dynamic bifurcations which link with system collapse. We show that the equilibrium point of the system undergoes three bifurcations: one saddle-node bifurcation and two Hopf bifurcations. The state variables dominating system collapse are different for different critical points, and the excitative control may play an important role in delaying system from collapsing. Simulations are presented to illustrate the dynamical behavior associated with the power system stability and collapse. Moreover, by computing the local quadratic approximation of the 5-dimensional stable manifold at an order 5 saddle point, an analytical expression for the approximate stability boundary is worked out.
Bifurcation of transition paths induced by coupled bistable systems
Tian, Chengzhe; Mitarai, Namiko
2016-06-01
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.
Malvè, M; Gharib, A M; Yazdani, S K; Finet, G; Martínez, M A; Pettigrew, R; Ohayon, J
2015-01-01
The purpose of the present study was to determine whether in vivo bifurcation geometric factors would permit prediction of the risk of atherosclerosis. It is worldwide accepted that low or oscillatory wall shear stress (WSS) is a robust hemodynamic factor in the development of atherosclerotic plaque and has a strong correlation with the local site of plaque deposition. However, it still remains unclear how coronary bifurcation geometries are correlated with such hemodynamic forces. Computational fluid dynamics simulations were performed on left main (LM) coronary bifurcation geometries derived from CT of eight patients without significant atherosclerosis. WSS amplitudes were accurately quantified at two high risk zones of atherosclerosis, namely at proximal left anterior descending artery (LAD) and at proximal left circumflex artery (LCx), and also at three high WSS concentration sites near the bifurcation. Statistical analysis was used to highlight relationships between WSS amplitudes calculated at these five zones of interest and various geometric factors. The tortuosity index of the LM-LAD segment appears to be an emergent geometric factor in determining the low WSS amplitude at proximal LAD. Strong correlations were found between the high WSS amplitudes calculated at the endothelial regions close to the flow divider. This study not only demonstrated that CT imaging studies of local risk factor for atherosclerosis could be clinically performed, but also showed that tortuosity of LM-LAD coronary branch could be used as a surrogate marker for the onset of atherosclerosis. PMID:24986333
Energy Technology Data Exchange (ETDEWEB)
Uchino, A.; Sawada, A.; Takase, Y.; Kudo, S. [Department of Radiology, Saga Medical School, 5-1-1, Nabeshima, Saga, 849-8501 (Japan); Koizumi, T. [Department of Neurosurgery, Saga Medical School, 5-1-1, Nabeshima, Saga, 849-8501 (Japan)
2002-07-01
The authors present a case of moyamoya disease associated with a persistent trigeminal artery from which the anterior inferior cerebellar artery arose. We reviewed previously reported cases of moyamoya disease associated with persistent carotid-basilar arterial anastomosis and investigated the embryology of this rare arterial variation. (orig.)
Winant, Celeste D.; Aparici, Carina Mari; Zelnik, Yuval R.; Reutter, Bryan W.; Sitek, Arkadiusz; Bacharach, Stephen L.; Gullberg, Grant T.
2012-01-01
Computer simulations, a phantom study and a human study were performed to determine whether a slowly rotating single-photon computed emission tomography (SPECT) system could provide accurate arterial input functions for quantification of myocardial perfusion imaging using kinetic models. The errors induced by data inconsistency associated with imaging with slow camera rotation during tracer injection were evaluated with an approach called SPECT/P (dynamic SPECT from positron emission tomography (PET)) and SPECT/D (dynamic SPECT from database of SPECT phantom projections). SPECT/P simulated SPECT-like dynamic projections using reprojections of reconstructed dynamic 94Tc-methoxyisobutylisonitrile (94Tc-MIBI) PET images acquired in three human subjects (1 min infusion). This approach was used to evaluate the accuracy of estimating myocardial wash-in rate parameters K1 for rotation speeds providing 180° of projection data every 27 or 54 s. Blood input and myocardium tissue time-activity curves (TACs) were estimated using spatiotemporal splines. These were fit to a one-compartment perfusion model to obtain wash-in rate parameters K1. For the second method (SPECT/D), an anthropomorphic cardiac torso phantom was used to create real SPECT dynamic projection data of a tracer distribution derived from 94Tc-MIBI PET scans in the blood pool, myocardium, liver and background. This method introduced attenuation, collimation and scatter into the modeling of dynamic SPECT projections. Both approaches were used to evaluate the accuracy of estimating myocardial wash-in parameters for rotation speeds providing 180° of projection data every 27 and 54 s. Dynamic cardiac SPECT was also performed in a human subject at rest using a hybrid SPECT/CT scanner. Dynamic measurements of 99mTc-tetrofosmin in the myocardium were obtained using an infusion time of 2 min. Blood input, myocardium tissue and liver TACs were estimated using the same spatiotemporal splines. The spatiotemporal maximum
International Nuclear Information System (INIS)
This paper deals with periodic solutions of the Hamilton equation x-dot (t)=J∇x H(x(t),λ), where H element of C2,0(R2n×Rk,R) and λ element of Rk is a parameter. Theorems on global bifurcation of solutions with periods (2π)/j, j element of N, from a stationary point (x0,λ0) element of R2n×Rk are proved. ∇x2 H(x0,λ0) can be singular. However, it is assumed that the local topological degree of ∇xH(·, λ0) at x0 is nonzero. For systems satisfying ∇xH(x0, λ) = 0 for all λ element of Rk it is shown that (global) bifurcation points of solutions with periods (2π)/j can be identified with zeros of appropriate continuous functions Fj:Rk→R. If, for all λ element of Rk, ∇x2H(x0,λ)=diag(A(λ),B(λ)), where A(λ) and B(λ) are (n × n)-matrices, then Fj can be defined by Fj(λ) = det[A(λ)B(λ) − j2I]. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis (Radzki 2005 Branching points of periodic solutions of autonomous Hamiltonian systems (Polish) PhD Thesis Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toruń)
Ecological consequences of global bifurcations in some food chain models.
van Voorn, George A K; Kooi, Bob W; Boer, Martin P
2010-08-01
Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models.
Ecological consequences of global bifurcations in some food chain models.
van Voorn, George A K; Kooi, Bob W; Boer, Martin P
2010-08-01
Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models. PMID:20447411
Directory of Open Access Journals (Sweden)
Kim Taehong
2007-03-01
Full Text Available Abstract Background This paper presents calculations of the temperature distribution in an atherosclerotic plaque experiencing an inflammatory process; it analyzes the presence of hot spots in the plaque region and their relationship to blood flow, arterial geometry, and inflammatory cell distribution. Determination of the plaque temperature has become an important topic because plaques showing a temperature inhomogeneity have a higher likelihood of rupture. As a result, monitoring plaque temperature and knowing the factors affecting it can help in the prevention of sudden rupture. Methods The transient temperature profile in inflamed atherosclerotic plaques is calculated by solving an energy equation and the Navier-Stokes equations in 2D idealized arterial models of a bending artery and an arterial bifurcation. For obtaining the numerical solution, the commercial package COMSOL 3.2 was used. The calculations correspond to a parametric study where arterial type and size, as well as plaque geometry and composition, are varied. These calculations are used to analyze the contribution of different factors affecting arterial wall temperature measurements. The main factors considered are the metabolic heat production of inflammatory cells, atherosclerotic plaque length lp, inflammatory cell layer length lmp, and inflammatory cell layer thickness dmp. Results The calculations indicate that the best location to perform the temperature measurement is at the back region of the plaque (0.5 ≤ l/lp ≤ 0.7. The location of the maximum temperature, or hot spot, at the plaque surface can move during the cardiac cycle depending on the arterial geometry and is a direct result of the blood flow pattern. For the bending artery, the hot spot moves 0.6 millimeters along the longitudinal direction; for the arterial bifurcation, the hot spot is concentrated at a single location due to the flow recirculation observed at both ends of the plaque. Focusing on the
Sharifulin, Albert N
2007-01-01
The analysis of vibration effect on non-isothermal fluid in closed cavity is important for planning technological experiments in space. Control and optimization of these processes critically depend on the understanding of liquid response to the vibrations. With this aim the theoretical investigation for infinite plane and cylindrical fluid layers are performed. We investigated simple case of the fluid response-thermal vibrational convection in a cylindrical fluid layer with rigid conducting boundaries. It is found that steady modes of thermal vibrational convection are subjected to various bifurcations. Bifurcations cause sharp changes in heat transfer. The Lorenz model is generalized (GLM) and used to conduct the analysis of bifurcations caused by the changing of the cavity shape and vibrational Rayleigh number. The shape of steady-state surface in 3D space of the streamfunction of mean flow, vibrational Rayleigh number and the cavity curvature is found. The numerical 2D solution is performed for plane and c...
Shell structure and orbit bifurcations in finite fermion systems
Energy Technology Data Exchange (ETDEWEB)
Magner, A. G., E-mail: magner@kinr.kiev.ua; Yatsyshyn, I. S. [National Academy of Sciences of Ukraine, Institute for Nuclear Research (Ukraine); Arita, K. [Nagoya Institute of Technology, Department of Physics (Japan); Brack, M. [University of Regensburg, Institute for Theoretical Physics (Germany)
2011-10-15
We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the 'periodic orbit theory'. We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called 'superdeformed' energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).
Complex Dynamics and Chaos Control in Coronary Artery System%冠状动脉系统的复杂动态与混沌控制
Institute of Scientific and Technical Information of China (English)
石艳香; 刘桂荣; 白定勇
2011-01-01
研究两类冠状动脉系统:N型与S型.利用Melnikov方法,得到两类系统在参数条件下产生Smale马蹄意义上的混沌的阀值.通过数值模拟,不仅可以证明理论分析的正确性,同时显示出理想的分支图形和更多新的复杂动力学行为.数值模拟包括相图、势能图、同宿分支曲线和分支图,通过这些较直观地反映出系统随周期激励外力强弱变化的动态特性、复杂性和非线性特征,揭示了系统的分支形式以及通向混沌运动的道路.最后对系统的混沌运动状态进行了有效的控制.%N-type and S-type, two types of coronary artery system are investigated. Applying Melnikov method,the threshold conditions for the occurrence of Smale horse chaos of the two types are obtained respectively. By numerical simulation,not only the correctness of theoretical analysis is proven but also the ideal graphics and more new bifurcation of the complex dynamic behavior are shown. Numerical simulations.including phase diagram, potential diagrams, homoclinic bifurcation curve diagrams and bifurcation diagrams,are used to investigate the dynamic characteristics,the complexity and the nonlinear dynamics characteristic of the two systems,and to reveal bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of motion are effectively controlled.
Climate bifurcation during the last deglaciation?
Directory of Open Access Journals (Sweden)
T. M. Lenton
2012-07-01
Full Text Available There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer
Microsurgical anatomy of the middle cerebral artery
Directory of Open Access Journals (Sweden)
Pai S
2005-01-01
Full Text Available Background: The microsurgical anatomy of the middle cerebral artery (MCA is of particular interest to the cerebrovascular surgeon. The purpose of this study was to define the microsurgical anatomy of the MCA and its various branches in the Indian population. Methods: Ten MCAs were studied from five cadaveric brain specimens. The authors studied the outer diameter, length, branches, perforators and site of these on the main trunk (M1, the division of the main trunk, the secondary trunks and their various cortical branches using the operating microscope under 5-20x magnification. Results: The outer diameter of the MCA main trunk ranges from 2.5 to 4 mm with a mean of 3.35 mm. The superolateral branches consisted of polar temporal artery and anterior temporal artery that had a common origin and sometimes the uncal artery or the accessory uncal artery. Perforators or lenticulostriate arteries were seen in the inferomedial surface all along the length of M1. Eight bifurcations and two trifurcations were noted. Cortical branches and their origin are discussed. Conclusion: Although the microsurgical anatomy of the MCA in Indian population correlated with the findings in the western literature, some structural and statistical variations were noted.
Kralev, Stefan; Haag, Benjamin; Spannenberger, Jens; Lang, Siegfried; Brockmann, Marc A.; Bartling, Soenke; Marx, Alexander; Haase, Karl-Konstantin; Borggrefe, Martin; Süselbeck, Tim
2011-01-01
Background Treatment of coronary bifurcation lesions remains challenging, beyond the introduction of drug eluting stents. Dedicated stent systems are available to improve the technical approach to the treatment of these lesions. However dedicated stent systems have so far not reduced the incidence of stent restenosis. The aim of this study was to assess the expansion of the Multi-Link (ML) Frontier™ stent in human and porcine coronary arteries to provide the cardiologist with useful in-vitro ...
Bifurcated SEN with Fluid Flow Conditioners
Directory of Open Access Journals (Sweden)
F. Rivera-Perez
2014-01-01
Full Text Available This work evaluates the performance of a novel design for a bifurcated submerged entry nozzle (SEN used for the continuous casting of steel slabs. The proposed design incorporates fluid flow conditioners attached on SEN external wall. The fluid flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through numerical simulations using the CFD technique. Numerical results were validated by means of physical simulations conducted on a scaled cold water model. Numerical and physical simulations confirmed that the performance of the proposed SEN is superior to a traditional one. Fluid flow conditioners reduce the liquid free surface fluctuations and minimize the occurrence of vortexes at the free surface.
Chua Corsage Memristor Oscillator via Hopf Bifurcation
Mannan, Zubaer Ibna; Choi, Hyuncheol; Kim, Hyongsuk
This paper demonstrates that the Chua Corsage Memristor, when connected in series with an inductor and a battery, oscillates about a locally-active operating point located on the memristor’s DC V-I curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance Y (s,V ) is derived from the small-signal equivalent circuit and the value of inductance is determined at a frequency where the real part of the admittance ReY (iω) of the small-signal equivalent circuit of Chua Corsage Memristor is zero. Oscillation of the circuit is analyzed via an in-depth application of the theory of Local Activity, Edge of Chaos and the Hopf-bifurcation.
Seo, Jae-Bin; Park, Kyung Woo; Lee, Hae-Young; Kang, Hyun-Jae; Koo, Bon-Kwon; Kim, Sang-Hyun; Kim, Hyo-Soo
2015-01-01
Although the favored strategy for coronary bifurcation intervention is stenting main vessel with provisional side branch (SB) stenting, we occasionally use two-stent strategy. The objective of this study was to investigate the angiographic outcome of SB ostium in two-stent group, compared with one-stent group. We analyzed 199 patients with bifurcation lesion who underwent percutaneous coronary intervention (PCI) with drug-eluting stent and follow up angiography. The patients were divided into...
Energy Technology Data Exchange (ETDEWEB)
Labine, Alexandre; Carrier, Jean-François; Bedwani, Stéphane [Centre hospitalier de l' Université de Montréal (Canada); Chav, Ramnada; De Guise, Jacques [Laboratoire de recherche en imagerie et d' orthopédie-CRCHUM, École de technologie supérieure (Canada)
2014-08-15
Purpose: To investigate an automatic bronchial and vessel bifurcations detection algorithm for deformable image registration (DIR) assessment to improve lung cancer radiation treatment. Methods: 4DCT datasets were acquired and exported to Varian treatment planning system (TPS) EclipseTM for contouring. The lungs TPS contour was used as the prior shape for a segmentation algorithm based on hierarchical surface deformation that identifies the deformed lungs volumes of the 10 breathing phases. Hounsfield unit (HU) threshold filter was applied within the segmented lung volumes to identify blood vessels and airways. Segmented blood vessels and airways were skeletonised using a hierarchical curve-skeleton algorithm based on a generalized potential field approach. A graph representation of the computed skeleton was generated to assign one of three labels to each node: the termination node, the continuation node or the branching node. Results: 320 ± 51 bifurcations were detected in the right lung of a patient for the 10 breathing phases. The bifurcations were visually analyzed. 92 ± 10 bifurcations were found in the upper half of the lung and 228 ± 45 bifurcations were found in the lower half of the lung. Discrepancies between ten vessel trees were mainly ascribed to large deformation and in regions where the HU varies. Conclusions: We established an automatic method for DIR assessment using the morphological information of the patient anatomy. This approach allows a description of the lung's internal structure movement, which is needed to validate the DIR deformation fields for accurate 4D cancer treatment planning.
Non-smooth Hopf-type bifurcations arising from impact-friction contact events in rotating machinery.
Mora, Karin; Budd, Chris; Glendinning, Paul; Keogh, Patrick
2014-11-01
We analyse the novel dynamics arising in a nonlinear rotor dynamic system by investigating the discontinuity-induced bifurcations corresponding to collisions with the rotor housing (touchdown bearing surface interactions). The simplified Föppl/Jeffcott rotor with clearance and mass unbalance is modelled by a two degree of freedom impact-friction oscillator, as appropriate for a rigid rotor levitated by magnetic bearings. Two types of motion observed in experiments are of interest in this paper: no contact and repeated instantaneous contact. We study how these are affected by damping and stiffness present in the system using analytical and numerical piecewise-smooth dynamical systems methods. By studying the impact map, we show that these types of motion arise at a novel non-smooth Hopf-type bifurcation from a boundary equilibrium bifurcation point for certain parameter values. A local analysis of this bifurcation point allows us a complete understanding of this behaviour in a general setting. The analysis identifies criteria for the existence of such smooth and non-smooth bifurcations, which is an essential step towards achieving reliable and robust controllers that can take compensating action.
Directory of Open Access Journals (Sweden)
Tanuja Agrawal
2014-03-01
Full Text Available In this paper, a two species host-parasitoid model system is considered. The global dynamic behavior of the model is investigated through (local stability results for its equilibriums and large time computer simulations. Many forms of complex dynamics such as chaos, periodic windows etc. are observed. The Hopf point and attractor crises exist for different set of parameter values. Keywords: Predator-Prey; Bifurcation; Chaos; Stability.
Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip
Institute of Scientific and Technical Information of China (English)
Shuliang SHUI; Deming ZHU
2006-01-01
Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.
CODIMENSION 3 BIFURCATIONS OF HOMOCLINIC ORBITS WITH ORBIT FLIPS AND INCLINATION FLIPS
Institute of Scientific and Technical Information of China (English)
SHUI SHULIANG; ZHU DEMING
2004-01-01
The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained.
Experimental bifurcation analysis—Continuation for noise-contaminated zero problems
DEFF Research Database (Denmark)
Schilder, Frank; Bureau, Emil; Santos, Ilmar Ferreira;
2015-01-01
Noise contaminated zero problems involve functions that cannot be evaluated directly, but only indirectly via observations. In addition, such observations are affected by a non-deterministic observation error (noise). We investigate the application of numerical bifurcation analysis for studying t......, we demonstrate and test our algorithms on a mechanical nonlinear oscillator experiment using control based continuation, which we used as a main application and test case for development of the Coco compatible Matlab toolbox Continex that implements our algorithms....
Emergency stenting to control massive bleeding of injured iliac artery following lumbar disk surgery
Energy Technology Data Exchange (ETDEWEB)
Bierdrager, Edwin; Rooij, Willem Jan van; Sluzewski, Menno [Department of Radiology, St. Elisabeth Ziekenhuis, Tilburg (Netherlands)
2004-05-01
The purpose of this study was to demonstrate the use of endovascular stenting to repair an iliac artery injury following lumbar discectomy, thus obviating the need for major surgery. A 57-year-old woman developed a distended abdomen and signs of hypovolemic shock immediately following discectomy at the L4-L5 level. Ultrasound showed a large amount of abdominal fluid. Angiography revealed a laceration of the right iliac artery bifurcation with extravasation of contrast material. After occlusion of the internal iliac artery with fibered coils to prevent retrograde flow to the iliac bifurcation, a self-expanding covered stent was inserted to seal the iliac laceration. The leakage of blood stopped immediately. The clinical condition of the patient gradually improved and she was discharged home 5 weeks later. Sealing of arterial laceration as a complication of lumbar disc surgery with a covered stent is a simple and effective alternative to major pelvic surgery. (orig.)
The Persistence of a Slow Manifold with Bifurcation
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P.; Robert, M.
2012-01-01
his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated...... by tethered satellites. It is shown that an almost full measure subset of a neighborhood of the slow manifold's normally elliptic branches persists in an adiabatic sense. We prove this using averaging and a blow-up near the bifurcation....
Bifurcation of learning and structure formation in neuronal maps
DEFF Research Database (Denmark)
Marschler, Christian; Faust-Ellsässer, Carmen; Starke, Jens;
2014-01-01
to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable...... states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance....
Bifurcation diagrams in relation to synchronization in chaotic systems
Indian Academy of Sciences (India)
Debabrata Dutta; Sagar Chakraborty
2010-06-01
We numerically study some of the three-dimensional dynamical systems which exhibit complete synchronization as well as generalized synchronization to show that these systems can be conveniently partitioned into equivalent classes facilitating the study of bifurcation diagrams within each class. We demonstrate how bifurcation diagrams may be helpful in predicting the nature of the driven system by knowing the bifurcation diagram of driving system and vice versa. The study is extended to include the possible generalized synchronization between elements of two different equivalent classes by taking the Rössler-driven-Lorenz-system as an example.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
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Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
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L. Borkowski
2015-01-01
Full Text Available The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.
Arctic melt ponds and bifurcations in the climate system
Sudakov, Ivan; Golden, Kenneth M
2014-01-01
Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo $-$ a key parameter in climate modeling. Here we explore the possibility of a simple sea ice climate model passing through a bifurcation point $-$ an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a nonlinear phase transition model for melt ponds, and bifurcation analysis of a simple climate model with ice - albedo feedback as the key mechanism driving the system to a potential bifurcation point.
Statistical multimoment bifurcations in random-delay coupled swarms
Mier-y-Teran-Romero, Luis; Lindley, Brandon; Schwartz, Ira B.
2012-11-01
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.
Bifurcations of a parametrically excited oscillator with strong nonlinearity
Institute of Scientific and Technical Information of China (English)
唐驾时; 符文彬; 李克安
2002-01-01
A parametrically excited oscillator with strong nonlinearity, including van der Poi and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt-Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.
Seasonal variability of the bifurcation of the North Equatorial Current
Institute of Scientific and Technical Information of China (English)
JU Qiang-chang; JIANG Song; TIAN Ji-wei; KONG Ling-hai; NI Guo-xi
2013-01-01
Seasonal variability of the bifurcation of the North Equatorial Current (NEC) is studied by constructing the analytic solution for the time-dependent horizontal linear shallow water quasi-geostrophic equations.Using the Florida State University wind data from 1961 through 1992,we find that the bifurcation latitude of the NEC changes with seasons.Furthermore,it is shown that the NEC bifurcation is at its southernmost latitude (12.7°N) in June and the northernmost latitude (14.4° N) in November.
Bifurcation control of nonlinear oscillator in primary and secondary resonance
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A weakly nonlinear oscillator was modeled by a sort of differential equation, a saddle-node bifurcation was found in case of primary and secondary resonance. To control the jumping phenomena and the unstable region of the nonlinear oscillator, feedback controllers were designed. Bifurcation control equations were obtained by using the multiple scales method. And through the numerical analysis, good controller could be obtained by changing the feedback control gain. Then a feasible way of further research of saddle-node bifurcation was provided. Finally, an example shows that the feedback control method applied to the hanging bridge system of gas turbine is doable.
Song, Yongli; Xu, Jian; Zhang, Tonghua
2011-06-01
In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the damping terms. Hopf bifurcations and amplitude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.
一氧化碳偶联反应器分岔行为%The Bifurcation Behavior of CO Coupling Reactor
Institute of Scientific and Technical Information of China (English)
徐艳; 马新宾; 许根慧
2005-01-01
The bifurcation behavior of the CO coupling reactor was examined based on the one-dimensional pseudohomogeneous axial dispersion dynamic model. The method of finite difference was used for solving the boundary value problem; the continuation technique and the direct method were applied to determine the bifurcation diagram.The effects of dimensionless adiabatic temperature rise, Damkohler number, activation energy, heat transfer coefficient and feed ratio on the bifurcation behavior were investigated. It was shown that there existed static bifurcation and the oscillations did not occur in the reactor. The result Mso revealed that the reactor exhibited at most 1-3-1 multiplilicity patterns within the range of practical possible parameters and the measures, such as weakening the axial dispersion of reactor, enhancing heat transfer, decreasing the concentration of ethyl nitrite, were efficient for avoiding the possible risk of multiple steady states.
Dynamical Analysis of Nonlinear Bifurcation in Current-Controlled Boost Converter
Institute of Scientific and Technical Information of China (English)
Quan-Min Niu; Bo Zhang; Yan-Ling Li
2007-01-01
Based on the bifurcation theory in nonlinear dynamics, this paper analyzes quantitatively period solution dynamic characteristic. In particular, the ones of period1 and period2 solutions are deeply studied. From locus of Jacobian matrix eigenvalue, we conclude that the bifurcations between period1 and period2 solutions are pitchfork bifurcations while the bifurcations between period2 and period3 solutions are border collision bifurcations. The double period bifurcation condition is verified from complex plane locus of eigenvalues,furthermore, the necessary condition occurred pitchfork bifurcation is obtained from the cause of border collisionbifurcation.
Institute of Scientific and Technical Information of China (English)
成万钧; 周玉杰; 赵迎新; 聂斌; 郭永和; 王志坚; 王建龙
2010-01-01
目的 对比分析TAP技术与必要性支架术在处理边支大于2.0 mm冠状动脉分叉病变的临床效果.方法 将患者随机分为必要性支架组和TAP组.入选病例的冠状动脉造影均证实为MEDINA(1,1,1)型分叉病变,主支血管参考直径≥2.5 mm,边支血管参考直径≥2.0 mm.主要研究终点:术后12个月主要不良心血管事件的发生率和支架血栓发生率.次要终点包括:术后8个月冠状动脉造影随访再狭窄率、手术操作时间、曝光时间、对比剂用量、手术操作成功率、手术相关心肌梗死.结果 TAP组均完成最终对吻球囊扩张.12个月随访结果显示,TAP组主要不良心血管事件和必要性支架组差异无统计学意义(13.0%比12.1%,P＞0.05).两组均发生1例支架血栓事件.TAP组与必要性支架组术后24 h操作相关心肌梗死发生率差异无统计学意义(8.7%比5.2%,P＞0.05).两组在手术时间、X线曝光时间、对比剂用量差异无统计学意义.8个月冠状动脉造影结果显示,必要性支架组边支开口再狭窄明显高于TAP组(17.1%比3.8%,P＜0.05),总体再狭窄率两组差异无统计学意义.结论 TAP技术在处理大分支冠状动脉分叉病变的有效性及长期安全性方面不亚于必要性支架术.%Objective To explore the feasibility and safety of T stenting and small protrusion(TAP)technique and compare the efficacy with simple stenting in patients with coronary bifurcation lesions and with big size side branch.Methods A total of 142 eligible patients were recruited and 127 patients completed the study(simple stenting group 58 and TAP technique group 69).Results Major adverse cardiovascular event rate was similar at 12 months follow up between the groups(TAP technique group 13.0%versus simple stenting group 12.1%,P＞0.05).The late of procedural-related myocardial infarction,procedure and fluoroscopy time,contrast volumes were also similar between 2 groups(all P＞0.05).At 8 months
Granillo, Gastón A Rodriguez; van Dijk, Lukas C; McFadden, Eugène P; Serruys, Patrick W
2005-01-01
Techniques used in the coronary circulation may be useful in peripheral intervention. We report a case of bilateral renal artery stenosis treated via a radial approach by direct stenting with distal protection at a right ostial lesion and modified crush stenting at a left renal bifurcation lesion using paclitaxel-eluting stents.
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-10-01
We study a stochastic dynamics of systems with hard excitement of auto-oscillations possessing a bistability mode with coexistence of the stable equilibrium and limit cycle. A principal difference in the results of the impact of additive and parametric random disturbances is shown. For the stochastic van der Pol oscillator with increasing parametric noise, qualitative transformations of the probability density function form "crater"-"peak+crater"-"peak" are demonstrated by numerical simulation. An analytical investigation of such P bifurcations is carried out for the stochastic Hopf-like model with hard excitement of self-oscillations. A detailed parametric description of the response of this model on the additive and multiplicative noise and corresponding stochastic bifurcations are presented and discussed.
Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System
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Chuanjun Dai
2013-01-01
Full Text Available We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.
Numerical modeling of Po-218 deposition in a physiologically realistic lung bifurcation model
Mously-Soroujy, Khalid Ahmad
Experimental data for lung bifurcations reveals complex geometries and distinct asymmetrical characteristic, which affects the localized distribution of particles deposited in the lung. This study is based on recently published numerical results for a symmetric physiological realistic bifurcation geometry Heistracher and Hofmann (1995) which has been extended here to the case of a asymmetric geometry. The asymmetric PRB model was used to study the flow field and the deposition of ultrafine particles for inspiratory and expiratory conditions. In the present study, we investigated the effect of different flow rates, representing human activity and deposition of different ultrafine particles representing radon daughter (Po-218), in the PRB model. Numerical results were compared with the limited available experimental and numerical data. The fluid dynamic computer program FIDAP was used for this purpose.