Impedance matching at arterial bifurcations.
Brown, N
1993-01-01
Reflections of pulse waves will occur in arterial bifurcations unless the impedance is matched continuously through changing geometric and elastic properties. A theoretical model is presented which minimizes pulse wave reflection through bifurcations. The model accounts for the observed linear changes in area within the bifurcation, generalizes the theory to asymmetrical bifurcations, characterizes changes in elastic properties from parent to daughter arteries, and assesses the effect of branch angle on the mechanical properties of daughter vessels. In contradistinction to previous models, reflections cannot be minimized without changes in elastic properties through bifurcations. The theoretical model predicts that in bifurcations with area ratios (beta) less than 1.0 Young's moduli of daughter vessels may be less than that in the parent vessel if the Womersley parameter alpha in the parent vessel is less than 5. Larger area ratios in bifurcations are accompanied by greater increases in Young's moduli of branches. For an idealized symmetric aortic bifurcation (alpha = 10) with branching angles theta = 30 degrees (opening angle 60 degrees) Young's modulus of common iliac arteries relative to that of the distal abdominal aorta has an increase of 1.05, 1.68 and 2.25 for area ratio of 0.8, 1.0 and 1.15, respectively. These predictions are consistent with the observed increases in Young's moduli of peripheral vessels.(ABSTRACT TRUNCATED AT 250 WORDS)
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
Anastasiou, A D; Spyrogianni, A S; Koskinas, K C; Giannoglou, G D; Paras, S V
2012-03-01
The scope of this work is to study the pulsatile flow of a blood mimicking fluid in a micro channel that simulates a bifurcated small artery, in which the Fahraeus-Lindqvist effect is insignificant. An aqueous glycerol solution with small amounts of xanthan gum was used for simulating viscoelastic properties of blood and in vivo flow conditions were reproduced. Local flow velocities were measured using micro Particle Image Velocimetry (μ-PIV). From the measured velocity distributions, the wall shear stress (WSS) and its variation during a pulse were estimated. The Reynolds numbers employed are relatively low, i.e. similar to those prevailing during blood flow in small arteries. Experiments both with a Newtonian and a non-Newtonian fluid (having asymptotic viscosity equal to the viscosity of the Newtonian one) proved that the common assumption that blood behaves as a Newtonian fluid is not valid for blood flow in small arteries. It was also shown that the outer wall of the bifurcation, which is exposed to a lower WSS, is more predisposed to atherosclerotic plaque formation. Moreover, this region in small vessels is shorter than the one in large arteries, as the developed secondary flow decays faster. Finally, the WSS values in small arteries were found to be lower than those in large ones.
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.
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....... 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....
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....
Dissection of a non-bifurcating cervical carotid artery.
Nas, Omer Fatih; Karakullukcuoglu, Zeynel; Hakyemez, Bahattin; Erdogan, Cuneyt
2016-06-01
A non-bifurcating cervical carotid artery is a rare anomaly in the population. Radiologic diagnosis of pathologies seen together with this anomaly can be challenging. Despite not being diagnostic all the time, digital subtraction angiography is accepted as the gold standard method for the diagnosis of dissection. We present a case of a non-bifurcating cervical carotid artery and concomitant dissection, which presented to the hospital with trauma and ischemic findings.
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.
Directory of Open Access Journals (Sweden)
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.
Wall Shear Stress Distribution in Patient Specific Coronary Artery Bifurcation
Directory of Open Access Journals (Sweden)
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.
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.
Joseph, George; Hooda, Amit; Thomson, Viji Samuel
2015-01-01
A 69-year-old man, who had earlier undergone reconstruction of the aortic bifurcation with kissing nitinol stents, presented with occlusion of the left external iliac artery. The occlusion was successfully and safely recanalized using contralateral femoral approach with passage of interventional hardware through the struts of the stents in the aortic bifurcation. Presence of contemporary flexible nitinol stents with open-cell design in the aortic bifurcation is not a contraindication to the use of the contralateral femoral approach.
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.
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Blagojević Milan
2014-01-01
Full Text Available Background/Aim. Practical difficulties, particularly long model development time, have limited the types and applicability of computational fluid dynamics simulations in numerical modeling of blood flow in serial manner. In these simulations, the most revealing flow parameters are the endothelial shear stress distribution and oscillatory shear index. The aim of this study was analyze their role in the diagnosis of the occurrence and prognosis of plaque development in coronary artery bifurcations. Methods. We developed a novel modeling technique for rapid cardiovascular hemodynamic simulations taking into account interactions between fluid domain (blood and solid domain (artery wall. Two numerical models that represent the observed subdomains of an arbitrary patient-specific coronary artery bifurcation were created using multi-slice computed tomography (MSCT coronagraphy and ultrasound measurements of blood velocity. Coronary flow using an in-house finite element solver PAK-FS was solved. Results. Overall behavior of coronary artery bifurcation during one cardiac cycle is described by: velocity, pressure, endothelial shear stress, oscillatory shear index, stress in arterial wall and nodal displacements. The places where (a endothelial shear stress is less than 1.5, and (b oscillatory shear index is very small (close or equal to 0 are prone to plaque genesis. Conclusion. Finite element simulation of fluid-structure interaction was used to investigate patient-specific flow dynamics and wall mechanics at coronary artery bifurcations. Simulation model revealed that lateral walls of the main branch and lateral walls distal to the carina are exposed to low endothelial shear stress which is a predilection site for development of atherosclerosis. This conclusion is confirmed by the low values of oscillatory shear index in those places.
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.
Institute of Scientific and Technical Information of China (English)
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.
Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation
Fan, Yubo; Jiang, Wentao; Zou, Yuanwen; Li, Jinchuan; Chen, Junkai; Deng, Xiaoyan
2009-04-01
Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had very similar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.
Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation
Institute of Scientific and Technical Information of China (English)
Yubo Fan; Wentao Jiang; Yuanwen Zou; Jinchuan Li; Junkai Chen; Xiaoyan Deng
2009-01-01
Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact,however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them,the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had very similar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.
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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)
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.
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.
The Blood Flow at Arterial Bifurcations Simulated by the Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
JI Yu-Pin; KANG Xiu-Ying; LIU Da-He
2009-01-01
The Programmed model of non-Newtonian blood flow (the Casson model) at arterial bifurcations is established by the lattice Boltzmann method. The blood flow field under different Reynolds numbers is simulated, and distri-bution of dynamic factors such as flow velocity, shear stress, pressure and shear rate are presented. The existence of the fluid separation zone is analyzed. This provides a basis for further studies of the relationship between hemodynamic factors and pathogenesis, as well as a reference for a better understanding of the pathological changes and location of sediments, and the plague factor in arteries.
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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
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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
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.
Hikichi, Yutaka; Umezu, Mitsuo; Node, Koichi; Iwasaki, Kiyotaka
2017-01-01
Stent struts protruding into ostial side branch called "jailed strut" at bifurcation lesions is a likely cause of thrombus formation. We aimed to investigate the influences of multiple kissing balloon inflation (KBI) for stent expansion, and stent platform design, respectively, on the reduction of incomplete stent apposition area (ISA area) caused by jailed struts at a side-branch ostium, using a three-dimensional elastic left main (LM) bifurcated coronary artery model. The referenced LM bifurcation angle data of 209 patients were stratified by tertiles focusing on the angle between the LM trunk (LMT) and left anterior descending artery (LAD). A bifurcation model was fabricated with angles of 129°, 122.2°, and 76.4° for LMT-LAD, LMT-left circumflex (LCx), and LAD-LCx, respectively, and with diameters of 5, 3.75, and 3.5 mm for LMT, LAD, and LCx, respectively; these diameters fulfill Murray's law. A 75 % stenosis was included along the LMT. One-time and three-time KBIs were conducted using two-link Nobori and three-link Xience Xpedition (n = 6 each). The ISA area was quantified using micro-CT. Three-time KBI was effective in reducing the ISA area compared with one-time KBI for both the Nobori (p = 0.05) and Xience Xpedition (p = 0.07). The ISA area was smaller in the Nobori than in the Xience Xpedition, both in one-time and three-time KBI (one-time KBI: p = 0.003; three-time KBI: p = 0.001). Our findings of this study on reducing the ISA area by focusing on an interventional technique and stent design may help to improve coronary bifurcation intervention for a possibly better long-term clinical outcome.
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.
Kefayati, Sarah; Poepping, Tamie L
2010-01-01
The carotid artery bifurcation is a common site of atherosclerosis which is a major leading cause of ischemic stroke. The impact of stenosis in the atherosclerotic carotid artery is to disturb the flow pattern and produce regions with high shear rate, turbulence, and recirculation, which are key hemodynamic factors associated with plaque rupture, clot formation, and embolism. In order to characterize the disturbed flow in the stenosed carotid artery, stereoscopic PIV measurements were performed in a transparent model with 50% stenosis under pulsatile flow conditions. Simulated ECG gating of the flowrate waveform provides external triggering required for volumetric reconstruction of the complex flow patterns. Based on the three-component velocity data in the lumen region, volumetric shear-stress patterns were derived.
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.
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.
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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.
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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.
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.
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
Background: Percutaneous coronary intervention (PCI) of coronary bifurcation lesions remains a subject of debate. Many studies have been published in this setting. They are often small scale and display methodological flaws and other shortcomings such as inaccurate designation of lesions, heterog...
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).
Farooq, Vasim; Serruys, Patrick W; Heo, Jung Ho; Gogas, Bill D; Okamura, Takayuki; Gomez-Lara, Josep; Brugaletta, Salvatore; Garcìa-Garcìa, Hector M; van Geuns, Robert Jan
2011-08-01
Coronary artery bifurcations are a common challenging lesion subset accounting for approximately 10% to 20% of all percutaneous coronary interventions. The provisional T-stenting approach is generally recommended as the first-line management of most lesions. Carina shift is suggested to be the predominant mechanism of side-branch pinching during provisional T-stenting and has been indirectly inferred from bench work and other intravascular imaging modalities. Offline 3-dimensional (3D) reconstructions of patients studied in the first-in-man trial of the high-frequency (160 frames/s) Terumo optical frequency domain imaging system were undertaken using volume-rendering software. Through a series of 3D reconstructions, several novel hypothesis-generating concepts are presented.
Non-local investigation of bifurcations of solutions of non-linear elliptic equations
Energy Technology Data Exchange (ETDEWEB)
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.
AN ACCESSORY/ABERRANT LEFT INFERIOR POLAR ARTERY AR ISING FROM THE AORTIC BIFURCATION
Directory of Open Access Journals (Sweden)
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.
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.
Baek, Hyoungsu; Jayaraman, Mahesh V; Karniadakis, George Em
2009-12-01
A growing number of cases of rupture at an infundibulum, progression of infundibulum to a frank aneurysm, and subarachnoid hemorrhage (SAH) in the posterior communicating artery (PCoA) have been reported. Using patient-specific geometric models of the supraclinoid internal carotid artery (ICA) with PCoA infundibulum or aneurysm, high-resolution computational fluid dynamics simulations were performed by solving the Navier-Stokes equations with a spectral/hp element method. Simulation results show that the flow impinges at the distal wall of infundibulum near the outside of the ICA bend and creates a region of higher pressure (4-5 mmHg) surrounded by a band of a high wall shear stress (WSS) (20-30 N/m(2) on average). At the proximal end of the infundibulum, another stagnation area is formed characterized by low WSS (shear index. This impingement region seems to coincide with the locations of the rupture of infundibulae or progression to aneurysms. In addition, the pulsatile flow becomes unstable due to the presence of aneurysms or aneurysm-like infundibulae, and this leads to WSS temporal fluctuations inside the aneurysm, which may accelerate the degenerative processes in the vessel walls.
Poon, Eric; Thondapu, Vikas; Chin, Cheng; Scheerlinck, Cedric; Zahtila, Tony; Mamon, Chris; Nguyen, Wilson; Ooi, Andrew; Barlis, Peter
2016-11-01
Blood flow dynamics directly influence biology of the arterial wall, and are closely linked with the development of coronary artery disease. Computational fluid dynamics (CFD) solvers may be employed to analyze the hemodynamic environment in patient-specific reconstructions of coronary arteries. Although coronary X-ray angiography (CA) is the most common medical imaging modality for 3D arterial reconstruction, models reconstructed from CA assume a circular or elliptical cross-sectional area. This limitation can be overcome with a reconstruction technique fusing CA with intravascular optical coherence tomography (OCT). OCT scans the interior of an artery using near-infrared light, achieving a 10-micron resolution and providing unprecedented detail of vessel geometry. We compared 3D coronary artery bifurcation models generated using CA alone versus OCT-angiography fusion. The model reconstructed from CA alone is unable to identify the detailed geometrical variations of diseased arteries, and also under-estimates the cross-sectional vessel area compared to OCT-angiography fusion. CFD was performed in both models under pulsatile flow in order to identify and compare regions of low wall shear stress, a hemodynamic parameter directly linked with progression of atherosclerosis. Supported by ARC LP150100233 and VLSCI VR0210.
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
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.
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...
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.
Continuum Hamiltonian Hopf Bifurcation II
Hagstrom, G I
2013-01-01
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (HH) bifurcation. Necessary notions pertaining to spectra, structural stability, signature of the continuous spectra, and normal forms are described. The theory developed is applicable to a wide class of 2+1 noncanonical Hamiltonian matter models, but the specific example of the Vlasov-Poisson system linearized about homogeneous (spatially independent) equilibria is treated in detail. For this example, structural (in)stability is established in an appropriate functional analytic setting, and two kinds of bifurcations are considered, one at infinite and one at finite wavenumber. After defining and describing the notion of dynamical accessibility, Kre\\u{i}n-like the...
Li, H. T.; Zu, J.; Yang, Y. F.; Qin, W. Y.
2016-12-01
Snap-through is used to improve the efficiencies of energy harvesters and extend their effective frequency bandwidths. This work uses the Melnikov method to explore the underlying snap-through mechanism and the conditions necessary for homoclinic bifurcations in a magnet-induced buckled energy harvester. First, an electromechanical model of the energy harvester is established analytically using the Euler-Bernoulli beam theory and the extended Hamilton's principle. Second, the Melnikov function of the model is derived, and the necessary conditions for homoclinic bifurcations and chaos are presented on the basis of this model. The analysis reveals that the distance between the magnets and the end-block mass significantly affect the thresholds for chaotic motions and the high-energy solutions. Numerical and experimental studies confirm these analytical predictions and provide guidelines for optimum design of the magnet-induced buckled energy harvester.
Bifurcation of Scramjet Unstart
Jang, Ik; Nichols, Joseph; Duraisamy, Karthik; Moin, Parviz
2011-11-01
We investigate the bifurcation structure of catastrophic unstart in scramjets. The bifurcation of quasi-one-dimensional Rayleigh flow is first analyzed, followed by a numerical investigation of a more realistic model scramjet isolator (Wagner et al., AIAA paper, 2010). We show that the quasi-one-dimensional model recovers a similar hysteresis behavior as that observed in steady Reynolds-Averaged Navier-Stokes simulations of the model scramjet isolator close to the onset of unstart. In the hysteresis zone, steady but unstable solutions are obtained by means of pseudo-arclength continuation. Automatic differentiation permits the use of fully discrete Jacobians that result in an accurate representation of functional dependencies and linearized dynamics. Furthermore, we use an Arnoldi method to extract the least stable direct and adjoint eigenfunctions spanning the system dynamics close to unstart and obtain the system response to both harmonic and stochastic forcing. This information, along with the final bifurcation structure, allows us to evaluate the effectiveness of different metrics as indicators of the onset of unstart. Supported by the PSAAP program of DOE
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.
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.
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.
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.
Investigation of Brain Arterial Circle Malformations Using Electrical Modelling and Simulation
Directory of Open Access Journals (Sweden)
Klara Capova
2006-01-01
Full Text Available The paper deals with the cerebral arterial system investigation by means of electrical modelling and simulations. The main attention is paid to the brain arterial circle malformations (stenoses and aneurysms and their determination and evaluation by computer-aided methods as tools of a non-invasive diagnostics. The compensation possibilities of brain arterial circle in case of presence of concrete arterial malformations are modelled and simulated. The simulation results of brain arteries blood pressures and volume flow velocities time dependences are presented and discussed under various health conditions.
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…
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...
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 slo...
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.
Border Collision Bifurcations in Two Dimensional Piecewise Smooth Maps
Banerjee, S; Banerjee, Soumitro; Grebogi, Celso
1999-01-01
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddle-node, pitchfork or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the theoretical problem: the development of a theory and classification of the new type of bifurcations resulting from border collision. We then present a systematic analysis of such bifurcations by deriving a normal form --- the piecewise linear approximation in the neighborhood of the border. We show that there can be eleven qualitatively different types of border collision bifurcations depending on the parameters of the normal form, and these are classified under six cases. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. This theoretical framework will help in explaining bifurcations in all syst...
Electron-Dominated Spontaneous Bifurcation of Harris Equilibrium
Lee, Kuang-Wu
2012-01-01
In this letter the spontaneous bifurcation of Harris equilibrium current sheet is reported. The collisionless current bifurcation is simulated by a 2D particle-in-cell approach. Explicit particle advancing method is used to resolve the transient electron dynamics. Unlike previous implicit investigations no initial perturbations is applied to trigger current bifurcation. Instead, an electron-dominated spontaneously bifurcation is observed. Electromagnetic fluctuations grow from thermal noise initially. Soon the noise triggers the eigenmodes and eventually causes current sheet bifurcation. The relative entropy of the bifurcated state exceeds the value of initial Harris equilibrium. It is also found that the Helmholtz free energy decreases in the bifurcation process. Hence it is concluded that Harris equilibrium evolves toward a more stable (smaller free energy) bifurcated state.
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.
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.
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.
Existing drugs and agents under investigation for pulmonary arterial hypertension.
Sharma, Mala; Pinnamaneni, Sowmya; Aronow, Wilbert S; Jozwik, Bartosz; Frishman, William H
2014-01-01
Pulmonary arterial hypertension is a progressive and debilitating disorder with an associated high morbidity and mortality rate. Significant advances in our understanding of the epidemiology, pathogenesis, and pathophysiology of pulmonary hypertension have occurred over the past several decades. This has allowed the development of new therapeutic options in this disease. Today, our selection of therapeutic modalities is broader, including calcium channel blockers, prostanoids, endothelin receptor antagonists, phosphodiesterase inhibitors, and soluble guanylate cyclase stimulators, but the disease remains fatal. This underscores the need for a continued search for novel therapies. Several potential pharmacologic agents for the treatment of pulmonary arterial hypertension are under clinical development and some promising results with these treatments have been reported. These agents include rho-kinase inhibitors, long-acting nonprostanoid prostacyclin receptor agonists, tyrosine protein kinase inhibitors, endothelial nitric oxide synthase couplers, synthetically produced vasoactive intestinal peptide, antagonists of the 5-HT2 receptors, and others. This article will review several of these promising new therapies and will discuss the current evidence regarding their potential benefit in pulmonary arterial hypertension.
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.
Femoral bifurcation disease: balloon or knife.
Bosiers, Marc; Deloose, Koen
2009-10-01
Arterial occlusive disease at the level of the femoral bifurcation mostly occurs in combination with inflow and/or outflow lesions. Surgical endarterectomy of the femoral bifurcation is a well-proven low-risk and easy surgical intervention with known durable success, while, although proven to be safe, evidence is lacking about the durability of the endovascular approach. Based on the evidence at hand, the surgical approach should be recommended for the vast majority of patients and the endovascular approach should only be indicated as the first strategy in selected cases presenting with factors that might compromise the outcome of surgery in the groin. If feasible, the hybrid approach with endarterectomy at the level of the bifurcation and endovascular repair of the inflow and outflow lesions is preferred in patients with multilevel disease.
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....
Energy Technology Data Exchange (ETDEWEB)
Santos, A. L.; Ramos, M.; Delgado, F.; Cano, A.; Bravo, F. [Hospital Universitario Reina Sofia. Cordoba (Spain)
2001-07-01
To determine the value of computed tomography (CT) angiography in grading cervical carotid artery stenosis, comparing it with that of intraarterial digital subtraction angiography (IADSA), and to demonstrate the utility of CT angiography, under certain circumstances, as an alternative to carotid angiography in the diagnosis of arterial disease. Of the 428 patients who underwent CT andiography of the supraaortic trunk in our hospital between lily 1998 and September 2000, the results in the first 55 in whom Id's was performed concomitantly were reviewed, and the findings with two techniques compared. In the discrimination of stenosis >70%, CT angiography showed a sensitivity of 92%, a specificity of 98% and an overall precision of 95% with respect to IADSA. The good correlation of the grading of carotid artery stenosis by CT angiography with that of IADSA suggests its high diagnostic reliability. (Author) 38 refs.
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.
The Investigation of Serum Vaspin Level in Atherosclerotic Coronary Artery Disease
Kobat, Mehmet Ali; Celik,Ahmet; Balin, Mehmet; Altas, Yakup; Baydas, Adil; Bulut, Musa; Aydin, Suleyman; DAGLI, Necati; YAVUZKIR, Mustafa Ferzeyn; Ilhan, Selcuk
2012-01-01
Background It was speculated that fatty tissue originated adipocytokines may play role in pathogenesis of atherosclerosis. These adipocytokines may alter vascular homeostasis by effecting endothelial cells, arterial smooth muscle cells and macrophages. Vaspin is a newly described member of adipocytokines family. We aimed to investigate whether plasma vaspin level has any predictive value in coronary artery disease (CAD). Methods Forty patients who have at least single vessel ≥ 70 % stenosis d...
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.
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....
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...
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.
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.
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 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)
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.
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.
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.
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.
Sequences of gluing bifurcations in an analog electronic circuit
Energy Technology Data Exchange (ETDEWEB)
Akhtanov, Sayat N.; Zhanabaev, Zeinulla Zh. [Physico-Technical Department, Al Farabi Kazakh National University, Al Farabi Av. 71, Almaty, 050038 Kazakhstan (Kazakhstan); Zaks, Michael A., E-mail: zaks@math.hu-berlin.de [Institute of Mathematics, Humboldt University, Rudower Chaussee 25, D-12489 Berlin (Germany)
2013-10-01
We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and replaces the Lorenz route to chaos by a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the irregular ones. Every single bifurcation “glues” in the phase space two stable periodic orbits and creates a new one, with the doubled length: a sequence of such bifurcations results in the birth of the chaotic attractor.
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Directory of Open Access Journals (Sweden)
Xin Qi
2015-02-01
Full Text Available 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 predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation 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 series 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.
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 PERIODIC SOLUTION IN A THREE-UNIT NEURAL NETWORK WITH DELAY
Institute of Scientific and Technical Information of China (English)
林怡平; ROLAND LEMMERT; PETER VOLKMANN
2001-01-01
A system of three-unit networks with no self-connection is investigated, the general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimation formula of the period for 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.
Numerical investigation of MHD flow of blood and heat transfer in a stenosed arterial segment
Majee, Sreeparna; Shit, G. C.
2017-02-01
A numerical investigation of unsteady flow of blood and heat transfer has been performed with an aim to provide better understanding of blood flow through arteries under stenotic condition. The blood is treated as Newtonian fluid and the arterial wall is considered to be rigid having deposition of plaque in its lumen. The heat transfer characteristic has been analyzed by taking into consideration of the dissipation of energy due to applied magnetic field and the viscosity of blood. The vorticity-stream function formulation has been adopted to solve the problem using implicit finite difference method by developing well known Peaceman-Rachford Alternating Direction Implicit (ADI) scheme. The quantitative profile analysis of velocity, temperature and wall shear stress as well as Nusselt number is carried out over the entire arterial segment. The streamline and temperature contours have been plotted to understand the flow pattern in the diseased artery, which alters significantly in the downstream of the stenosis in the presence of magnetic field. Both the wall shear stress and Nusselt number increases with increasing magnetic field strength. However, wall shear stress decreases and Nusselt number enhances with Reynolds number. The results show that with an increase in the magnetic field strength upto 8 T, does not causes any damage to the arterial wall, but the study is significant for assessing temperature rise during hyperthermic treatment.
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.
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.
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...
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...
Directory of Open Access Journals (Sweden)
Marjan Molavi Zarandi
2012-01-01
Full Text Available Coronary artery bifurcation lesions are complex and several classifications are presented to describe them. Recently, the Medina classification has been proposed. This classification uses binary values for characterization of stenosis. Flow conditions according to Medina classification have not been described. In this paper, bifurcation lesions corresponding to anatomical Medina lesion classification are compared on the basis of flow and Wall Shear Stress (WSS. Computational models of healthy and stenosed coronary artery bifurcations ((1, 1, 1, (0, 1, 1 and (1, 0, 1 with moderate and severe stenoses of 50% and 75% diameter were analyzed. The results showed that, flow conditions vary in bifurcation lesion types according to the clinically-oriented Medina classification. The flow in SB of bifurcation was dependent of the Medina lesion type and was more affected in lesion type (1, 0, 1. The magnitudes of WSS on the inner and outer walls of SB of bifurcation lesion (1, 0, 1 in post-stenotic region and along the arterial wall were smaller than bifurcations lesions (0, 1, 1 and (1, 1, 1 respectively. Our results suggest that SB of bifurcation lesion (1, 0, 1 is more prone to atherosclerosis progression compared to types (0, 1, 1 and (1, 1, 1.
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.
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.
The dynamo bifurcation in rotating spherical shells
Morin, Vincent; 10.1142/S021797920906378X
2010-01-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.
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 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 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.
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.
Local Bifurcations in DC-DC Converters
2012-01-01
Three local bifurcations in DC-DC converters are reviewed. They are period-doubling bifurcation, saddle-node bifurcation, and Neimark bifurcation. A general sampled-data model is employed to study the types of loss of stability of the nominal (periodic) solution and their connection with local bifurcations. More accurate prediction of instability and bifurcation than using the averaging approach is obtained. Examples of bifurcations associated with instabilities in DC-DC converters are given.
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.
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.
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.
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.
Bifurcations of nontwisted heteroclinic loop
Institute of Scientific and Technical Information of China (English)
田清平; 朱德明
2000-01-01
Bifurcations of nontwisted and fine heteroclinic loops are studied for higher dimensional systems. The existence and its associated existing regions are given for the 1-hom orbit and the 1-per orbit, respectively, and bifurcation surfaces of the two-fold periodic orbit are also obtained. At last, these bifurcation results are applied to the fine heteroclinic loop for the planar system, which leads to some new and interesting results.
Directory of Open Access Journals (Sweden)
Sandra Maria Pontes
2011-09-01
Full Text Available CONTEXTO: A ecografia das artérias carótidas extracranianas já se estabeleceu como método diagnóstico de imagem pré-operatória, e para seguimento de pacientes. OBJETIVO: Avaliar diferenças do mapeamento ecográfico em função do gênero masculino ou feminino dos pacientes. MÉTODOS: Ultrassonografia de alta resolução foi realizada antes do tratamento cirúrgico de 500 bifurcações carotídeas em 192 mulheres e 308 homens. Análise de diferenças baseadas no gênero foi feita em imagens modo B e fluxo a cor, transversal e longitudinal, e medidas duplex doppler de velocidades. Porcentual de estenose expressa em redução de diâmetro, comprimento de placa, diâmetros das artérias carótida interna distal e comum, e distância da bifurcação ao lóbulo da orelha foram comparados. Média, desvio padrão, mínimo e máximo foram descritos. Comparações estatísticas foram baseadas em testes t de Student e do Χ2. RESULTADOS: Estenoses carotídeas mediram 70±11% (30-95% em mulheres e 72±12% (40-98% em homens (p=0,013. Prevalência de estenoses no intervalo 90-99% foi mais alta em homens, 14,3 vs 7,8% (p=0,029. As placas foram mais extensas nos homens, 2,3±0,8 vs 1,9±0,6 cm (pCONTEXT: Doppler ultrasonography is an established method for diagnosis, preoperative imaging and follow-up of extracranial carotid artery disease. OBJETIVE: The evaluation of gender differences in carotid artery bifurcation Doppler ultrasonography mapping. METHODS: High resolution Doppler ultrasonography of 500 carotid bifurcations was performed in 192 women and 308 men before surgical treatment. Gender differences were analyzed based on B-mode, color-flow, duplex doppler transverse and longitudinal images. Diameter percent stenoses, plaque length, distal internal and common carotid artery diameters, and distance from the carotid bifurcation to the ear lobe were compared. Mean, standard deviation, minimum and maximum values were described. Statistical
Xu, Yong-Jiang; Ho, Wanxing Eugene; Xu, Fengguo; Wen, Tao; Ong, Choon Nam
2013-10-01
Fatty acids and eicosanoids are two important classes of signaling lipid molecules involved in the pathogenesis of cardiovascular diseases. To investigate the physiological functions and interplay between fatty acids and eicosanoids in coronary artery disease (CAD) patients, we developed an analytical approach for parallel quantitative analysis of plasma fatty acids and eicosanoids, using gas chromatography-tandem mass spectrometry (GC-MS/MS) and liquid chromatography-tandem mass spectrometry (LC-MS/MS). In this study, 26 fatty acids and 12 eicosanoids were confidently detected in 12 patients with confirmed coronary artery disease and 11 healthy subjects. Pattern recognition analysis (principal components analysis, orthogonal partial least-square discriminate analysis, and hierarchical clustering analysis) demonstrated that the plasma lipid profile of fatty acids and eicosanoids enabled robust discrimination of CAD patients versus healthy subjects. Significant differences in six fatty acids and five eicosanoids were noted among CAD patients and healthy subjects. The development of cardiovascular disease-induced metabolic change of fatty acids and eicosanoids, such as eicosapentaenoic acid, docosahexaenoic acid, arachidonic acid, hydroxyeicosatetraenoic acids and hydroxyoctadecadienoic acid, were consistent with previous isolated observations. Moderate-strong correlations between three plasma fatty acids and three eicosanoids from arachidonic acid metabolism were also observed. In brief, findings from this exploratory study offered a new insight on the roles of various bioactive lipid molecules in the development of coronary artery disease biomarkers.
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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.
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.
Blowout bifurcation of chaotic saddles
Directory of Open Access Journals (Sweden)
Tomasz Kapitaniak
1999-01-01
Full Text Available Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this 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.
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.
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.
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.
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.
Doubly twisted Neimark–Sacker bifurcation and two coexisting two-dimensional tori
Energy Technology Data Exchange (ETDEWEB)
Sekikawa, Munehisa, E-mail: sekikawa@cc.utsunomiya-u.ac.jp [Department of Mechanical and Intelligent Engineering, Utsunomiya University, Utsunomiya 321-8585 (Japan); Inaba, Naohiko [Organization for the Strategic Coordination of Research and Intellectual Properties, Meiji University, Kawasaki 214-8571 (Japan)
2016-01-08
We discuss a complicated bifurcation structure involving several quasiperiodic bifurcations generated in a three-coupled delayed logistic map where a doubly twisted Neimark–Sacker bifurcation causes a transition from two coexisting periodic attractors to two coexisting invariant closed circles (ICCs) corresponding to two two-dimensional tori in a vector field. Such bifurcation structures are observed in Arnol'd tongues. Lyapunov and bifurcation analyses suggest that the two coexisting ICCs and the two coexisting periodic solutions almost overlap in the two-parameter bifurcation diagram. - Highlights: • This study investigates a three-coupled delayed logistic map. • It generates complex quasiperiodic bifurcations. • Two periodic solution coexist in a conventional Arnol'd tongue. • Two two-tori coexist in a high-dimensional Arnol'd tongue.
Volkenstein, M V; Livshits, M A
1989-01-01
The interrelations of physics and biology are discussed. It is shown that Darwin can be considered as one of the founders of the important field of contemporary physics called physics of dissipative structures or synergetics. The theories of gradual and punctual evolution are presented. The contradiction between these theories can be solved on the basis of molecular theory of evolution and on the basis of the phenomenological physical treatment. The general physical properties of living systems, considered as open systems being far from equilibrium, are listed and simple non-linear mathematical models describing gradual and punctual speciation are suggested. The usual pictures which present these two kinds of speciation can possess physico-mathematical sense. Punctuated speciation means bifurcation, a kind of non-equilibrium phase transition.
Surgical repair of pulmonary artery branches.
Ghez, Olivier; Saeed, Imran; Serrato, Maria; Quintero, Diana Bernal; Kreitmann, Bernard; Fraisse, Alain; Uemura, Hideki; Seale, Anna; Daubeney, Piers; McCarthy, Karen; Ho, S Yen
2013-01-01
Surgical repair of pulmonary artery (PA) branches encompasses many different clinical scenarios and technical challenges. The most common, such as bifurcation and central PA reconstruction, are described, as well as the challenges of complex and peripheral reconstruction.
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.
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.
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...
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
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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.
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.
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.
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 of Periodic Orbits and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
Mei-xiang Cai; Jian-ping Yang
2006-01-01
Duffing equation with fifth nonlinear-restoring force, one external forcing and a phase shift is investigated. The conditions of existences for primary resonance, second-order, third-order subharmonics, morder subharmonics and chaos are given by using second-averaging method, Melnikov methods and bifurcation theory. Numerical simulations including bifurcation diagrams, bifurcation surfaces, phase portraits, not only show the consistence with the theoretical analysis, but also exhibit the new dynamical behaviors. We show the onset of chaos, chaos suddenly disappearing to period orbit, one-band and double-band chaos, period-doubling bifurcations from period 1, 2, and 3 orbits, period-windows (period-2, 3 and 5) in chaotic regions.
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.
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 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.
Asimov, M. M.; Korolevich, A. N.
2008-06-01
A novel method of direct control of local tissue oxygenation based on laser-induced photodissociation of oxyhemoglobin in cutaneous blood vessels is discussed. New technology in selective and local increase of the concentration of free molecular oxygen in tissue that enhances metabolism of cells is demonstrated. Direct in vivo measurements of the tissue oxygen tension are carried out on human skin. Kinetics of oxygen tension in tissue is investigated under the effect of He-Ne laser radiation at the power of 1mW relatively to initial value of tissue oxygen tension. The results of experimental study the kinetics of oxygen distribution into tissue from arterial blood is presented. Biomedical applications of proposed new technology in laser therapy of pathologies where elimination of local tissue hypoxia is critical are discussed.
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.
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.
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.
Subcritical Hopf bifurcations in low-density jets
Zhu, Yuanhang; Gupta, Vikrant; Li, Larry K. B.
2016-11-01
Low-density jets are known to bifurcate from a steady state (a fixed point) to self-excited oscillations (a periodic limit cycle) when the Reynolds number increases above a critical value corresponding to the Hopf point, ReH . In the literature, this Hopf bifurcation is often considered to be supercritical because the self-excited oscillations appear only when Re > ReH . However, we find that under some conditions, there exists a hysteretic bistable region at ReSN ReSN denotes a saddle-node bifurcation point. This shows that the Hopf bifurcation can also be subcritical, which has three main implications. First, low-density jets could be triggered into self-excited oscillations even when Re < ReH . Second, in the modeling of low-density jets, the subcritical or supercritical nature of the Hopf bifurcation should be taken into account because the former is caused by cubic nonlinearity whereas the latter is caused by square nonlinearity. Third, the response of the system to external forcing and noise depends on its proximity to the bistable region. Therefore, when investigating the forced response of low-density jets, it is important to consider whether the Hopf bifurcation is subcritical or supercritical.
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).
Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting
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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.
Stability and Bifurcation in a State-Dependent Delayed Predator-Prey System
Hou, Aiyu; Guo, Shangjiang
In this paper, we consider a class of predator-prey equations with state-dependent delayed feedback. Firstly, we investigate the local stability of the positive equilibrium and the existence of the Hopf bifurcation. Then we use perturbation methods to determine the sub/supercriticality of Hopf bifurcation and hence the stability of Hopf bifurcating periodic solutions. Finally, numerical simulations supporting our theoretical results are also provided.
Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems
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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.
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...
Qiu, B.; Chen, S.
2010-12-01
Satellite altimeter sea surface height (SSH) data from the past 17 years are used to investigate the interannual-to-decadal changes in the bifurcation of the North Equatorial Current (NEC) along the Philippine coast. The NEC bifurcation latitude migrated quasi-decadally between 10N and 15N with northerly bifurcations observed in late 1992, 1997-98 and 2003-04, and southerly bifurcations in 1999-2000 and 2008-09. The observed NEC bifurcation latitude can be approximated well by the SSH anomalies in the 12-14N and 127-130E box east of the mean NEC bifurcation point. Using a 1.5-layer reduced-gravity model forced by the ECMWF reanalysis wind stress data, we find that the SSH anomalies in this box can be simulated favorably to serve as a proxy for the observed NEC bifurcation. With the availability of the long-term reanalysis wind stress data, this allows us to lengthen the NEC bifurcation time series back to 1962. Although quasi-decadal variability was prominent in the last two decades, the NEC bifurcation was dominated by changes with a 3~5-yr period during the 1980s and had low variance prior to the 1970s. These inter-decadal modulations in the characteristics of the NEC bifurcation reflect similar inter-decadal modulations in the wind forcing field over the western tropical North Pacific Ocean. Although the NEC bifurcation on the interannual and longer timescales is in general related to the Nino-3.4 index with a positive (negative) index corresponding to a northerly (southerly) bifurcation, the exact location of bifurcation is determined by wind forcing in the 12-14N band that contains variability not fully representable by the Nino-3.4 index.
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
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. The condition after the deployment of a pipeline embolization device is also simulated. Hemodynamic factors such as flow velocity, pressure, and wall shear stress are studied. Aneurysms with a larger side branch vessel might have greater risk after treatment in terms of hemodynamics. Although a stent could lead to flow reduction entering the aneurysm, it would drastically alter the flow rate inside the side branch vessel. This may result in side-branch hypoperfusion subsequent to stenting. In addition, two patient-specific bifurcation aneurysms are tested, and the results show good agreement with the idealized models. Furthermore, the peripheral resistance of downstream vessels is investigated by varying the outlet pressure conditions. This quantitative analysis can assist in treatment planning and therapeutic decision-making.
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.
Ren, Jingli; Li, Xueping
A seasonally forced predator-prey system with generalized Holling type IV functional response is considered in this paper. The influence of seasonal forcing on the system is investigated via numerical bifurcation analysis. Bifurcation diagrams for periodic solutions of periods one and two, containing bifurcation curves of codimension one and bifurcation points of codimension two, are obtained by means of a continuation technique, corresponding to different bifurcation cases of the unforced system illustrated in five bifurcation diagrams. The seasonally forced model exhibits more complex dynamics than the unforced one, such as stable and unstable periodic solutions of various periods, stable and unstable quasiperiodic solutions, and chaotic motions through torus destruction or cascade of period doublings. Finally, some phase portraits and corresponding Poincaré map portraits are given to illustrate these different types of solutions.
Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model
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Xueli Chen
2017-01-01
Full Text Available A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Lin Wenhui [College of Science, China Agricultural University, Beijing 100083 (China); Zhao Yapu [State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080 (China)
2007-03-21
The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.
Lin, Wen-Hui; Zhao, Ya-Pu
2007-03-01
The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.
Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays
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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....
Global hopf bifurcation on two-delays leslie-gower predator-prey system with a prey refuge.
Liu, Qingsong; Lin, Yiping; Cao, Jingnan
2014-01-01
A modified Leslie-Gower predator-prey system with two delays is investigated. By choosing τ 1 and τ 2 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.
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.
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
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.
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.
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.
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 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.
Bifurcations of optimal vector fields
Kiseleva, T.; Wagener, F.
2015-01-01
We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one-dimensional state spaces, as well as their bifurcations, as problem parameters are varied. The solutions are represented as the integral curves of a multivalued optimal vector field on sta
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.
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.
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.
Bifurcation Analysis for a Delayed Predator-Prey System with Stage Structure
Directory of Open Access Journals (Sweden)
Jiang Zhichao
2010-01-01
Full Text Available Abstract A delayed predator-prey system with stage structure is investigated. The existence and stability of equilibria are obtained. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the normal form and the center manifold theory. Finally, a numerical example supporting the theoretical analysis is given.
Structure of the Bifurcation Solutions for a Predator-Prey Model
Institute of Scientific and Technical Information of China (English)
WANG Yi-fu; MENG Yi-jie
2006-01-01
A system of reaction diffusion equations modeling the predator-prey interaction in an unstirred chemostat is considered. After transforming the model, the global bifurcation theorem is used to investigate the global structure of solutions of the system with b as the bifurcation parameter.
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.
Weak Centers and Local Bifurcations of Critical Periods at Infinity for a Class of Rational Systems
Institute of Scientific and Technical Information of China (English)
Wen-tao HUANG; Valery G. ROMANOVSKI; WEI-NIAN ZHANG
2013-01-01
We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems.We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.
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.
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 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.
Numerical bifurcation of Hamiltonian relative periodic orbits
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2009-01-01
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...... 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...
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.
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.
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.)
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.
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.
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
Optimal Revascularization Strategy on Medina 0,1,0 Left Main Bifurcation Lesions in Type 2 Diabetes
Directory of Open Access Journals (Sweden)
Xuwei Zheng
2016-01-01
Full Text Available 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.
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
Energy Technology Data Exchange (ETDEWEB)
Rayneau-Kirkhope, Daniel, E-mail: ppxdr@nottingham.ac.u [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom); Farr, Robert [Unilever R and D, Olivier van Noortlaan 120, AT3133, Vlaardingen (Netherlands); London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London (United Kingdom); Ding, K. [Department of Physics, Fudan University, Shanghai, 200433 (China); Mao, Yong [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
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 and transitions to chaos in an inverted pendulum
Kim, Sang-Yoon; Hu, Bambi
1998-09-01
We consider a parametrically forced pendulum with a vertically oscillating suspension point. It is well known that, as the amplitude of the vertical oscillation is increased, its inverted state (corresponding to the vertically-up configuration) undergoes a cascade of ``resurrections,'' i.e., it becomes stabilized after its instability, destabilize again, and so forth ad infinitum. We make a detailed numerical investigation of the bifurcations associated with such resurrections of the inverted pendulum by varying the amplitude and frequency of the vertical oscillation. It is found that the inverted state stabilizes via alternating ``reverse'' subcritical pitchfork and period-doubling bifurcations, while it destabilizes via alternating ``normal'' supercritical period-doubling and pitchfork bifrucations. An infinite sequence of period-doubling bifurcations, leading to chaos, follows each destabilization of the inverted state. The critical behaviors in the period-doubling cascades are also discussed.
Bogdanov-Takens bifurcation in a predator-prey model
Liu, Zhihua; Magal, Pierre; Xiao, Dongmei
2016-12-01
In this paper, we investigate a class of predator-prey model with age structure and discuss whether the model can undergo Bogdanov-Takens bifurcation. The analysis is based on the normal form theory and the center manifold theory for semilinear equations with non-dense domain combined with integrated semigroup theory. Qualitative analysis indicates that there exist some parameter values such that this predator-prey model has an unique positive equilibrium which is Bogdanov-Takens singularity. Moreover, it is shown that under suitable small perturbation, the system undergoes the Bogdanov-Takens bifurcation in a small neighborhood of this positive equilibrium.
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.
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. A...
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.
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.
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.
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.
Air effects on subharmonic bifurcations of impact in vertically vibrated granular beds
Jiang, Z. H.; Han, H.; Zhang, R.; Li, X. R.
2013-06-01
Experiments have been performed to investigate the effects of interstitial air on the impact bifurcations in vertically vibrated granular beds. The impact of particles on the container bottom commonly undergoes a series of subharmonic bifurcations in the sequence of period-2, period-4, chaos, period-3, period-6, chaos, period-4, period-8, and so on. In the container with an air impermeable bottom, air flows are induced and air drag on the particles causes the bifurcations to be dependent on the particle size; the bifurcation point increases with the decreasing of particle size. This makes the higher-order bifurcations become unobservable when the particle size is sufficiently small. Meanwhile, such bifurcations are shown to be controlled by both the normalized vibration acceleration and the vibration frequency. However, in the container with an air permeable bottom the size dependence of bifurcations is cancelled, and the bifurcations turn to be controlled solely by the normalized vibration acceleration. The observed results are explained in terms of an inelastic bouncing ball model with air dragging terms involved.
Institute of Scientific and Technical Information of China (English)
张永力; 刘方军; 孙玉明; 石祥恩
2011-01-01
Objective To observe the clinical efficacy of bypass vascular grafting in the treatment of fusiform aneurysms distal to middle cerebral artery bifurcation. Methods Nine patients with unruptured fusiform aneurysm distal to middle cerebral artery bifurcation were treated by bypass grafting in Beijing Sanbo Brain Hospital from November 2006 to October 2010. Eight patients had single aneurysm and one had multiple aneurysms. The size of aneurysms were medium in one, large in 2, giant in 5 and serpentine aneurysm in 1 patient. Intracranial bypass grafting were performed in 7 patients, and extracranial-intracranial (EC-IC) bypass grafting were performed in 2 patients. All the aneurysms were resected or trapped.Results ①The postoperative DSA and/or CTA demonstrated that the aneurysms in 9 patients were all disappeared. The grafts were patent in 7 patients and not patent in 2 patients. Of the 2 patients, CTA revealed that the graft was patent in 1 patient 10 months after surgery; DSA showed that the graft was not patent in another patient 17 days after surgery, the cortical blood supply of the distal aneurysm was compensated by the collateral vessels. ②The muscle strength declined slightly in 1 patient; however, he recovered completely before discharge; 3 patients had transient perioral twitching, 1 had bilateral oculomotor nerve palsy,and 1 had venous hemorrhagic infarction. Glasgow Outcome Scale (GOS) score in 1 patient at discharge was 4 and in 8 patients were 5. ③All the patients were followed up for 6 months to 4.5 years, and their GOS scores were all 5. Conclusion Cerebrovascular bypass, especially the local intracranial bypass grafting, is a effective treatment for fusifonn aneurysms distal to middle cerebral artery bifurcation.%目的 观察不同方式的血管旁路移植术加动脉瘤切除或孤立术治疗大脑中动脉分叉以远梭形动脉瘤的临床疗效.方法 2006年11月-2010年10月北京三博脑科医院采用血管旁路移植术治疗9
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.
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.
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.
Tankam, Israel; Tchinda Mouofo, Plaire; Mendy, Abdoulaye; Lam, Mountaga; Tewa, Jean Jules; Bowong, Samuel
2015-06-01
We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator-prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.
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.
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.
Roatta, S; Mohammed, M; Turturici, M; Milano, L; Passatore, M
2010-09-01
The complex interplay of neural, metabolic, myogenic and mechanical mechanisms that regulate blood flow in skeletal muscle (MBF) is still incompletely understood. For the first time, a method is presented for high time-resolution recording of MBF from a purely muscular artery in physiological conditions. Ultrasound perivascular flow probes were implanted (n = 15) mono- or bilaterally around the masseteric branch of the facial artery in nine rabbits and tested up to 16 days after implant. Reliable and stable recordings were achieved in 50% of implants. Blood flow was observed to increase from a resting level of 0.2-0.3 ml min(-1) up to 4.0-6.0 ml min(-1) during spontaneous masticatory activity. In addition, within single masticatory cycles marked back flow transients could be observed (peak flow = -10 ml min(-1)) during powerful masticatory strokes but not during mild mastication. The possibility of (1) surgically removing the sympathetic supply to the relevant vascular bed and of (2) bilaterally monitoring the perfusion of masseter muscles thus allowing to use one side as control side for different types of interventions makes this model a useful tool for disentangling the different mechanisms involved in the control of MBF.
Bifurcations of Invariant Tori and Subharmonic Solutions for Periodic Perturbed Systems
Institute of Scientific and Technical Information of China (English)
韩茂安
1994-01-01
The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a subharmonic solution are obtained.
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...
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.
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.
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.
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.)
Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting
Biwen Li; Zhenwei Li; Boshan Chen; Gan Wang
2015-01-01
A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numeric...
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.
Local and Global Bifurcations With Nonhyperbolic Equilibria
Institute of Scientific and Technical Information of China (English)
孙建华; 罗定军
1994-01-01
The normal forms of coupling functions governing local and global bifurcations are studied for a generic (d+1) -parameter family of three-dimensional systems with a heteroclinic orbit connecting a hyperbolic saddle and a nonhyperbolic equilibrium occurring in the saddle-node,transcritical and pitchfork bifurcations,respectively.Singularity theory and a version of Melnikov function are used in this paper.
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.
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.
Twisted and Nontwisted Bifurcations Induced by Diffusion
Lin, X B
1996-01-01
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.
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.
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.
Hopf Bifurcation and Stability Analysis for a Predator-prey Model with Time-delay
Institute of Scientific and Technical Information of China (English)
CHEN Hong-bing
2015-01-01
In this paper, a predator-prey model of three species is investigated, the necessary and sucient of the stable equilibrium point for this model is studied. Further, by introduc-ing a delay as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ cross some critical values. And, the stability and direction of hopf bifurcation are determined by applying the normal form theory and center manifold theory. numerical simulation results are given to support the theoretical predictions. At last, the periodic solution of this system is computed.
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.
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.
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.
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.
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.
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 Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback
Directory of Open Access Journals (Sweden)
Lei Li
2016-10-01
Full Text Available The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS, which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.
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.
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.
Judd, S L; Judd, Stephen L.; Silber, Mary
1998-01-01
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from eight or twelve Fourier modes, and feature structure at two different length scales. Using perturbation theory, we derive simple analytical expressions for the bifurcation equation coefficients on both rhombic and hexagonal lattices. These expressions show that, no matter how complicated the reaction kinectics, the nonlinear reaction terms reduce to just four effective terms within the bifurcation equation coefficients. Moreover, at the hexagonal degeneracy -- when the quadratic term in the hexagonal bifurcation equation disappears -- the number of effective system parameters drops to two, allowing a complete characterization of the possible bifurcation results at this degeneracy. The general results are then applied to specific model equations, to investigate the stabilit...
"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.
Bifurcation and Solitary-Like Solutions for Compound KdV-Burgers-Type Equation
Directory of Open Access Journals (Sweden)
Yin Li
2015-01-01
Full Text Available Firstly, based on the improved sub-ODE method and the bifurcation method of dynamical systems, we investigate the bifurcation of solitary waves in the compound KdV-Burgers-type equation. Secondly, numbers of solitary patterns solutions are given for each parameter condition and numerical simulations are used to display the dynamical characteristics. Finally, we obtain twelve solitary patterns solutions under some parameter conditions, such as the trigonometric function solutions and the hyperbolic function solutions.
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.
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)).
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....
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.
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.
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.
DEFF Research Database (Denmark)
Willerslev, Anne; Li, Xiao Q; Munch, Inger C
2014-01-01
PURPOSE: To study intravascular characteristics of flowing blood in retinal vessels using spectral-domain optical coherence tomography (SD-OCT). METHODS: Examination of selected arterial bifurcations and venous sites of confluence in 25 healthy 11-year-old children recruited as an ad hoc subsample...... be determined using SD-OCT. This feature may assist the identification of flow reversal near sites of vascular occlusion, the analysis of blood flow near vascular malformations and the segmentation of retinal SD-OCT images....
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.
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.
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.
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.
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.
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.
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.
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.
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.
Bifurcation and synchronization of synaptically coupled FHN models with time delay
Energy Technology Data Exchange (ETDEWEB)
Wang Qingyun [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Inner College of Mongolia Finance and Economics, Huhhot 010051 (China); Lu Qishao [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Chen Guanrong [Department of Electronic Engineering, City University of Hong Kong, Hong Kong (China); Feng Zhaosheng [Department of Mathematics, University of Texas - Pan American, Edinburg, TX 78441 (United States)], E-mail: zsfeng@utpa.edu; Duan Lixia [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)
2009-01-30
This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.
Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion
Directory of Open Access Journals (Sweden)
Shaban Aly
2016-01-01
Full Text Available The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008. The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.
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.
The Influence of Machine Saturation on Bifurcation and Chaos in Multimachine Power Systems
Alomari, Majdi M.; Zhu, Jian Gue
A bifurcation theory is applied to the multimachine power system to investigate the effect of iron saturation on the complex dynamics of the system. The second system of the IEEE second benchmark model of Subsynchronous Resonance (SSR) is considered. The system studied can be mathematically modeled as a set of first order nonlinear ordinary differential equations with (µ = Xc/XL) as a bifurcation parameter. Hence, bifurcation theory can be applied to nonlinear dynamical systems, which can be written as dx/dt = F(x;µ). The results show that the influence of machine saturation expands the unstable region when the system loses stability at the Hopf bifurcation point at a less value of compensation.
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.
Hopf bifurcation in a environmental defensive expenditures model with time delay
Energy Technology Data Exchange (ETDEWEB)
Russu, Paolo [D.E.I.R., University of Sassari, Via Torre Tonda, 34, 07100 Sassari (Italy)], E-mail: russu@uniss.it
2009-12-15
In this paper a three-dimensional environmental defensive expenditures model with delay is considered. The model is based on the interactions among visitors V, quality of ecosystem goods E, and capital K, intended as accommodation and entertainment facilities, in Protected Areas (PAs). The tourism user fees (TUFs) are used partly as a defensive expenditure and partly to increase the capital stock. The stability and existence of Hopf bifurcation are investigated. It is that stability switches and Hopf bifurcation occurs when the delay t passes through a sequence of critical values, {tau}{sub 0}. It has been that the introduction of a delay is a destabilizing process, in the sense that increasing the delay could cause the bio-economics to fluctuate. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the results.
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...... in a periodic strip is considered. The classical results of von Kármán concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued...
Bifurcation and instability problems in vortex wakes
Energy Technology Data Exchange (ETDEWEB)
Aref, H [Center for Fluid Dynamics and Department of Physics, Technical University of Denmark, Kgs. Lyngby, DK-2800 (Denmark); Broens, M [Center for Fluid Dynamics and Department of Mathematics, Technical University of Denmark, Kgs. Lyngby, DK-2800 (Denmark); Stremler, M A [Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (United States)
2007-04-15
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 and Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices in a periodic strip is considered. The classical results of von Karman concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued to be relevant to the wake behind an oscillating body.
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.
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.
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 ...
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.
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.
Bifurcation of a Swelling Gel with a Mechanical Load and Geometric Constraint
Institute of Scientific and Technical Information of China (English)
XUE Feng; YONG Hua-Dong; ZHOU You-He
2011-01-01
We present an analysis of the bifurcation phenomenon of a gel in contact with a solvent. When a Mooney-Rivlin form-free energy function is introduced, an asymmetric swelling may appear for a gel swelling under uniaxial constraint or subjected to equal dead loads, which results in an interesting pitchfork bifurcation phenomenon. We present an analytical investigation of this problem based on the classical theory of continuum mechanics. The bifurcation points are obtained for different values of the chemical potential of the solvent molecules. The results demonstrate that the free swelling of the gel under uniaxial constraint will not result in the bifurcation unless further mechanical loads are applied.%We present an analysis of the bifurcation phenomenon of a gel in contact with a solvent.When a Mooney-Rivlin form-free energy function is introduced,an asymmetric swelling may appear for a gel swelling under uniaxial constraint or subjected to equal dead loads,which results in an interesting pitchfork bifurcation phenomenon.We present an analytical investigation of this problem based on the classical theory of continuum mechanics.The bifurcation points are obtained for different values of the chemical potential of the solvent molecules.The results demonstrate that the free swelling of the gel under uniaxial constraint will not result in the bifurcation unless further mechanical loads are applied.Since gels commonly exist in our daily life and engineering society,they have aroused the great interest of a large number of researchers and have been intensely studied over the past few decades.[1-7] Most possible technical and biological applications include medical devices,[8] tissue engineering[9] and actuators responsive to physiological cues.[10,11] Many mechanical models[12-14] have been reported to develop a rigorous description of gels from either an experimental or a theoretical viewpoint.
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.
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
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.
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.
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.
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.
Coronary bifurcation angle from 3-D predicts clinical outcomes after stenting bifurcation lesions
Institute of Scientific and Technical Information of China (English)
CHEN Shao-liang; DING Shi-qing; Tak W Kwan; Teguh Santoso; ZHANG Jun-jie; YE Fei; XU Ya-wei; FU Qiang; KAN Jing; Chitprapai Paiboon; ZHOU Yong
2012-01-01
Background The predictive value of bifurcation angle (BA) for worse events after stenting bifurcation lesions remains to be unknown.The present study was to investigate the dynamic change of BA and clinical relevance for patients with coronary bifurcation lesions treated by drug-eluting stent (DES).Methods BA was calculated by 3-D quantitative coronary analysis from 347 patients in DKCRUSH-Ⅱ study.Primary endpoint was the occurrence of composite major adverse cardiac events (MACE) at 12-month,including cardiac death,myocardial infarction (MI) and target vessel revascularization (TVR).Secondary end points were the rate of binary restenosis and stent thrombosis at 12-month.Results Stenting was associated with the reduction of distal BA.The cut-off value of distal BAfor predicting MACE was 60° Distal BA in ＜60° group had less reduction after stenting ((-1.96±13.58)° vs.(-12.12±23.58)°,P ＜0.001 ); two-stent technique was associated with significant reduction of distal BA (△(-4.05±14.20)°),compared to single stent group (△+1.55±11.73,P=0.003); the target lesion revascularization (TLR),TVR and MACE rate was higher in one-stent group (16.5％,19.0％ and 21.5％),compared to two-stent group (3.8％,P=0.002; 7.5％,P=0.016; and 9.8％,P=0.024),respectively.Among patients in ≥60° group,there were no significant differences in distal BA,stent thrombosis (ST),MI,MACE,death,TLR,TVR between one- and two-stent groups; after stenting procedure,there was only slight change of distal BA in left anterior descending (LAD)-Ieft circumflex (LCX) subgroup (from (88.54±21.33)° at baseline to (82.44±31.72)° post-stenting),compared to either LAD-diagonal branch (Di),or LCX-obtuse marginal branch (OM),or RCA distal (RCAd) (all P ＜0.001 ).Conclusion Two-stent technique was associated with significant reduction of distal BA.DK crush stenting had reduced rate of MACE in patients in ＜60° group,compared to one-stent technique.
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels Ramsing; 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— B...
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.
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.
Secondary flow behavior in a double bifurcation
Leong, Fong Yew; Smith, Kenneth A.; Wang, Chi-Hwa
2009-04-01
Secondary flows in the form of multivortex structures can occur in bifurcation models as the result of upstream influence. Results from numerical modeling of steady inspiratory flows indicate that, for the case of a symmetric planar double bifurcation, four counter-rotating vortices develop in each of the grand daughter branches. In this paper, experimental visualization and verification is provided by particle image velocimetry measurements on a modified single bifurcation model. A splitter plate was positioned in the mother tube so that secondary vorticity was introduced into the fluid core. The axial velocity profile before the bifurcation junction resembles the M-shaped velocity profile commonly observed in bifurcated tube flows. The result of this manipulation is the development of a physically observable four-vortex configuration in the cross sections of the daughter branches, thus demonstrating the strong influence of upstream secondary vorticity. Through numerical visualization of vortex lines, it is shown that secondary vorticity is amplified by the extension of vortex lines due to secondary flow within the daughter tube. Order-of-magnitude arguments have been applied to the vorticity transport equation; and key dimensionless parameters have been obtained, accounting for curvature effects. Results indicate that the secondary vorticity goes through a maximum with increasing downstream distance, as a result of the interplay between vortex stretching and viscous effects.
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.
Anatomical description of arterial segments in the crab-eating raccoon kidney (Procyon cancrivorus
Directory of Open Access Journals (Sweden)
Natane Barbosa Barcelos
2012-06-01
Full Text Available Crab-eating raccoon is a middle-sized animal with a long tail, which is yellowish and has a black and ornate tip, presenting from 5 to 10 dark and yellow rings. The specimens live in equatorial and tropical forests, always close to rivers, swamps, marshes, and mangroves. Two specimens of Procyon cancrivorus were used, both killed by accident and, later on, sent to the Anatomy Laboratory of Universidade Federal de Goias (UFG, in the Jatai campus, where, starting from the renal arteries, the arterial segments were dissected with the aid of a stereoscopic microscope. As a result, the renal arteries were always viewed in a single manner, bifurcating into dorsal and ventral segments, subdivided into ventro-cranial, ventro-medial-cranial, ventro-medial, ventromedial-caudal, ventro-caudal, dorso-cranial, dorso-medial-cranial, dorso-medial, dorso-medial-caudal, and dorso-caudal segments, also observed in rabbit, agouti, wild boar, and ovines. This study showed an arterial distribution pattern which is also identified in the right and left kidneys, the penetration site of renal arteries coincide with the findings in mouse and differ from those in rat, golden hamster, and agouti. According to the distribution and arrangement, the renal morphology of Procyon cancrivorus is similar to that found in pets and wild animals. The recognition of renal artery branches shows to be highly relevant both for surgical interventions and future investigations which enhance the knowledge on this species.
Nonequilibrium Chemical Patterns and Their Bifurcations
Lee, Kyoung Jin
Stationary and dynamic patterns that arise in reaction-diffusion systems are investigated in laboratory experiments. Our study reveals several new types of pattern that have not been observed in previous studies. The new patterns are observed in a ferrocyanide-iodate-sulfite (FIS) system, and they include stationary lamellae, self -replicating spots, and repulsive waves. All are large amplitude patterns that are initiated by a finite amplitude perturbation. Our simulation results on a four-species FIS reaction diffusion model as well as several recent studies on other models by other researchers reveal similar patterns and pattern forming instabilities. The stationary lamellae form through transverse front instability and front repulsion, whereas the much studied small amplitude Turing structures form spontaneously at the onset of the Turing instability. The mechanism of self-replicating spots, which undergo a life-like process of birth through replication and death through overcrowding, is explained heuristically and rigorously by the Ising-Bloch front bifurcation recently studied by Meron and co-workers. The repulsive excitable waves are different from conventional excitable waves in that they do not collide and annihilate. Our earlier study investigates Turing patterns in chlorite-iodide-malonic acid (CIMA) system. We demonstrate that Turing patterns can form in a CIMA system even without the presence of a large molecule, the starch color indicator, which in a popular model plays a crucial role in Turing pattern formation. We speculate that the polyacrylamide gel used in our study plays a similar role to that of the starch indicator. The morphological transition of a Turing structure in a CIMA system was also investigated by changing the thickness of the gel medium.
Directory of Open Access Journals (Sweden)
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
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.
A model for the nonautonomous Hopf bifurcation
Anagnostopoulou, V.; Jäger, T.; Keller, G.
2015-07-01
Inspired by an example of Grebogi et al (1984 Physica D 13 261-8), we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold (1998 Random Dynamical Systems (Berlin: Springer)). The specific structure of these models allows a rigorous and thorough analysis of the bifurcation pattern. In particular, we show the existence of an invariant ‘generalised torus’ splitting off a previously stable central manifold after the second bifurcation point. The scenario is described in two different settings. First, we consider deterministically forced models, which can be treated as continuous skew product systems on a compact product space. Secondly, we treat randomly forced systems, which lead to skew products over a measure-preserving base transformation. In the random case, a semiuniform ergodic theorem for random dynamical systems is required, to make up for the lack of compactness.
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 ...
Lee, Chang-Joon; Uemiya, Nahoko; Ishihara, Shoichiro; Zhang, Yu; Qian, Yi
2013-06-01
Computational fluid dynamics simulations can provide important hemodynamic insights for investigating the effectiveness of carotid artery stenting, but its accuracy is dependent on the boundary conditions such as the outflow pressure, which is difficult to obtain by measurements. Many computational fluid dynamics simulations assume that the outflow pressure is constant (P = 0), but this method is likely to produce different results compared to clinical measurements. We have developed an alternative estimation method called the minimum energy loss method based on the concept of energy loss minimization at flow bifurcation. This new method has been tested on computational fluid dynamics simulation of two patients treated with carotid artery stenting, and its flow ratio at internal carotid artery and wall shear stress distribution was compared with the constant zero outlet pressure method. Three different procedure stages (prestent, poststent, and follow-up) were analyzed. The internal carotid artery flow ratio using the minimum energy loss method generally matched well with ultrasound measurements, but the internal carotid artery flow ratio based on zero outlet pressure method showed a large difference. Wall shear stress distributions varied between methods in response to the change in internal carotid artery flow rate. This study demonstrates the importance of accurate outlet boundary condition for assessing the long-term efficacy of carotid artery stenting and the risk of restenosis in treated patients.
Congenital pseudoarthrosis of the clavicle with bifurcation
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Narender Kumar Magu
2014-01-01
Full Text Available Congenital pseudoarthrosis of clavicle is a rare clinical entity. It usually presents as a swelling in the clavicular region at birth or soon after birth. Fitzwilliam′s original description of 60 subtypes of congenital pseudoarthrosis of clavicle have addressed several anatomical variants, e.g. association with cervical rib and abnormally vertical and elevated upper ribs. However, congenital pseudoarthrosis of clavicle associated with bifurcation is an atypical anatomic variant. To the best of our knowledge, this variant has never been mentioned in the literature. In the present report, we have described this subtype of symptomatic congenital pseudoarthrosis of the clavicle with bifurcation and its possible management.
Heteroclinic Bifurcation of Strongly Nonlinear Oscillator
Institute of Scientific and Technical Information of China (English)
ZHANG Qi-Chang; WANG Wei; LI Wei-Yi
2008-01-01
Analytical prediction of heteroclinic bifurcation of the strongly nonlinear oscillator is presented by using the extended normal form method.We consider the approximate periodic solution of the system subject to the quintic nonlinearity by introducing the undetermined fundamental frequency.For the occurrence of heteroclinicity,the bifurcation criterion is accomplished.It depends on the contact of the limit cycle with the saddle equilibrium.As is illustrated,the explicit application shows that the new results coincide very well with the results of numerical simulation when disturbing parameter is of arbitrary magnitude.PACS: 82.40.Bj,47.20.Ky,02.30.Hq
Basin bifurcation in quasiperiodically forced systems
Energy Technology Data Exchange (ETDEWEB)
Feudel, U.; Witt, A.; Grebogi, C. [Institut fuer Physik, Universitaet Potsdam, Am Neuen Palais, PF 601553, D-14415, Potsdam (Germany); Lai, Y. [Departments of Physics and Astronomy and of Mathematics, The University of Kansas, Lawrence, Kansas 66045 (United States); Grebogi, C. [Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States)
1998-09-01
In this paper we study quasiperiodically forced systems exhibiting fractal and Wada basin boundaries. Specifically, by utilizing a class of representative systems, we analyze the dynamical origin of such basin boundaries and we characterize them. Furthermore, we find that basin boundaries in a quasiperiodically driven system can undergo a unique type of bifurcation in which isolated {open_quotes}islands{close_quotes} of basins of attraction are created as a system parameter changes. The mechanism for this type of basin boundary bifurcation is elucidated. {copyright} {ital 1998} {ital The American Physical Society}
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
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.
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.
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.
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.
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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.
Johst, Sören; Maderwald, Stefan; Fischer, Anja; Quick, Harald H.; Ladd, Mark E.; Orzada, Stephan
2015-01-01
When performing non-enhanced time-of-flight MR angiography of the lower extremity arteries at 7 T with cardiac triggering, the acquisition time is a crucial consideration. Therefore, in previous studies, saturation RF pulses were applied only every second TR. In the axial source images a slight artifact with an appearance similar to aliasing could be observed. The purpose of this study was to investigate the origin of this artifact. The reason for the artifact is supposed to be related to the two effective TRs during acquisition caused by the sparsely applied saturation RF pulse. Several sequence variants were simulated and implemented within the sequence source code to examine this hypothesis. An adaptation of the excitation flip angles for each TR as well as a correction factor for the k-space data was calculated. Additionally, a different ordering of the k-space data during acquisition was implemented as well as the combination of the latter with the k-space correction factor. The observations from the simulations were verified using both a static and a flow phantom and, finally, in a healthy volunteer using the same measurement setup as in previous volunteer and patient studies. Of all implemented techniques, only the reordering of the k-space was capable of suppressing the artifact almost completely at the cost of creating a ringing artifact. The phantom measurements showed the same results as the simulations and could thus confirm the hypothesis regarding the origin of the artifact. This was additionally verified in the healthy volunteer. The origin of the artifact could be confirmed to be the periodic signal variation caused by two effective TRs during acquisition. PMID:25785837
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
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.
Comments on the Bifurcation Structure of 1D Maps
DEFF Research Database (Denmark)
Belykh, V.N.; Mosekilde, Erik
1997-01-01
-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...
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).
Stochastic Parameter Resonance of Road-Vehicle Systems and Related Bifurcation Problems
Wedig, Walter V.
The paper investigates stochastic dynamics of road-vehicle systems and related bifurcation problems. The ride on rough roads generates vertical car vibrations whose root-mean-squares are resonant for critical car speeds and vanish when the car velocity is increasing, infinitely. These investigations are extended to wheel suspensions with progressive spring characteristics. For weak but still positive damping, the car vibrations become unstable when the velocity reaches the parameter resonance near twice the critical speed bifurcating into stochastic chaos of larger non-stationary car vibrations.
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.
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....
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.
Bifurcation of Fredholm Maps II; The Dimension of the Set of Bifurcation Points
Pejsachowicz, Jacobo
2010-01-01
We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of nonlinear elliptic boundary value problems from the principal symbol of the linearization of the problem along the trivial branch of solutions.
Tarnopolski, Mariusz
2013-01-01
This paper presents bifurcation and generalized bifurcation diagrams for a rotational model of an oblate satellite. Special attention is paid to parameter values describing one of Saturn's moons, Hyperion. For various oblateness the largest Lyapunov Characteristic Exponent (LCE) is plotted. The largest LCE in the initial condition as well as in the mixed parameter-initial condition space exhibits a fractal structure, for which the fractal dimension was calculated. It results from the bifurcation diagrams of which most of the parameter values for preselected initial conditions lead to chaotic rotation. The First Recurrence Time (FRT) diagram provides an explanation of the birth of chaos and the existence of quasi-periodic windows occuring in the bifurcation diagrams.
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.
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
[Longitudinal stent deformation during bifurcation lesion treatment].
Mami, Z; Monsegu, J
2014-12-01
Longitudinal stent deformation is defined as a compression of stent length after its implantation. It's a rare complication but dangerous seen with several stents. We reported a case of longitudinal stent deformation during bifurcation lesion treatment with a Promus Element(®) and we perform a short review of this complication.
On the direction of pitchfork bifurcation
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Xiaojie Hou
2007-02-01
Full Text Available We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.
Moment of inertia, backbending, and molecular bifurcation.
Tyng, Vivian; Kellman, Michael E
2007-07-28
We predict an anomaly in highly excited bending spectra of acetylene with high vibrational angular momentum. We interpret this in terms of a vibrational shape effect with moment of inertia backbending, induced by a sequence of bifurcations with a transition from "local" to "orthogonal" modes.
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.
Bifurcation structure of successive torus doubling
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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.
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...
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.
Effect of particle collisions and aggregation on red blood cell passage through a bifurcation.
Chesnutt, J K W; Marshall, J S
2009-12-01
Blood flow through bifurcating vessels in the microvasculature leads to uneven distribution of red blood cells (RBC) in the downstream channels when the channels have different sizes or the flow rates through the channels are different. This phenomenon, known as plasma skimming, is responsible for the large variation in hematocrit throughout the circulatory system. Furthermore, the strong streamline curvature present within bifurcations leads to frequent collisions between the blood elements (red and white blood cells and platelets) and the vessel walls, as well as a rearrangement of the distribution of the blood elements in the channels downstream of the bifurcation. Computational models of bifurcation flows typically neglect collision and adhesion of RBCs with each other. In this paper, we use a new type of discrete-element model to investigate the effect of particle-particle collisions and RBC aggregation on modeling of plasma skimming in bifurcations. Cases are examined with and without RBC adhesion and for different hematocrit values, including validation against previous computational results. Results show significant plasma skimming in the low-flow daughter branch and an increase in fractional particle flux with increased hematocrit, as in experimental studies. Accounting for particle-particle collisions leads to a considerable increase in collision rate of particles with the vessel wall. Particles are found to approximately follow fluid velocity streamlines, and consequently particle-particle collisions and aggregation do not significantly affect plasma skimming.
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.
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.
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.
Patient-specific structural effects on hemodynamics in the ischemic lower limb artery
Xu, Pengcheng; Liu, Xin; Song, Qi; Chen, Guishan; Wang, Defeng; Zhang, Heye; Yan, Li; Liu, Dan; Huang, Wenhua
2016-12-01
Lower limb peripheral artery disease is a prevalent chronic non-communicable disease without obvious symptoms. However, the effect of ischemic lower limb peripheral arteries on hemodynamics remains unclear. In this study, we investigated the variation of the hemodynamics caused by patient-specific structural artery characteristics. Computational fluid dynamic simulations were performed on seven lower limb (including superficial femoral, deep femoral and popliteal) artery models that were reconstructed from magnetic resonance imaging. We found that increased wall shear stress (WSS) was mainly caused by the increasing severity of stenosis, bending, and branching. Our results showed that the increase in the WSS value at a stenosis at the bifurcation was 2.7 Pa. In contrast, the isolated stenosis and branch caused a WSS increase of 0.7 Pa and 0.5 Pa, respectively. The WSS in the narrow popliteal artery was more sensitive to a reduction in radius. Our results also demonstrate that the distribution of the velocity and pressure gradient are highly structurally related. At last, Ultrasound Doppler velocimeter measured result was presented as a validation. In conclusion, the distribution of hemodynamics may serve as a supplement for clinical decision-making to prevent the occurrence of a morbid or mortal ischemic event.
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.
Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
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Jie Ran
2015-01-01
Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.
A Fractional-Order Phase-Locked Loop with Time-Delay and Its Hopf Bifurcation
Yu, Ya-Juan; Wang, Zai-Hua
2013-11-01
A fractional-order phase-locked loop (PLL) with a time-delay is firstly proposed on the basis of the fact that a capacitor has memory. The existence of Hopf bifurcation of the fractional-order PLL with a time-delay is investigated by studying the root location of the characteristic equation, and the bifurcated periodic solution and its stability are studied simply by using “pseudo-oscillator analysis". The results are checked by numerical simulation. It is found that the fractional-order PLL with a time-delay reduces the locking time, and it minimizes the amplitude of the bifurcated periodic solution when the order is properly chosen.
Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model
Ren, Jingli; Yu, Liping
2016-12-01
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.
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.
Sixth International Symposium on Bifurcations and Instabilities in Fluid Dynamics (BIFD2015)
DEFF Research Database (Denmark)
Bar-Yoseph, P. Z.; Brøns, Morten; Gelfgat, A.
2016-01-01
Hydrodynamic stability is of fundamental importance in fluid dynamics. As a well-established subject of scientific investigation, it continues to attract great interest in the fluid mechanics community. Bifurcations and instabilities are observed in all areas of fundamental and applied fluid...... dynamics and remain a challenge for experimental, theoretical and computational studies. Examples of prototypical hydrodynamic instabilities are the Rayleigh–Bénard, Taylor–Couette, Bénard–Marangoni, Rayleigh–Taylor, and Kelvin–Helmholtz instabilities. A fundamental understanding of bifurcation patterns...... International Symposium on Instability and Bifurcations in Fluid Dynamics (BIFD) held at the ESPCI, Paris, 15–17 July2015. With four invited and nearly 400 contributed talks, the symposium gave an overview of the state of the art of the field including experimental, theoretical, and computational approaches...
Control-based continuation: Bifurcation and stability analysis for physical experiments
Barton, David A. W.
2017-02-01
Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.
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.
Bifurcation and chaos in a ratio-dependent predator-prey system with time delay
Energy Technology Data Exchange (ETDEWEB)
Gan Qintao [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China)], E-mail: ganqintao@sina.com; Xu Rui [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China); Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China); Yang Pinghua [Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003 (China)
2009-02-28
In this paper, a ratio-dependent predator-prey model with time delay is investigated. We first consider the local stability of a positive equilibrium and the existence of Hopf bifurcations. By using the normal form theory and center manifold reduction, we derive explicit formulae which determine the stability, direction and other properties of bifurcating periodic solutions. Finally, we consider the effect of impulses on the dynamics of the above time-delayed population model. Numerical simulations show that the system with constant periodic impulsive perturbations admits rich complex dynamic, such as periodic doubling cascade and chaos.
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.
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.
Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without ilnikov Orbits
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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.
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.
Automated characterization of blood vessels as arteries and veins in retinal images.
Mirsharif, Qazaleh; Tajeripour, Farshad; Pourreza, Hamidreza
2013-01-01
In recent years researchers have found that alternations in arterial or venular tree of the retinal vasculature are associated with several public health problems such as diabetic retinopathy which is also the leading cause of blindness in the world. A prerequisite for automated assessment of subtle changes in arteries and veins, is to accurately separate those vessels from each other. This is a difficult task due to high similarity between arteries and veins in addition to variation of color and non-uniform illumination inter and intra retinal images. In this paper a novel structural and automated method is presented for artery/vein classification of blood vessels in retinal images. The proposed method consists of three main steps. In the first step, several image enhancement techniques are employed to improve the images. Then a specific feature extraction process is applied to separate major arteries from veins. Indeed, vessels are divided to smaller segments and feature extraction and vessel classification are applied to each small vessel segment instead of each vessel point. Finally, a post processing step is added to improve the results obtained from the previous step using structural characteristics of the retinal vascular network. In the last stage, vessel features at intersection and bifurcation points are processed for detection of arterial and venular sub trees. Ultimately vessel labels are revised by publishing the dominant label through each identified connected tree of arteries or veins. Evaluation of the proposed approach against two different datasets of retinal images including DRIVE database demonstrates the good performance and robustness of the method. The proposed method may be used for determination of arteriolar to venular diameter ratio in retinal images. Also the proposed method potentially allows for further investigation of labels of thinner arteries and veins which might be found by tracing them back to the major vessels.
Uncertainty analysis near bifurcation of an aeroelastic system
Ghommem, M.; Hajj, M. R.; Nayfeh, A. H.
2010-08-01
Variations in structural and aerodynamic nonlinearities on the dynamic behavior of an aeroelastic system are investigated. The aeroelastic system consists of a rigid airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We follow two approaches to determine the effects of variations in the linear and nonlinear plunge and pitch stiffness coefficients of this aeroelastic system on its stability near the bifurcation. The first approach is based on implementation of intrusive polynomial chaos expansion (PCE) on the governing equations, yielding a set of nonlinear coupled ordinary differential equations that are numerically solved. The results show that this approach is capable of determining sensitivity of the flutter speed to variations in the linear pitch stiffness coefficient. On the other hand, it fails to predict changes in the type of the instability associated with randomness in the cubic stiffness coefficient. In the second approach, the normal form is used to investigate the flutter (Hopf bifurcation) boundary that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing LCO. The results show that this mathematical approach provides detailed aspects of the effects of the different system nonlinearities on its dynamic behavior. Furthermore, this approach could be effectively used to perform sensitivity analysis of the system's response to variations in its parameters.
Energy Technology Data Exchange (ETDEWEB)
Yamada, Naoaki; Ogino, Hitoshi; Hanabusa, Yuji; Sasaki, Hiroaki; Minatoya Kenji [National Cardiovascular Center, Suita, Osaka (Japan)
2003-01-01
We reviewed 106 cases who underwent MR angiography to visualize the Adamkiewicz artery (AKA) as a preoperative evaluation of the thoracic descending and thoracoabdominal aortic aneurysms. MR angiography depicted the AKA successfully in 68% of the patients. However, segmental artery that gives rise the AKA was occluded in 41% at its origin from the aorta. In one patient with postoperative paraplegia, broad infarction in the upper thoracic cord seems not to be related to the territory of the AKA that was visualized by MR angiography. Preoperative MR angiography serves planning of surgery, and can reduce time of aortic cross-clamping. However, our understanding of the value of MR angiography to prevent spinal cord ischemic injury requires further clinical investigation. (author)
Institute of Scientific and Technical Information of China (English)
Ma Shao-Juan; Xu Wei; Li Wei; Fang Tong
2006-01-01
The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter.Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.
Directory of Open Access Journals (Sweden)
Liming Zhao
2016-01-01
Full Text Available First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.
Lesauskaite, Vaiva; Stalioraityte, Elena; Tanganelli, Piero; Epistolato, Maria Carmela
2004-01-01
We present a review of data from epidemiological and morphological studies carried out in Kaunas of atherosclerosis in youths. Since 1985, Kaunas has been a Collaborating Center involved with the World Health Organization and International Society and Federation of Cardiology studying the pathobiological determinants of atherosclerosis in youth. During the pilot study (1985-1987), we estimated the prevalence and extent of atherosclerotic lesions in the aorta and coronary arteries correlated to various risk factors in Kaunas residents aged 5 to 44 years. Within the framework of this international study, we compared histomorphometric characteristics of arteries collected from trauma victims aged 5 to 34 years in Budapest (Hungary), Heidelberg (Germany), Kaunas (Lithuania), Yaounde (Cameroon), and Mexico City (Mexico). These data revealed that males from countries with a high mortality from ischemic heart disease (Hungary, Lithuania, Germany) tended to have thicker intima in the thoracic and abdominal aorta and left anterior descending coronary artery than did males from countries with low mortality from ischemic heart disease (Mexico, Cameroon). We detected an increased mean intimal thickness of the abdominal aorta in male smokers aged 25-34 years. Males with hypertension aged 15-24 and 25-34 years had a thicker intima in the aorta and left anterior descending coronary artery than normotensive males. The morphological and epidemiological studies of atherosclerosis in youths carried out in Kaunas demonstrated that aortic and coronary atherosclerotic lesions appeared as early as childhood and advanced until the lesions become clinically apparent in adulthood. Histomorphometric findings support the postulate that increased intimal thickness can be considered a structural determinant of atherogenesis. These data draw attention to the means for the primary prevention of atherosclerosis in youth.
Energy Technology Data Exchange (ETDEWEB)
Nadeem, S.; Ijaz, S., E-mail: shagufta.me2011@yahoo.com
2016-07-15
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. - Highlights: • The contribution of copper and silver nanoparticles as drug carrier reveals that they are important to reduce hemodynamic of stenosis. • The heat is dissipated throughout the considered inclined artery with an increase in the nanoparticle volume fraction. • The stress on the wall of inclined arteries decreases with an increase in the magnetic Reynolds number and Strommers number.
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.
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...
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.
Experimental bifurcation analysis of an impact oscillator - Tuning a non-invasive control scheme
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Santos, Ilmar
2013-01-01
We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype for electromag...
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...
Bifurcation in a Class of Planar Piecewise Smo oth Systems with 3-parameters
Institute of Scientific and Technical Information of China (English)
Liu Yuan-yuan; Chai Zhen-hua; Ma Fu-ming(Communicated)
2014-01-01
This paper is concerned with the bifurcation properties on the line of discontinuity of planar piecewise smooth systems. The existence of equilibria and periodic solutions with sliding motion in a class of planar piecewise smooth systems with 3-parameters is investigated in this paper using the theory of differential inclu-sion and tools of Poincar´e maps.
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Torus bifurcations in multilevel converter systems
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes....... 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....
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.
A STUDY OF INSULAR SEGMENT OF MIDDLE CEREBRAL ARTERY IN NORTHERN INDIA
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Medha Das
2016-08-01
Full Text Available The microsurgical anatomy of middle cerebral artery is of particular interest to the cerebrovascular surgeons as it supplies most of the superolateral surface of cerebral hemispheres and is the most commonly involved artery in stroke. The insular segment (M2 segment begins at the limen insulae and runs on the surface of the insula in the sylvian insular cistern with a superoposterior direction. The M2 segment consists of two or three branches that arise from the bifurcation or trifurcation of the M1. After reaching the top of the insula, these branches turn inferolaterally and exit from the sylvian insular cistern forming the M3 segment. OBJECTIVE Certain clinical conditions like aneurysms and glioma of the M2 segment aneurysms demands special attention due to vascular complexity of the insular area and peculiar clinical characteristics. The present study was carried out for a better understanding and to define further the microsurgical anatomy of the insular segment of middle cerebral artery hoping to find immediate application of our findings in the field of microsurgical cerebral revascularisation and better interpretation of radiological angiographic investigations performed in cases of young cerebral haemorrhages. The present study also elaborates the directly observed dissection findings rather than the other studies, which are mostly based on radiological findings. MATERIALS AND METHODS Total 20 Middle Cerebral Arteries (MCA were studied obtained from 10 brains. Meticulous dissection was done and middle cerebral artery and its branches were exposed and cleaned in lateral sulcus on the inferior surface of brain. Digital photographs were taken. The number of samples was based on the availability of cadavers in the mentioned institute during the time of study. RESULT In all 20 MCAs, bifurcation was noted. In 15 out of 20 specimens, more than one major cortical branch was given by M1 segment before its division into secondary trunks at insula
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
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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.
Directory of Open Access Journals (Sweden)
Baskar Sekar
2015-01-01
Full Text Available 462 patients presenting with chest pain to a rural district general hospital underwent calcium scoring and pretest clinical risk assessment in order to stratify subsequent investigations and treatment was retrospectively reviewed. The patients were followed up for two years and further investigations and outcomes recorded. Of the 206 patients with zero calcium score, 132 patients were immediately discharged from cardiac follow-up with no further investigation on the basis of their calcium score, low pretest risk of coronary artery disease, and no significant incidental findings. After further tests, 267 patients were discharged with no further cardiac therapy, 88 patients were discharged with additional medical therapy, and 19 patients underwent coronary artery by-pass grafting or percutaneous intervention. 164 patients with incidental findings on the chest CT (computed tomography accompanying calcium scoring were reviewed, of which 88 patients underwent further tests and follow-up for noncardiac causes of chest pain. The correlations between all major risk factors and calcium scores were weak except for a combination of diabetes and hypertension in the male gender (P=0.012, The use of calcium scoring and pretest risk appeared to reduce the number of unnecessary cardiac investigations in our patients: however, the calcium scoring test produced a high number of incidental findings on the associated CT scans.
Energy Technology Data Exchange (ETDEWEB)
Ji, Cheol; Ahn, Jae Geun; Cho, Song Mee [Catholic University, St. Paul' s Hospital, Seoul (Korea, Republic of)
2009-06-15
A ruptured aneurysm at the bifurcation of the left middle cerebral artery with an infra- optic course of the bilateral anterior cerebral arteries was found in a 28-year-old woman. Both abnormal anterior cerebral arteries arose from the ipsilateral internal carotid arteries, at the level of the origin of ophthalmic arteries, passed underneath the ipsilateral optic nerves and turned upward at the ventral portion of the optic chiasm. In addition, an aortic coarctation was found with the use of thoracic aortography. An infra-optic course of the bilateral anterior cerebral arteries is an extremely rare anomaly. An infra-optic course of the bilateral anterior cerebral arteries is frequently associated with cerebral aneurysms and possibly with a coarctation aorta. The clinical features, radiological findings and possible genesis of this anomaly are presented.
Higashino, Takuya; Kawashima, Masatou; Mannoji, Hiromichi
2005-03-01
An 89-year-old man and a 60-year-old man presented with superficial temporal artery (STA) pseudoaneurysms which developed secondary to trauma. Conventional cerebral angiography and three-dimensional computed tomography (3D CT) angiography clearly demonstrated the STA pseudoaneurysms. The patients underwent surgical excision of the aneurysms based on the conventional cerebral angiography findings in one patient and 3D CT angiography findings in other patient. 3D CT angiography is an excellent noninvasive diagnostic method for detecting extracranial aneurysms such as STA pseudoaneurysm, especially the relationship between the aneurysm and surrounding structures, including the calvarium.
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.
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.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
Institute of Scientific and Technical Information of China (English)
吴金平; 侯安新; 黄定华; 鲍征宇; 高志农; 屈松生
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.
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.
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS IN VARIANT BOUSSINESQ EQUATIONS
Institute of Scientific and Technical Information of China (English)
YUAN Yu-bo; PU Dong-mei; LI Shu-min
2006-01-01
The bifurcations of solitary waves and kink waves for variant Boussinesq equations are studied by using the bifurcation theory of planar dynamical systems. The bifurcation sets and the numbers of solitary waves and kink waves for the variant Boussinesq equations are presented. Several types explicit formulas of solitary waves solutions and kink waves solutions are obtained. In the end, several formulas of periodic wave solutions are presented.
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
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.
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.
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...
Automatic segmentation of the lumen of the carotid artery in ultrasound B-mode images
Santos, AMF; tavares, jmrs; Sousa, L.; Santos, R.; CASTRO,P; E. Azevedo
2013-01-01
A new algorithm is proposed for the segmentation of the lumen and bifurcation boundaries of the carotid artery in B-mode ultrasound images. It uses the hipoechogenic characteristics of the lumen for the identification of the carotid boundaries and the echogenic characteristics for the identification of the bifurcation boundaries. The image to be segmented is processed with the application of an anisotropic diffusion filter for speckle removal and morphologic operators are employed in the dete...
AUTOMATIC SEGMENTATION ALGORITHM FOR THE LUMEN OF THE CAROTID ARTERY IN ULTRASOUND B-MODE IMAGES
Santos, AMF; João Manuel R. S. Tavares; Sousa, L.; Santos, R.; CASTRO,P; E. Azevedo
2012-01-01
A new algorithm is proposed for the identification and segmentation of the lumen and bifurcation boundaries of the carotid artery in 2D longitudinal ultrasound B-mode images. It uses the hipoechogenic characteristics defining the lumen of the carotid for its identification and echogenic characteristics for the identification of the bifurcation. The input image is preprocessed with the application of an anisotropic diffusion filter for speckle removal, and morphologic operators for the detecti...
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.
Bifurcation and stability for a nonlinear parabolic partial differential equation
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
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.
The Structure and Bifurcation of Atmospheric Motions
Institute of Scientific and Technical Information of China (English)
刘式适; 刘式达; 付遵涛; 辛国君; 梁福明
2004-01-01
The 3-D spiral structure resulting from the balance between the pressure gradient force, Coriolis force, and viscous force is a common atmospheric motion pattern. If the nonlinear advective terms are considered, this typical pattern can be bifurcated. It is shown that the surface low pressure with convergent cyclonic vorticity and surface high pressure with divergent anticyclonic vorticity are all stable under certain conditions. The anomalous structure with convergent anticyclonic vorticity is always unstable. But the anomalous weak high pressure structure with convergent cyclonic vorticity can exist, and this denotes the cyclone's dying out.
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.
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.
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.
Directory of Open Access Journals (Sweden)
F Joibar
2013-12-01
Results: The outcome of nitric oxide plasmatic density measurement showed that nitric oxide level in animal ’s blood in 175 mg/kg/day dose recipient group and 350 mg/kg/day dose recipient group increased significantly compared with the control group at the level of P ≤ 0.05. Also thickness of media layer decreased in maximum dose group (350 mg/kg/day dose compared to the control group. Conclusion: Based on the results of different doses of sodium nitrite, the nitric oxide levels in the blood were increased, and the thickness of middle layer of the lung arteries at dose 350 mg of sodium nitrite was reduced.
Bifurcation analysis of vertical transmission model with preventive strategy
Directory of Open Access Journals (Sweden)
Gosalamang Ricardo Kelatlhegile
2016-07-01
Full Text Available We formulate and analyze a deterministic mathematical model for the prevention of a disease transmitted horizontally and vertically in a population of varying size. The model incorporates prevention of disease on individuals at birth and adulthood and allows for natural recovery from infection. The main aim of the study is to investigate the impact of a preventive strategy applied at birth and at adulthood in reducing the disease burden. Bifurcation analysis is explored to determine existence conditions for establishment of the epidemic states. The results of the study showed that in addition to the disease-free equilibrium there exist multiple endemic equilibria for the model reproduction number below unity. These results may have serious implications on the design of intervention programs and public health policies. Numerical simulations were carried out to illustrate analytical results.
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.
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.
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.
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.
KURISU, Kota; OSANAI, Toshiya; KAZUMATA, Ken; NAKAYAMA, Naoki; ABUMIYA, Takeo; SHICHINOHE, Hideo; SHIMODA, Yusuke; HOUKIN, Kiyohiro
2016-01-01
Although ultrasound (US) guidance for venous access is becoming the “standard of care” for preventing access site complications, its feasibility for arterial access has not been fully investigated, especially in the neuro-interventional population. We conducted the first prospective cohort study on US-guided femoral artery access during neuro-interventional procedure. This study included 64 consecutive patients who underwent US-guided femoral artery access through 66 arterial access sites for diagnostic and/or neuro-interventional purposes. The number of attempts required for both the sheath insertion and the success of anterior wall puncture were recorded. In addition, the occurrence of major complications and hematoma formation on the arterial access site examined by US were statistically analyzed. The median number of attempts was 1 (1–2) and first-pass success rate was 63.6%. Anterior wall puncture was achieved in 98.5%. In one case (1.5%), a pseudoaneurysm was observed. In all cases, US clearly depicted a common femoral artery (CFA) and its bifurcation. Post-procedural hematoma was detected in 13 cases (19.7%), most of which were “tiny” or “moderate” in size. Low body mass index and antiplatelet therapy were the independent risk factors for access site hematoma. The US-guided CFA access was feasible even in neuro-interventional procedure. The method was particularly helpful in the patients with un-palpable pulsation of femoral arteries. To prevent arterial access site hematoma, special care should be taken in patients with low body mass index and who are on antiplatelet therapy. PMID:27194178
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.
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.
Ecological public goods games: cooperation and bifurcation.
Hauert, Christoph; Wakano, Joe Yuichiro; Doebeli, Michael
2008-03-01
The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565-2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation.
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...
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.
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.
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.
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.
Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues
Institute of Scientific and Technical Information of China (English)
Tian Si ZHANG; De Ming ZHU
2006-01-01
Codimension-3 bifurcations of an orbit-flip homoclinic orbit with resonant principal eigenvalues are studied for a four-dimensional system. The existence, number, co-existence and non-coexistence of 1-homoclinic orbit, 1-periodic orbit, 2n-homoclinic orbit and 2n-periodic orbit are obtained. The bifurcation surfaces and existence regions are also given.
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.
Verification of bifurcation diagrams for polynomial-like equations
Korman, Philip; Li, Yi; Ouyang, Tiancheng
2008-03-01
The results of our recent paper [P. Korman, Y. Li, T. Ouyang, Computing the location and the direction of bifurcation, Math. Res. Lett. 12 (2005) 933-944] appear to be sufficient to justify computer-generated bifurcation diagram for any autonomous two-point Dirichlet problem. Here we apply our results to polynomial-like nonlinearities.
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.
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...
Intermittency and Jakobson's theorem near saddle-node bifurcations
Homburg, A.J.; Young, T.
2007-01-01
Abstract. We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. We show that there is a parameter set of positive but not full Lebesgue density at the bifurcation, for which the maps exhibit absolutely continuous invariant measu
Coarse-grained numerical bifurcation analysis of lattice Boltzmann models
Leemput, P. Van; Lust, K.W.A.; Kevrekidis, I.G.
2005-01-01
In this paper we study the coarse-grained bifurcation analysis approach proposed by I.G. Kevrekidis and collaborators in PNAS [C. Theodoropoulos, Y.H. Qian, I.G. Kevrekidis, "Coarse" stability and bifurcation analysis using time-steppers: a reaction-diffusion example, Proc. Natl. Acad. Sci. 97 (18)
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
Directory of Open Access Journals (Sweden)
Xianbin Wang
2015-01-01
Full Text Available The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.
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.
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.
Critical bifurcation surfaces of 3D discrete dynamics
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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.
Streamline topologies and their bifurcations for mixed convective peristaltic flow
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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.
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.
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.
Acute arterial occlusion - kidney
Acute renal arterial thrombosis; Renal artery embolism; Acute renal artery occlusion; Embolism - renal artery ... kidney can often result in permanent kidney failure. Acute arterial occlusion of the renal artery can occur after injury or trauma to ...
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.
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.
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.
Local effects of atherosclerotic plaque on arterial distensibility.
Giannattasio, C; Failla, M; Emanuelli, G; Grappiolo, A; Boffi, L; Corsi, D; Mancia, G
2001-11-01
Hypertension, diabetes, and hypercholesterolemia are characterized by a reduction in arterial distensibility and by accelerated atherosclerosis. Whether arterial stiffening is an inherent feature of these conditions or just the consequence of the atherosclerotic clinical or subclinical lesions is not known, however. Our aim was to obtain information on this issue by directly measuring, in humans, arterial distensibility both at the site of an atherosclerotic lesion and at the proximal normal site. In 10 patients (8 men; mean+/-SEM age, 65.2+/-3.4 years) affected by monolateral hemodynamic significant internal carotid artery stenosis, we measured arterial distensibility (Wall Track System; PIE Medical) bilaterally, both at the internal carotid artery and at the common carotid artery level. In the common carotid artery, measurements were made 3 cm below the bifurcation. In the affected internal carotid artery, measurements were made at the plaque shoulder (wall thickness of 2 mm). Measurements were made in the contralateral internal carotid artery at a symmetrical level. Arterial wall thickness was measured in the same site of arterial distensibility. Arterial distensibility was less in the internal than in the common carotid artery, with a marked reduction at the plaque internal carotid artery level compared with the corresponding contralateral site (-45%, P<0.01). It was also less, however, in the common carotid artery branching into the atherosclerotic internal carotid artery than in the contralateral common carotid artery (-25%, P<0.05). Wall thickness was similar in the 2 common carotid arteries and obviously greater in the affected internal carotid artery than in the contralateral artery. Arterial distensibility was markedly less in the internal carotid artery where there was a plaque compared with the intact contralateral internal carotid artery; it was also less, however, in the common carotid artery of the affected side in comparison with the contralateral
Long-term effect of stenting in unprotected left main coronary artery disease in the elderly
Institute of Scientific and Technical Information of China (English)
Caiyi LU; Pinfa LIU; Jicai ZANG; Shiwen WANG; Lingling LIU; Qiao XUE; Xinli WU; Taohong HU; Pingshuan DONG; Zhiping WANG; Shenfang TIAN
2005-01-01
To evaluate the feasibility, safety and efficacy of percutaneous stent implantation for treating left main coronary artery (LMCA) stenosis. Methods Consecutive patients with unprotected left main coronary artery disease treated by stent-based percutaneous intervention (PCI) at 6 medical centers in China were enrolled. Procedural data and clinical outcomes were obtained from all patients. Results From January 2001 to December 2004, 138 patients (79 males and 59 females; mean age: 69.7±5.8 years)underwent PCI for LMCA stenosis. Bare metal stents (BMS) were implanted in 51 patients with non-bifurcational lesions and in 5 patients with bifurcational lesions from January of 2001 to June of 2003 (BMS group);. Drug eluting stents (DES) were used unselectively to cover both bifurcational and non-bifurcational lesions in 86 patients from July of 2003 to December of 2004 (DES group). Procedural success rate of the 138 cases was 98% (135/138). One patient (0.7%) with bifurcation lesion who was treated with DES died from severe heart failure 2 weeks after the procedure. During a mean follow up period of 21.3 ± 5.6 months, one patient died from renal failure, one from sudden cardiac death, 4 underwent target lesion revascularization (TLR) in the BMS group, which all occurred in patients with bifurcational lesions; whereas in the DES group no deaths occurred and only one patient with bifurcational lesion had TLR. Conclusions (1) PCI is feasible and relatively safe to treat unprotected left main coronary artery disease in elderly patients at medical centers with experienced professionals. (2) BMS and DES have similar immediate and long-term efficacy in the treatment of ostium and shaft lesions of the LMCA. (3) DES are strongly suggested in the therapy of distal bifurcation lesion of unprotected LMCA.
Shell structure and orbit bifurcations in finite fermion systems
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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).
Climate bifurcation during the last deglaciation?
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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
Blood tracer kinetics in the arterial tree.
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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.
Bifurcated SEN with Fluid Flow Conditioners
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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.
Transport Bifurcation in Plasma Interchange Turbulence
Li, Bo
2016-10-01
Transport bifurcation and mean shear flow generation in plasma interchange turbulence are explored with self-consistent two-fluid simulations in a flux-driven system with both closed and open field line regions. The nonlinear evolution of interchange modes shows the presence of two confinement regimes characterized by the low and high mean flow shear. By increasing the input heat flux above a certain threshold, large-amplitude oscillations in the turbulent and mean flow energy are induced. Both clockwise and counter-clockwise types of oscillations are found before the transition to the second regime. The fluctuation energy is decisively transferred to the mean flows by large-amplitude Reynolds power as turbulent intensity increases. Consequently, a transition to the second regime occurs, in which strong mean shear flows are generated in the plasma edge. The peak of the spectrum shifts to higher wavenumbers as the large-scale turbulent eddies are suppressed by the mean shear flow. The transition back to the first regime is then triggered by decreasing the input heat flux to a level much lower than the threshold for the forward transition, showing strong hysteresis. During the back transition, the mean flow decreases as the energy transfer process is reversed. This transport bifurcation, based on a field-line-averaged 2D model, has also been reproduced in our recent 3D simulations of resistive interchange turbulence, in which the ion and electron temperatures are separated and the parallel current is involved. Supported by the MOST of China Grant No. 2013GB112006, US DOE Contract No. DE-FC02-08ER54966, US DOE by LLNL under Contract DE-AC52-07NA2734.
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:
Neimark-Sacker Bifurcation and Chaotic Behaviour of a Modified Host-Parasitoid Model
Din, Qamar; Gümüş, Özlem Ak; Khalil, Hammad
2017-01-01
We study some qualitative behaviour of a modified discrete-time host-parasitoid model. Modification of classical Nicholson-Bailey model is considered by introducing Pennycuick growth function for the host population. Furthermore, the existence and uniqueness of positive equilibrium point of proposed system is investigated. We prove that the positive solutions of modified system are uniformly bounded and the unique positive equilibrium point is locally asymptotically stable under certain parametric conditions. Moreover, it is also investigated that system undergoes Neimark-Sacker bifurcation by using standard mathematical techniques of bifurcation theory. Complexity and chaotic behaviour are confirmed through the plots of maximum Lyapunov exponents. In order to stabilise the unstable steady state, the feedback control strategy is introduced. Finally, in order to support theoretical discussions, numerical simulations are provided.
Bistability and Bifurcation in Minimal Self-Replication and Nonenzymatic Catalytic Networks.
Wagner, Nathaniel; Mukherjee, Rakesh; Maity, Indrajit; Peacock-Lopez, Enrique; Ashkenasy, Gonen
2017-01-23
Bistability and bifurcation, found in a wide range of biochemical networks, are central to the proper function of living systems. We investigate herein recent model systems that show bistable behavior based on nonenzymatic self-replication reactions. Such models were used before to investigate catalytic growth, chemical logic operations, and additional processes of self-organization leading to complexification. By solving for their steady-state solutions by using various analytical and numerical methods, we analyze how and when these systems yield bistability and bifurcation and discover specific cases and conditions producing bistability. We demonstrate that the onset of bistability requires at least second-order catalysis and results from a mismatch between the various forward and reverse processes. Our findings may have far-reaching implications in understanding early evolutionary processes of complexification, emergence, and potentially the origin of life.
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.
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.
Ye, Swe Soe; Ju, Meongkeun; Kim, Sangho
2016-07-01
Unequal RBC partitioning at arteriolar bifurcations contributes to dissimilar flow developments between daughter vessels in a bifurcation. Due to the importance of the cell-free layer (CFL) and the wall shear stress (WSS) to physiological processes such as vasoregulation and gas diffusion, we investigated the effects of a bifurcation disturbance on the development of the CFL width and WSS in bifurcation daughter branches. The analysis was performed on a two-dimensional (2-D) computational model of a transverse arteriole at three different flow rates corresponding to parent branch (PB) pseudoshear rates of 60, 170 and 470s(-1), while maintaining a 2-D hematocrit of about 55% in the PB. Flow symmetry was defined using the statistical similarity of the CFL and WSS distributions between the two walls of the vessel branch. In terms of the flow symmetry recovery, higher flow rates caused larger reductions in the flow symmetry indices in the MB and subsequently required longer vessel lengths for complete recovery. Lower tube hematocrits in the SB led to complete symmetry recovery for all flow rates despite the higher initial asymmetry in the SB than in the MB. Arteriolar bifurcations produce unavoidable local CFL asymmetry and the persistence of the asymmetry downstream may increase effective blood viscosity which is especially significant at higher physiological flow rates.
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.
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.
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.
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.
Influence of arterial geometry on a model for growth rate of atheromas
Energy Technology Data Exchange (ETDEWEB)
Gessaghi, Valeria C [Facultad de Ingenieria, Universidad Nacional de La Pampa, General Pico, La Pampa (Argentina); Raschi, Marcelo A [Facultad de Ingenieria y Ciencias Exactas y Centro de Estudios Avanzados, Universidad Argentina de la Empresa, Ciudad Autonoma de Buenos Aires (Argentina); Larreteguy, Axel E [Facultad de Ingenieria y Ciencias Exactas y Centro de Estudios Avanzados, Universidad Argentina de la Empresa, Ciudad Autonoma de Buenos Aires (Argentina); Perazzo, Carlos A [Facultad de Ingenieria y Ciencias Exactas y Naturales, Universidad de Favaloro, Ciudad Autonoma de Buenos Aires, Argentina y CONICET (Argentina)
2007-11-15
Atherosclerosis is a disease that affects medium and large size arteries and it can partially or totally obstruct blood flow through them. The lack of blood supply to the heart or the brain can cause an infarct or a stroke with fatal consequences or permanent effects. This disease involves the proliferation of cells and the accumulation of fat, cholesterol, cell debris, calcium and other substances in the artery wall. Such accumulation results in the formation of atherosclerotic plaques called atheromas, which may cause the obstruction of the blood flow. Cardiovascular diseases, among which atherosclerosis is the most frequent, are the first cause of death in developed countries. The published works in the subject suggest that hemodynamic forces on arterial walls have influence on the localization, initial development and growth rate of atheromas. This paper presents a model for this growth rate, and explores the influence of the bifurcation angle on the blood flow patterns and on the predictions of the model in a simplified carotid artery. The choice of the carotid bifurcation as the subject for this study obeys the fact that atheromas in this artery are often responsible for strokes. Our model predicts a larger initial growth rate in the external walls of the bifurcation and smaller growth area and lower growth rates as the bifurcation angle is increased. The reason for this seems to be the appearance of helical flow patterns as the angle is increased.
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.
Bifurcation control in the Burgers-KdV equation
Energy Technology Data Exchange (ETDEWEB)
Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, 00015 Monterotondo (Rome) (Italy)], E-mail: solitone@yahoo.it
2008-03-15
We consider the bifurcation control for the forced Burgers-KdV equation by means of delay feedback linear terms. We use a perturbation method in order to find amplitude and phase modulation equations as well as external force-response and frequency-response curves. We observe in the resonance response a saddle-node bifurcation that leads to jump and hysteresis phenomena. We compare the uncontrolled and controlled systems and demonstrate that control terms can delay or remove the occurrence of the saddle-node bifurcation and reduce the amplitude peak of the resonant response.
Bifurcation of limit cycles from quartic isochronous systems
Directory of Open Access Journals (Sweden)
Linping Peng
2014-04-01
Full Text Available This article concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quartic homogeneous perturbations, at most two limit cycles bifurcate from the period annulus of the considered system, and this upper bound can be reached. In addition, we study a family of perturbed isochronous systems and prove that there are at most three limit cycles bifurcating from the period annulus of the unperturbed one, and the upper bound is sharp.
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.
{ital {Delta}I}=4 Bifurcation in Identical Superdeformed Bands
Energy Technology Data Exchange (ETDEWEB)
Haslip, D.; Flibotte, S.; Gervais, G.; Nieminen, J.; Svensson, C.; Waddington, J.; Wilson, J. [Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1 (CANADA); de France, G. [Centre de Recherches Nucleaires et ULP, F-67037 Strasbourg Cedex 2 (France); Devlin, M.; LaFosse, D.; Lerma, F.; Sarantites, D. [Chemistry Department, Washington University, St. Louis, Missouri 63130 (United States); Galindo-Uribarri, A. [AECL, Chalk River Laboratories, Chalk River, Ontario, K0J 1J0 (CANADA); Hackman, G. [Argonne National Laboratory, Argonne, Illinois 60439 (United States); Lee, I.; Macchiavelli, A.; MacLeod, R. [Nuclear Science Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 (United States); Mullins, S. [Department of Nuclear Physics, RSPhysSE, ANU, Canberra, ACT 0200 (Australia)
1997-05-01
{Delta}I=4 bifurcation has been observed in two superdeformed bands, the newly discovered yrast superdeformed band of {sup 148}Eu, and a previously known excited band in {sup 148}Gd. Both of these bands have moments of inertia that are identical to the yrast band of {sup 149}Gd, the first superdeformed band in which this bifurcation was observed. This first observation of {Delta}I=4 bifurcation in identical superdeformed bands provides a crucial test of recent models. {copyright} {ital 1997} {ital The American Physical Society}
Multi-Stream Inflation: Bifurcations and Recombinations in the Multiverse
Wang, Yi
2010-01-01
In this Letter, we briefly review the multi-stream inflation scenario, and discuss its implications in the string theory landscape and the inflationary multiverse. In multi-stream inflation, the inflation trajectory encounters bifurcations. If these bifurcations are in the observable stage of inflation, then interesting observational effects can take place, such as domain fences, non-Gaussianities, features and asymmetries in the CMB. On the other hand, if the bifurcation takes place in the eternal stage of inflation, it provides an alternative creation mechanism of bubbles universes in eternal inflation, as well as a mechanism to locally terminate eternal inflation, which reduces the measure of eternal inflation.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
Directory of Open Access Journals (Sweden)
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.
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.
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.
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
Winant, Celeste D; Aparici, Carina Mari; Zelnik, Yuval R; Reutter, Bryan W; Sitek, Arkadiusz; Bacharach, Stephen L; Gullberg, Grant T
2012-01-21
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 (94)Tc-methoxyisobutylisonitrile ((94)Tc-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 K(1) 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 K(1). 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 (94)Tc-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 (99m)Tc-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
Ferruzzo Correa, Diego P.; Bueno, Átila M.; Castilho Piqueira, José R.
2017-04-01
In this paper we investigate stability conditions for small-amplitude periodic solutions emerging near symmetry-preserving Hopf bifurcations in a time-delayed fully-connected N-node PLL network. The study of this type of systems which includes the time delay between connections has attracted much attention among researchers mainly because the delayed coupling between nodes emerges almost naturally in mathematical modeling in many areas of science such as neurobiology, population dynamics, physiology and engineering. In a previous work it has been shown that symmetry breaking and symmetry preserving Hopf bifurcations can emerge in the parameter space. We analyze the stability along branches of periodic solutions near fully-synchronized Hopf bifurcations in the fixed-point space, based on the reduction of the infinite-dimensional space onto a two-dimensional center manifold in normal form. Numerical results are also presented in order to confirm our analytical results.
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
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.
de Man, Karen; Patterson, Mark; Kiemeneij, Ferdinand
2006-11-01
Acute occlusion of the left main coronary artery frequently causes cardiogenic shock and, when this occurs with an initial TIMI 0 flow, has an extremely poor prognosis. The use of a bifurcation system has not been described previously in this situation but has advantages that may result in a simpler and quicker solution then other strategies. This case describes a distal LMCA occlusion, 2 weeks post-stenting of the proximal LAD and proximal Cx, where this strategy was successfully used as a bridge to surgery. Such a strategy may be crucially beneficial in this commonly fatal condition.
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.)
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.
Knoche, H; Kienecker, E W
1977-10-21
Two postganglionic branches of the superior cervical ganglion enter the area of the carotid bifurcation in the rabbit and the cat. The common and external carotid arteries receive a rich adrenergic nerve supply, which can be demonstrated by fluorophores of biogenic amines appearing after formaldehyde treatment. The internal carotid artery is only sparsely innervated; however, it shows a dense sympathetic supply at the site of pressor receptors. Following removal of the superior cervical ganglion, a total loss of fluorescent adrenergic nerves occurs and degeneration of nerve endings possessing dense core vesicles is conspicuous. These nerve terminals are situated mainly subendothelially in the carotid body sinusoids; they only rarely terminate on type I cells.
Classification of boundary equilibrium bifurcations in planar Filippov systems.
Glendinning, Paul
2016-01-01
If a family of piecewise smooth systems depending on a real parameter is defined on two different regions of the plane separated by a switching surface, then a boundary equilibrium bifurcation occurs if a stationary point of one of the systems intersects the switching surface at a critical value of the parameter. We derive the leading order terms of a normal form for boundary equilibrium bifurcations of planar systems. This makes it straightforward to derive a complete classification of the bifurcations that can occur. We are thus able to confirm classic results of Filippov [Differential Equations with Discontinuous Right Hand Sides (Kluwer, Dordrecht, 1988)] using different and more transparent methods, and explain why the 'missing' cases of Hogan et al. [Piecewise Smooth Dynamical Systems: The Case of the Missing Boundary Equilibrium Bifurcations (University of Bristol, 2015)] are the only cases omitted in more recent work.
Bifurcations of double homoclinic flip orbits with resonant eigenvalues
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Concerns double homoclinic loops with orbit flips and two resonant eigenvalues in a four-dimensional system. We use the solution of a normal form system to construct a singular map in some neighborhood of the equilibrium, and the solution of a linear variational system to construct a regular map in some neighborhood of the double culation gives explicitly an expression of the associated successor function. By a delicate analysis of the bifurcation equation, we obtain the condition that the original double homoclinic loops are kept, and prove the existence and the existence regions of the large 1-homoclinic orbit bifurcation surface, 2-fold large 1-periodic orbit bifurcation surface,large 2-homoclinic orbit bifurcation surface and their approximate expressions. We also locate the large periodic orbits and large homoclinic orbits and their number.
BIFURCATION-THEORY APPLIED TO CHIRAL SYMMETRY-BREAKING
ATKINSON, D
1990-01-01
Chiral symmetry breaking in quantum electrodynamics and quantum chromodynamics is considered as a problem in bifurcation theory. Inequalities and positivity play key roles, as they do in much of the work of Andre Martin.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
Stochastic Bifurcations induced by correlated Noise in a Birhythmic van der Pol System
Yonkeu, R Mbakob; Filatrella, G; Tchawoua, C
2015-01-01
We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated Fokker-Planck equation. This approach allows to analytically derive the probability distributions as well as the activation energies associated to switching between coexisting attractors. The stationary probability density function of the van der Pol oscillator reveals the influence of the correlation time on the dynamics. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that noise intensity and correlation time can be treated as bifurcation parameters. Comparing the analytical and numerical results, we find good agreement both when the frequencies of the attractors are about equal or when they are markedly different.
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.
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
Directory of Open Access Journals (Sweden)
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.
Bifurcations in a nonlinear model of the baroreceptor-cardiac reflex
Seidel, H.; Herzel, H.
1998-04-01
We investigate the dynamic properties of a nonlinear model of the human cardio-baroreceptor control loop. As a new feature we use a phase effectiveness curve to describe the experimentally well-known phase dependency of the cardiac pacemaker's sensitivity to neural activity. We show that an increase of sympathetic time delays leads via a Hopf bifurcation to sustained heart rate oscillations. For increasing baroreflex sensitivity or for repetitive vagal stimulation we observe period-doubling, toroidal oscillations, chaos, and entrainment between the rhythms of the heart and the control loop. The bifurcations depend crucially on the involvement of the cardiac pacemaker's phase dependency. We compare the model output with experimental data from electrically stimulated anesthetized dogs and discuss possible implications for cardiac arrhythmias.
Bifurcation and chaos of a pest-control food chain model with impulsive effects
Energy Technology Data Exchange (ETDEWEB)
Wang Fengyan [Department of Mathematics, Wenzhou University, Wenzhou Zhejiang 325000 (China) and College of Science, Jimei University, Xiamen Fujian 361021 (China)], E-mail: wangfy68@163.com; Pang Guoping [Department of Mathematics and Computer Science, Yulin Normal University, Yulin Guangxi 537000 (China)], E-mail: g.p.pang@163.com; Lu Zhengyi [Department of Mathematics, Wenzhou University, Wenzhou Zhejiang 325000 (China)
2009-02-28
According to biological and chemical control strategy for pest control, we investigate the dynamics of a predator-prey food chain with impulsive effect, periodic releasing natural enemies and spraying pesticide at different fixed times, by using impulsive differential equation. Choose pest birth rate r{sub 2} as control parameter, we show that there exists a stable pest-eradication periodic solution when r{sub 2} is less than some critical value r{sub 2}* and the system is permanence when r{sub 2} is larger than the critical value r{sub 2}*. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in prey, middle-predator and top predator. Furthermore, bifurcation diagrams have shown that there exists complexity for the pulsed system including periodic doubling cascade.
The steady expiratory pressure-flow relation in a model pulmonary bifurcation.
Collins, J M; Shapiro, A H; Kimmel, E; Kamm, R D
1993-08-01
Experiments were conducted over a range of Reynolds numbers from 50 to 8000 to study the pressure-flow relationship for a single bifurcation in a multi-generation model during steady expiratory flow. Using the energy equation, the measured static pressure drop was decomposed into separate components due to fluid acceleration and viscous energy dissipation. The frictional pressure drop was found to closely approximate that for an equivalent length of curved tube with the same curvature ratio as in the model bifurcation. The sensitivity of these results to changes in airway cross-sectional shape, non-planar configuration, and flow regime (laminar-turbulent) was investigated. In separate experiments using dye visualization and hot-wire anemometry, a transition to turbulent flow was observed at Reynolds numbers between 1000 and 1500. Transition had very little effect on the pressure-flow relation.
Experimental bifurcation analysis of an impact oscillator—Tuning a non-invasive control scheme
Bureau, Emil; Schilder, Frank; Ferreira Santos, Ilmar; Juel Thomsen, Jon; Starke, Jens
2013-10-01
We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype for electromagnetic bearings and other machinery with build-in actuators. We propose a sequence of experiments that allows one to choose optimal control-gains, filter parameters and settings for a continuation method without a priori study of a model. Depending on the algorithm for estimating the Jacobian required by Newton's method we find two almost disjoint sets of suitable control parameters. Control-based continuation succeeds reliably in producing the full bifurcation diagram including both stable and unstable equilibrium states for an appropriately tuned controller.
Wang, Tong; Xing, Zhongwen
2016-01-01
Blood exhibits a heterogeneous nature of hematocrit, velocity, and effective viscosity in microcapillaries. Microvascular bifurcations have a significant influence on the distribution of the blood cells and blood flow behavior. This paper presents a simulation study performed on the two-dimensionalmotions and deformation of multiple red blood cells in microvessels with diverging and converging bifurcations. Fluid dynamics and membrane mechanics were incorporated. Effects of cell shape, hematocrit, and deformability of the cell membrane on rheological behavior of the red blood cells and the hemodynamics have been investigated. It was shown that the blood entering the daughter branch with a higher flow rate tended to receive disproportionally more cells. The results also demonstrate that red blood cells in microvessels experienced lateral migration in the parent channel and blunted velocity profiles in both straight section and daughter branches, and this effect was influenced by the shape and the initial posit...
Super Persistent Chaotic Transients And Catastrophic Bifurcation From Riddled To Fractal Basins
Andrade, V A
2002-01-01
This dissertation treats two related problems in chaotic dynamics: (1) super persistent chaotic transients in physical systems, and (2) catastrophic bifurcation from riddled to fractal basins. For the first problem, we investigate super persistent chaotic transient by studying the effect of noise on phase synchronization of coupled chaotic oscillators. A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multi...
Hasegawa, Hideo
2008-02-01
We have studied the dynamical properties of finite N-unit FitzHugh-Nagumo (FN) ensembles subjected to additive and/or multiplicative noises, reformulating the augmented moment method (AMM) with the Fokker-Planck equation (FPE) method [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. In the AMM, original 2N-dimensional stochastic equations are transformed to eight-dimensional deterministic ones, and the dynamics is described in terms of averages and fluctuations of local and global variables. The stochastic bifurcation is discussed by a linear stability analysis of the deterministic AMM equations. The bifurcation transition diagram of multiplicative noise is rather different from that of additive noise: the former has the wider oscillating region than the latter. The synchronization in globally-coupled FN ensembles is also investigated. Results of the AMM are in good agreement with those of direct simulations (DSs).
Institute of Scientific and Technical Information of China (English)
Liu Su-Hua; Tang Jia-Shi; Qin Jin-Qi; Yin Xiao-Bo
2008-01-01
Bifurcation characteristics of the Langford system in a general form are systematically analysed,and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved.Analytical relationship between control gain and bifurcation parameter is obtained.Bifurcation diagrams are drawn,showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos.Numerical simulations of quasi-periodic tori validate analytic predictions.
Institute of Scientific and Technical Information of China (English)
Pengnian CHEN; Huashu QIN; Shengwei MEI
2005-01-01
This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented;Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator, which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.
Iterative Controller Tuning for Process with Fold Bifurcations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
2007-01-01
Processes involving fold bifurcation are notoriously difficult to control in the vicinity of the fold where most often optimal productivity is achieved . In cases with limited process insight a model based control synthesis is not possible. This paper uses a data driven approach with an improved ...... version of iterative feedback tuning to optimizing a closed loop performance criterion, as a systematic tool for tuning process with fold bifurcations....
Subcritical dynamo bifurcation in the Taylor-Green flow.
Ponty, Y; Laval, J-P; Dubrulle, B; Daviaud, F; Pinton, J-F
2007-11-30
We report direct numerical simulations of dynamo generation for flow generated using a Taylor-Green forcing. We find that the bifurcation is subcritical and show its bifurcation diagram. We connect the associated hysteretic behavior with hydrodynamics changes induced by the action of the Lorentz force. We show the geometry of the dynamo magnetic field and discuss how the dynamo transition can be induced when an external field is applied to the flow.
BIFURCATIONS OF ROUGH 3-POINT-LOOP WITH HIGHER DIMENSIONS
Institute of Scientific and Technical Information of China (English)
金银来; 朱德明; 郑庆玉
2003-01-01
The authors study the bifurcation problems of rough heteroclinic loop connecting threesaddle points for the case β1 ＞ 1, β2 ＞ 1, β3 ＜ 1 and β1β2β3 ＜ 1. The existence, number, co-existence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are studied.Meanwhile, the bifurcation surfaces and existence regions are given.
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
A Bifurcation Monte Carlo Scheme for Rare Event Simulation
Liu, Hongliang
2016-01-01
The bifurcation method is a way to do rare event sampling -- to estimate the probability of events that are too rare to be found by direct simulation. We describe the bifurcation method and use it to estimate the transition rate of a double well potential problem. We show that the associated constrained path sampling problem can be addressed by a combination of Crooks-Chandler sampling and parallel tempering and marginalization.
Bunch lengthening with bifurcation in electron storage rings
Energy Technology Data Exchange (ETDEWEB)
Kim, Eun-San; Hirata, Kohji [National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan)
1996-08-01
The mapping which shows equilibrium particle distribution in synchrotron phase space for electron storage rings is discussed with respect to some localized constant wake function based on the Gaussian approximation. This mapping shows multi-periodic states as well as double bifurcation in dynamical states of the equilibrium bunch length. When moving around parameter space, the system shows a transition/bifurcation which is not always reversible. These results derived by mapping are confirmed by multiparticle tracking. (author)
A bifurcation analysis for the Lugiato-Lefever equation
Godey, Cyril
2016-01-01
The Lugiato-Lefever equation is a cubic nonlinear Schr\\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of ste...
Bifurcations and chaos control in discrete small-world networks
Institute of Scientific and Technical Information of China (English)
Li Ning; Sun Hai-Yi; Zhang Qing-Ling
2012-01-01
An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed.The control method is then applied to a discrete small-world network model.Qualitative analyses and simulations show that under a generic condition,the bifurcations and the chaos can be delayed or eliminated completely.In addition,the periodic orbits embedded in the chaotic attractor can be stabilized.
Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs
Energy Technology Data Exchange (ETDEWEB)
Inayat-Hussain, Jawaid I. [School of Engineering, Monash University Malaysia, No. 2, Jalan Kolej, Bandar Sunway, 46150 Petaling Jaya, Selangor Darul Ehsan (Malaysia)], E-mail: jawaid.inayat-hussain@eng.monash.edu.my
2009-01-30
Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, {alpha}, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, {omega}, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of {alpha} reduces the onset speed of bifurcation. For a specific combination of K and {alpha} values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of {alpha} = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of {alpha}; in fact non-synchronous rotor response was totally absent for {alpha}=0.4. With the exception of the case {alpha} = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of {omega} for various combinations of parameters W, {alpha} and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical
Bifurcations of a flexible rotor response in squeeze-film dampers without centering springs
Energy Technology Data Exchange (ETDEWEB)
Inayat-Hussain, Jawaid I. [School of Engineering, Monash University Malaysia, No. 2, Jalan Kolej, Bandar Sunway, Petaling Jaya 46150, Selangor Darul Ehsan (Malaysia)]. E-mail: jawaid.inayat-hussain@eng.monash.edu.my
2005-04-01
the onset speed of bifurcation was observed to decrease as {alpha} was increased. The numerical results presented in this work were obtained for an unbalance parameter, U, of 0.1, which is considered to be at the upper end of the acceptable range of balance quality specifications for practical rotor systems. The non-synchronous vibrations that were observed in the rotor response, for the range of practical design and operating parameters investigated in this work, are detrimental to the performance of rotating machinery as they cause alternating stresses in the rotor that may eventually lead to fatigue failure.