Relative Lyapunov Center Bifurcations
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....
Graphene induced bifurcation of energy levels at low input power
Li, Rujiang; Lin, Shisheng; Liu, Xu; Chen, Hongsheng
2015-01-01
We study analytically the energy states in the waveguide system of graphene coated dielectric nanowire based on the explicit form of nonlinear surface conductivity of graphene. The energy levels of different plasmonic modes can be tuned by the input power at the order of a few tenths of mW. The self-focusing behavior and self-defocusing behavior are exhibited in the lower and upper bifurcation branches, respectively, which are separated by a saturation of input power. Moreover, due to the nonlinearity of graphene, the dispersion relations for different input powers evolve to an energy band which is in sharp contrast with the discrete energy level in the limit of zero power input.
Numerical bifurcation of Hamiltonian relative periodic orbits
Wulff, Claudia; Schilder, Frank
2009-01-01
Relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and the motion of rigid bodies. RPOs are solutions which are periodic orbits of the symmetry-reduced system. In this paper we analyze certain symmetry...
Bifurcation diagrams in relation to synchronization in chaotic systems
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 and chaos analysis of a nonlinear electromechanical coupling relative rotation system
Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Hopf bifurcation control for a coupled nonlinear relative rotation system with time-delay feedbacks
Liu, Shuang; Li, Xue; Tan, Shu-Xian; Li, Hai-Bin
2014-10-01
This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time-delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.
Stability and bifurcations of relative equilibria of a pendulum suspended on the equator
Burov, A. A.; Kosenko, I. I.
2013-05-01
The problem of equilibria of a pendulum suspended at an equatorial point relative to the rotating Earth is considered. An altitude is determined at which the degree of instability of the inverted pendulum changes from two to unity. Relative equilibria are investigated that bifurcate from the radial one when its degree of instability changes. Their stability properties are studied.
Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P;
2011-01-01
crush, 118 culotte, and 59 T-stenting techniques. A composite end point at 9 months of all-cause death, myocardial infarction, and target vessel revascularization occurred in 10.1% of the simple versus 17.3% of the complex group (hazard ratio 1.84 [95% confidence interval 1.28 to 2.66], P=0.......001). Procedure duration, contrast, and x-ray dose favored the simple approach. Subgroup analysis revealed similar composite end point results for true bifurcations (n=657, simple 9.2% versus complex 17.3%; hazard ratio 1.90 [95% confidence interval 1.22 to 2.94], P=0.004), wide-angled bifurcations >60 to 70° (n......=217, simple 9.6% versus complex 15.7%; hazard ratio 1.67 [ 95% confidence interval 0.78 to 3.62], P=0.186), large (=2.75 mm) diameter side branches (n=281, simple 10.4% versus complex 20.7%; hazard ratio 2.42 [ 95% confidence interval 1.22 to 4.80], P=0.011), longer length (>5 mm) ostial side branch...
This paper studies the bifurcation and nonlinear behaviors of a flexible rotor supported by relative short gas film bearings. A time-dependent mathematical model for gas journal bearings is presented. The finite difference method with successive over relation method is employed to solve the Reynolds' equation. The system state trajectory, Poincare maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and subharmonic response of the rotor and journal center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems
Wang, C.-C. [Department of Mechanical Engineering, Far East College, 49, Hsin-Shih, Tainan 744, Taiwan (China)]. E-mail: ccwang@cc.fec.edu.tw; Jang, M.-J. [Department of Automation and Control Engineering, Far East College, Hsin-Shih, Tainan, Taiwan (China); Yeh, Y.-L. [Department of Automation and Control Engineering, Far East College, Hsin-Shih, Tainan, Taiwan (China)
2007-04-15
This paper studies the bifurcation and nonlinear behaviors of a flexible rotor supported by relative short gas film bearings. A time-dependent mathematical model for gas journal bearings is presented. The finite difference method with successive over relation method is employed to solve the Reynolds' equation. The system state trajectory, Poincare maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and subharmonic response of the rotor and journal center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
Rawat, Subhandu; Cossu, Carlo; Rincon, François
2016-06-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when Lz is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic
Liu, Shuang; Wang, Zhao-Long; Zhao, Shuang-Shuang; Li, Hai-Bin; Li, Jian-Xiong
2015-07-01
Grazing bifurcation of a relative rotation system with backlash non-smooth characteristic is studied along with the change of the external excitation in this paper. Considering the oil film, backlash, time-varying stiffness and time-varying error, the dynamical equation of a relative rotation system with a backlash non-smooth characteristic is deduced by applying the elastic hydrodynamic lubrication (EHL) and the Grubin theories. In the process of relative rotation, the occurrence of backlash will lead to the change of dynamic behaviors of the system, and the system will transform from the meshing state to the impact state. Thus, the zero-time discontinuous mapping (ZDM) and the Poincare mapping are deduced to analyze the local dynamic characteristics of the system before as well as after the moment that the backlash appears (i.e., the grazing state). Meanwhile, the grazing bifurcation mechanism is analyzed theoretically by applying the impact and Floquet theories. Numerical simulations are also given, which confirm the analytical results. Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).
Bifurcation analysis of a relative short spherical aerodynamic journal bearing system
This paper studies the nonlinear dynamic behavior and bifurcation of a rigid rotor supported by relative short spherical aerodynamic journal bearings. The modified Reynolds equation is solved by a hybrid numerical method combined with the differential transformation method and the finite difference method. The analytical results reveal a complex dynamic behavior including periodic, sub-harmonic, and quasi-periodic responses of the rotor center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number increase. The current analytical results are found to be in good agreement with those of other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of relative short spherical aerodynamic rotor-bearing systems
Bifurcation analysis of a relative short spherical aerodynamic journal bearing system
Wang, C C [Department of Mechanical Engineering, Far East University, No.49, Chung Hua Rd., Hsin-Shih. Tainan County 744, Taiwan (China); Yau, H T [Department of Electrical Engineering, Far East University, No.49, Chung Hua Rd., Hsin-Shih. Tainan County 744, Taiwan (China); Yeh, Y L; Jang, M J [Department of Automation and Control Engineering, Far East University, No.49, Chung Hua Rd., Hsin-Shih. Tainan County 744, Taiwan (China)], E-mail: wccpipn@yahoo.com.tw
2008-02-15
This paper studies the nonlinear dynamic behavior and bifurcation of a rigid rotor supported by relative short spherical aerodynamic journal bearings. The modified Reynolds equation is solved by a hybrid numerical method combined with the differential transformation method and the finite difference method. The analytical results reveal a complex dynamic behavior including periodic, sub-harmonic, and quasi-periodic responses of the rotor center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number increase. The current analytical results are found to be in good agreement with those of other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of relative short spherical aerodynamic rotor-bearing systems.
The bifurcation theory is the part of the nonlinear analysis which considers the changes in the number of solutions of a system of equations depending continuously on a parameter, as the parameter varies. The present lecture is dedicated to the illustration of the relations between the bifurcation theory and the stability properties of a plasma equilibrium, both from the point of view of the dynamics or of the thermodynamics of the collisionless plasma equilibria. In fact the existence of a bifurcation depends on very general mathematical properties of the system. One should distinguish between the existence of bifurcation in a problem of static plasma equilibrium or in the problem of the dynamical behaviour of the perturbed equilibrium. The two cases coincide for 'adiabatic' perturbations, namely such that the functional form of the distribution function is unchanged. In this case the system is unstable both from the point of view of the dynamical or of the thermodynamical description. However situations occur in which a bifurcation exists in the equilibrium problem while the system is dynamically stable. In this case the equilibrium is still thermodynamically unstable with respect to nondynamical perturbations, namely such that the system is describing a succession of equilibria, as a consequence of an external slow time dependence of the parameters, resulting e.g. from a small amount of dissipation. The existence of the bifurcation then implies a disruption of the old equilibrium and the realisation of a new thermodynamically more favoured equilibrium. The disruption observed in Tokamaks is quite likely related to a process of this kind. (Auth.)
The Newton filtration and d-determination of bifurcation problems related to C0 contact equivalence
SU Dan; ZHANG Dunmu
2006-01-01
In this paper, from the Newton filtration's point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C0 contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.
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.
Numerical Modeling of Bifurcation Evolution in a Sand-bed Braided River
De Haas, T.; Schuurman, F.; Kleinhans, M. G.
2012-12-01
River bifurcations are key units in a braided river. Although simple bifurcations are well understood and can be analyzed by 1D models (e.g. Bolla Pittaluga et al., 2003 and Kleinhans et al., 2008), predicting the stability and dynamics of multiple interacting bifurcations in a braided river with migrating bars requires understanding of the interaction between braid bars, channel network and bifurcations, in particular the upstream curvature and downstream backwater effects. Our objective is to understand the evolution of bifurcations at migrating bars in a braided river and the effects on bar evolution. We used the 3D numerical morphodynamic model Delft3D to produce a dynamically braiding sand bed river. This model solves the 3D-flow and computes sediment transport and bed level change accounting for effects of transverse bed slope. It includes a simple bank erosion model to reactivate emerged areas. The morphology of mid-channel bars produced by the model was analyzed and the partitioning of water and sediment over the bifurcating channels are compared with a 1D model concept. Next, the evolution of bars is linked to that of the bifurcations, in order to infer relations between bar morphology and bifurcation evolution. We find that upstream bar dynamics have a major effect on the stability of bifurcations. Migration and elongation of bars can close the upstream entrance of a bifurcation channel, independent of the stability of the bifurcation. Moreover, bifurcation angle and upstream curvature can be affected by upstream bar migration and elongation, which steers flow and sediment partitioning at the bifurcation. At the same time, the partitioning of water and sediment over a bifurcation affects bar shape. Sediment eroded at one of the bar sides just downstream of the bifurcation deposits downstream of the braid bar in the form of tail bars. Hence bar shape as observable on imagery contains useful information about the evolution of the upstream bifurcation and
U.S. Environmental Protection Agency — This point dataset represents changes in relative sea level along U.S. coasts, 1960-2013. Data were provided by the National Oceanic and Atmospheric Administration...
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...
Region based level set segmentation of the outer wall of the carotid bifurcation in CTA
VUKADINOVIC, D.; Van Walsum, T.; Manniesing, R.; Rozie, S.; van der Lugt, A.; Niessen, W.J.
2011-01-01
This paper presents a level set based method for segmenting the outer vessel wall and plaque components of the carotid artery in CTA. The method employs a GentleBoost classification framework that classifies pixels as calcified region or not, and inside or outside the vessel wall. The combined result of both classifications is used to construct a speed function for level set based segmentation of the outer vessel wall; the segmented lumen is used to initialize the level set. The method has be...
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.
Region based level set segmentation of the outer wall of the carotid bifurcation in CTA
Vukadinovic, D.; van Walsum, T.; Manniesing, R.; Rozie, S.; van der Lugt, A.; Niessen, W. J.
2011-03-01
This paper presents a level set based method for segmenting the outer vessel wall and plaque components of the carotid artery in CTA. The method employs a GentleBoost classification framework that classifies pixels as calcified region or not, and inside or outside the vessel wall. The combined result of both classifications is used to construct a speed function for level set based segmentation of the outer vessel wall; the segmented lumen is used to initialize the level set. The method has been optimized on 20 datasets and evaluated on 80 datasets for which manually annotated data was available as reference. The average Dice similarity of the outer vessel wall segmentation was 92%, which compares favorably to previous methods.
Noise induced Hopf bifurcation
Shuda, I. A.; Borysov, S S; A.I. Olemskoi
2008-01-01
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle in dependence of relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest vari...
Multiple Bifurcations in the Periodic Orbit around Eros
Ni, Yanshuo; Baoyin, Hexi
2016-01-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real ...
Energetics and monsoon bifurcations
Seshadri, Ashwin K.
2016-04-01
Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.
Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
Guirao, Juan L G; Vera, Juan A, E-mail: juan.garcia@upct.e, E-mail: juanantonio.vera@upct.e [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Region de Murcia (Spain)
2010-05-14
In this paper we consider the non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Using geometric/mechanic methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we refer to as Lagrange type following the analogy with the standard techniques. We provide necessary and sufficient conditions for the linear stability of Lagrangian relative equilibria if the gyrostat morphology form is close to a sphere. Thus, we generalize the classical results on equilibria of the three-body problem and many results on them obtained by the classic approach for the case of rigid bodies.
Multiple bifurcations in the periodic orbit around Eros
Ni, Yanshuo; Jiang, Yu; Baoyin, Hexi
2016-05-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real saddle bifurcation, two tangent bifurcations, and two period-doubling bifurcations.
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...
Haiyan Hu
1996-01-01
Full Text Available One critical case for the motion of a periodically excited oscillator with continuous and piecewise-linear restoring force is that the motion happens to graze a switching plane between two linear regions of the restoring force. This article presents a numerical scheme for locating the periodic grazing orbit first. Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency.
Unfolding the Riddling Bifurcation
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.......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....
We show that maps describing border collision bifurcations (continuous but non-differentiable discrete time maps) are subject to a curse of dimensionality: it is impossible to reduce the study of the general case to low dimensions, since in every dimension the bifurcation can produce fundamentally different attractors (contrary to the case of local bifurcations in smooth systems). In particular we show that n-dimensional border collision bifurcations can have invariant sets of dimension k for integer k from 0 to n. We also show that the border collision normal form is related to grazing-sliding bifurcations of switching dynamical systems. This implies that the dynamics of these two apparently distinct bifurcations (one for discrete time dynamics, the other for continuous time dynamics) are closely related and hence that a similar curse of dimensionality holds in grazing-sliding bifurcations. (paper)
Semiclassical interference of bifurcations
Schomerus, H
1997-01-01
In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this fact and derive the correct semiclassical contribution of the bifurcating orbits to the trace of the unitary time evolution operator. That contribution has a certain collective character rather than being additive in the individual periodic orbits involved. The relevance of our observation is demonstrated by a numerical study of the kicked top; the collective contribution derived is found to considerably improve the semiclassical approximation of the trace.
Oscillatory flow in bifurcating tubes
Respiratory fluid mechanics is characterized by flow through bifurcating, Y-shaped, tubes. Steady flow through such geometries has been studied in detail by several authors. However, the recent widespread use of high frequency mechanical assistance of ventilation has generated interest in unsteady flows. A symmetric, singly branching pipe has been constructed, with its bifurcation shaped to model pulmonary conditions. The form of the bifurcation is based on CAT scans of human tracheal carinas. Its features include an area change of the parent tube from circular to roughly elliptical near the junction, a pinch-off effect on the parent tube, smoothly curved outer walls at the junction, and a sharp flow divider. Parent and daughter tubes have an l/d ratio of > 50, so that entrance effects are avoided. In order to better understand the effects of unsteadiness, piston driven, laminar, purely oscillatory flow has been established in the pipe for a variety of Womersley numbers. By appropriate choices of flow frequency and amplitude, fluid viscosity, and pipe diameter, tracheal Reynolds and Womersley numbers have been matched for resting breathing (tidal volume of 600 ml to 0.25 Hz), high frequency breathing (50 ml at 5 Hz), and intermediate breathing levels
Codimension Two Bifurcations and Rythms in Neural Mass Models
Touboul, Jonathan
2009-01-01
Temporal lobe epilepsy is one of the most common chronic neurological disorder characterized by the occurrence of spontaneous recurrent seizures which can be observed at the level of populations through electroencephalogram (EEG) recordings. This paper summarizes some preliminary works aimed to understand from a theoretical viewpoint the occurrence of this type of seizures and the origin of the oscillatory activity in some classical cortical column models. We relate these rhythmic activities to the structure of the set of periodic orbits in the models, and therefore to their bifurcations. We will be mainly interested Jansen and Rit model, and study the codimension one, two and a codimension three bifurcations of equilibria and cycles of this model. We can therefore understand the effect of the different biological parameters of the system of the apparition of epileptiform activity and observe the emergence of alpha, delta and theta sleep waves in a certain range of parameter. We then present a very quick stud...
Bifurcation phenomena in control flows
Colonius, Fritz; Fabbri, Roberta; Johnson, Russell; Spadini, Marco
2007-01-01
We study bifurcation phenomena in control flows and the bifurcation of control sets. A Mel'nikov method and the Conley index together with exponential dichotomy theory and integral manifold theory are used.
Safe, explosive, and dangerous bifurcations in dissipative dynamical systems
Thompson, J.M.T. (Centre for Nonlinear Dynamics and Its Applications, Civil Engineering Building, University College London, Gower Street, London WC1E6BT (United Kingdom)); Stewart, H.B. (Mathematical Sciences Group, Building 490-A, Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973 (United States)); Ueda, Y. (Department of Electrical Engineering, Kyoto University, Kyoto 606 (Japan))
1994-02-01
A comprehensive listing of the generic codimension-1 attractor bifurcations of dissipative dynamical systems is presented. It includes local and global bifurcations of regular and chaotic attractors. The bifurcations are classified according to the continuity or discontinuity of the attractor path, which governs the physical outcome that would be observed under a slow control sweep. Related issues of determinacy, hysteresis, basin structure, and intermittency are addressed. Recently discovered chaotic bifurcations are discussed in some detail, with particular reference to the regular or chaotic saddle-type destroyer with which an attractor may collide.
Safe, explosive, and dangerous bifurcations in dissipative dynamical systems
A comprehensive listing of the generic codimension-1 attractor bifurcations of dissipative dynamical systems is presented. It includes local and global bifurcations of regular and chaotic attractors. The bifurcations are classified according to the continuity or discontinuity of the attractor path, which governs the physical outcome that would be observed under a slow control sweep. Related issues of determinacy, hysteresis, basin structure, and intermittency are addressed. Recently discovered chaotic bifurcations are discussed in some detail, with particular reference to the regular or chaotic saddle-type destroyer with which an attractor may collide
Views on the Hopf bifurcation with respect to voltage instabilities
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.
Internal carotid artery bifurcation aneurysms. Surgical experience
Internal carotid artery (ICA) bifurcation aneurysms are relatively uncommon and frequently rupture at a younger age compared to other intracranial aneurysms. We have treated a total of 999 patients for intracranial aneurysms, of whom 89 (8.9%) had ICA bifurcation aneurysms, and 42 of the 89 patients were 30 years of age or younger. The present study analyzed the clinical records of 70 patients with ICA bifurcation aneurysms treated from mid 1997 to mid 2003. Multiple aneurysms were present in 15 patients. Digital subtraction angiography films were studied in 55 patients to identify vasospasm and aneurysm projection. The aneurysm projected superiorly in most of these patients (37/55, 67.3%). We preferred to minimize frontal lobe retraction, so widely opened the sylvian fissure to approach the ICA bifurcation and aneurysm neck. Elective temporary clipping was employed before the final dissection and permanent clip application. Vasospasm was present in 24 (43.6%) of 55 patients. Forty-eight (68.6%) of the 70 patients had good outcome, 14 (20%) had poor outcome, and eight (11.4%) died. Patients with ICA bifurcation aneurysms tend to bleed at a much younger age compared to those with other intracranial aneurysms. Wide opening of the sylvian fissure and elective temporary clipping of the ICA reduces the risk of intraoperative rupture and perforator injury. Mortality was mainly due to poor clinical grade and intraoperative premature aneurysm rupture. (author)
Backward bifurcation and control in transmission dynamics of arboviral diseases.
Abboubakar, Hamadjam; Claude Kamgang, Jean; Tieudjo, Daniel
2016-08-01
In this paper, we derive and analyze a compartmental model for the control of arboviral diseases which takes into account an imperfect vaccine combined with individual protection and some vector control strategies already studied in the literature. After the formulation of the model, a qualitative study based on stability analysis and bifurcation theory reveals that the phenomenon of backward bifurcation may occur. The stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the reproduction number, R0, is less than unity. Using Lyapunov function theory, we prove that the trivial equilibrium is globally asymptotically stable. When the disease-induced death is not considered, or/and, when the standard incidence is replaced by the mass action incidence, the backward bifurcation does not occur. Under a certain condition, we establish the global asymptotic stability of the disease-free equilibrium of the principal model. Through sensitivity analysis, we determine the relative importance of model parameters for disease transmission. Numerical simulations show that the combination of several control mechanisms would significantly reduce the spread of the disease, if we maintain the level of each control high, and this, over a long period. PMID:27321192
Global Bifurcations With Symmetry
Porter, J B
2001-01-01
Symmetry is a ubiquitous feature of physical systems with profound implications for their dynamics. This thesis investigates the role of symmetry in global bifurcations. In particular, the structure imposed by symmetry can encourage the formation of complex solutions such as heteroclinic cycles and chaotic invariant sets. The first study focuses on the dynamics of 1:n steady-state mode interactions in the presence of O(2) symmetry. The normal form equations considered are relevant to a variety of physical problems including Rayleigh-Bénard convection with periodic boundary conditions. In open regions of parameter space these equations contain structurally stable heteroclinic cycles composed of connections between standing wave, pure mode, and trivial solutions. These structurally stable cycles exist between two global bifurcations, the second of which involves an additional mixed mode state and creates as many as four distinct kinds of structurally unstable heteroclinic cycles. The various cycles c...
Comments on the Bifurcation Structure of 1D Maps
Belykh, V.N.; Mosekilde, Erik
1997-01-01
The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box-within-a-box struct......The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box......-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory, are...
Symmetric/asymmetric bifurcation behaviours of a bogie system
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue; True, Hans
2013-02-01
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel-rail contact relation are investigated in detail by the 'resultant bifurcation diagram' method with slowly increasing and decreasing speed. It is found that the stationary equilibrium solution and the periodic motions coexist due to the sub-critical Hopf bifurcation in the railway bogie system. It is also found that multiple solutions coexist in many speed ranges. The coexistence of multiple solutions may result in a jump and hysteresis of the oscillating amplitude for different kinds of disturbances. It should be avoided in the normal operation. Furthermore, it is found that symmetry-breaking of the system through a pitchfork bifurcation leads to asymmetric chaotic motions in the railway bogie system. The speed ranges of asymmetric chaotic motions are, however, small.
Hormone levels in radiotherapy treatment related fatigue
Radiotherapy is known to cause debilitating treatment related fatigue. Fatigue in general is a conglomeration of psychological, physical, hematological and unknown factors influencing the internal milieu of the cancer patient. Radiotherapy can add stress at the cellular and somatic level to aggravate further fatigue in cancer patients undergoing radiotherapy. Stress related hormones might be mediating in the development of fatigue. This is an ongoing prospective study to evaluate if the hormonal profile related to stress is influenced by radiotherapy treatment related fatigue. The study was conducted from September 2002 onwards in the division of Radiotherapy and Oncology of our Medical School. Previously untreated patients with histopathology proof of malignancy requiring external beam radiotherapy were considered for this study. Selection criteria were applied to exclude other causes of fatigue. Initial fatigue score was obtained using Pipers Fatigue Score questionnaire containing 23 questions, subsequently final fatigue score was obtained at the end of radiotherapy. Blood samples were obtained to estimate the levels of ACTH, TSH, HGH, and cortisol on the final assessment. The hormone levels were compared with resultant post radiotherapy fatigue score. At the time of reporting 50 patients were evaluable for the study. The total significant fatigue score was observed among 12 (24%) patients. The individual debilitating fatigue score were behavioral severity 14 (28%), affective meaning 14(28%), Sensory 13 (26%) and cognitive mood 10 (20%) respectively. From the analysis of hormonal profile, growth hormone level > 1 ng/mL and TSH <0.03 appears to be associated with high fatigue score (though statistically not significant); whereas there was no correlation with ACTH and serum cortisol level. In our prospective study severe radiotherapy treatment related fatigue was found among our patient population. Low levels of TSH and high levels of GH appear to be associated
Colloids related to low level and intermediate level waste
A comprehensive research investigation has been undertaken to improve the understanding of the potential role of colloids in the context of disposal and storage of low level and intermediate level waste immobilized in cement. Several topics have been investigated which include: (a) the study of the formation and characteristics of colloids in cement leachates; (b) the effects of the near-field aqueous chemistry on the characteristics of colloids in repository environments; (c) colloid sorption behaviour; (d) interactions of near-field materials with leachates; (e) characteristics of near-field materials in EC repository simulation tests; and (f) colloid migration behaviour. These experimental investigations should provide data and a basis for the development of transport models and leaching mechanisms, and thus relate directly to the part of the Task 3 programme concerned with migration and retention of radionuclides in the near field. 114 Figs.; 39 Tabs.; 12 Refs
Introduction to bifurcation theory
Bifurcation theory is a subject with classical mathematical origins. The modern development of the subject starts with Poincare and the qualitative theory of differential equations. In recent years, the theory has undergone a tremendous development with the infusion of new ideas and methods from dynamical systems theory, singularity theory, group theory, and computer-assisted studies of dynamics. As a result, it is difficult to draw the boundaries of the theory with any confidence. In this review, the objects in question will be parameterized families of dynamical systems (vector fields or maps). In the sciences these families commonly arise when one formulates equations of motion to model a physical system. We specifically analyze how the time evolution near an equilibrium can change as parameters are varied; for simplicity we consider the case of a single parameter only
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...
Coastal subsidence and relative sea level rise
Ingebritsen, Steven E.; Galloway, Devin L.
2014-01-01
Subsurface fluid-pressure declines caused by pumping of groundwater or hydrocarbons can lead to aquifer-system compaction and consequent land subsidence. This subsidence can be rapid, as much as 30 cm per year in some instances, and large, totaling more than 13 m in extreme examples. Thus anthropogenic subsidence may be the dominant contributor to relative sea-level rise in coastal environments where subsurface fluids are heavily exploited. Maximum observed rates of human-induced subsidence greatly exceed the rates of natural subsidence of unconsolidated sediments (~0.1–1 cm yr−1) and the estimated rates of ongoing global sea-level rise (~0.3 cm yr−1).
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
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 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...
Bifurcations, instabilities, degradation in geomechanics
Exadaktylos, George
2007-01-01
Leading international researchers and practitioners of bifurcations and instabilities in geomechanics debate the developments and applications which have occurred over the last few decades. The topics covered include modeling of bifurcation, structural failure of geomaterials and geostructures, advanced analytical, numerical and experimental techniques, and application and development of generalised continuum models etc. In addition analytical solutions, numerical methods, experimental techniques, and case histories are presented. Beside fundamental research findings, applications in geotechni
CISM Session on Bifurcation and Stability of Dissipative Systems
1993-01-01
The first theme concerns the plastic buckling of structures in the spirit of Hill’s classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
Bursting oscillations, bifurcation and synchronization in neuronal systems
Highlights: → We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. → Two types of fast-slow bursters are analyzed in detail. → We show the properties of some crucial bifurcation points. → Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.
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).
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. PMID:26428557
Bifurcations and intermittent magnetic activity
The sequence of equilibria of two-dimensional reduced magnetohydrodynamics has been studied as a function of the tearing mode stability parameter Δ'. After a symmetry-breaking bifurcation occurring at Δ' ∼ 0, which originates a state with a small magnetic island, the system undergoes a second bifurcation, of tangent type, at Δ' ∼ 1. Above this value, no stationary solutions with small islands exist. The system rapidly develops an island of macroscopic size. This general property is proposed as a basic ingredient of the intermittent events observed in magnetically confined plasmas. (author)
Bifurcations and intermittent magnetic activity
Tebaldi, C.; Ottaviani, M.; Porcelli, F. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking
1996-04-01
The sequence of equilibria of two-dimensional reduced magnetohydrodynamics has been studied as a function of the tearing mode stability parameter {Delta}`. After a symmetry-breaking bifurcation occurring at {Delta}` {approx} 0, which originates a state with a small magnetic island, the system undergoes a second bifurcation, of tangent type, at {Delta}` {approx} 1. Above this value, no stationary solutions with small islands exist. The system rapidly develops an island of macroscopic size. This general property is proposed as a basic ingredient of the intermittent events observed in magnetically confined plasmas. (author).
Multiple Bifurcations of a Cylindrical Dynamical System
Han Ning; Cao Qingjie
2016-01-01
This paper focuses on multiple bifurcations of a cylindrical dynamical system, which is evolved from a rotating pendulum with SD oscillator. The rotating pendulum system exhibits the coupling dynamics property of the bistable state and conventional pendulum with the ho- moclinic orbits of the first and second type. A double Andronov-Hopf bifurcation, two saddle-node bifurcations of periodic orbits and a pair of homoclinic bifurcations are detected by using analytical analysis and nu- merical ...
Bifurcations associated with sub-synchronous resonance
Mitani, Yasunori; K. Tsuji; M.Varghese; Wu, F. F.; VARAIYA, P
1998-01-01
This paper describes a set of results of detecting nonlinear phenomena appearing in a turbine generator power system with series-capacitor compensation. The analysis was based on the Floquet theory as well as the Hopf bifurcation theorem. After the first Hopf bifurcation, the stable limit cycle bifurcates to a stable torus and an unstable limit cycle which connects to a stable limit cycle by a supercritical torus bifurcation. The stable limit cycle joins with an unstable limit cycle at a cycl...
Bifurcation of steady tearing states
We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now
Colloids related to low level and intermediate level waste
A comprehensive investigation has been undertaken to improve the understanding of the potential role of colloids in the context of disposal and storage of low and intermediate level waste immobilised in cement. Several topics have been investigated using a wide range of advanced physico-chemical and analytical techniques. These include: (a) the study of formation and characteristics of colloids in cement leachates, (b) the effects of the near-field aqueous chemistry on the characteristics of colloids in repository environments, (c) colloid sorption behaviour, (d) interactions of near-field materials with leachates, and (e) preliminary assessment of colloid migration behaviour. It has been shown that the generation of colloids in cement leachates can arise from a process of nucleation and growth leading to an amorphous phase which is predominantly calcium silicate hydrate. Such colloidal material has a capacity for association with polyvalent rare earths and actinides and these may be significant in the source term and processes involving radionuclide retention in the near field. It has also been shown that the near-field aqueous chemistry (pH, Ca2+ concentration) has a marked effect on colloid behaviour (deposition and stability). A mechanistic approach to predict colloid sorption affinity has been developed which highlights the importance of colloid characteristics and the nature of the ionic species. (author)
Homoclinic bifurcation in Chua’s circuit
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
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.
Public relations work at a regional level
Kirchhoff, H.R.
1982-04-01
With 'Elektrizitaets-AG Mitteldeutschland (EAM)' (power corporation central Germany) - head office in Kassel and five works maintained in Kassel, Goettingen, Marburg, Dillenburg and Hanau - public relations work has a tradition. It is seen as conscious, planned and continued effort to build up the public understanding: Public relations work is intended to present the enterprise as a community with a multitude of technical, economic and social tasks, which can be carried out with optimal success only if supported by the confidence of society.
Bifurcations analysis of turbulent energy cascade
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.
Bifurcation phenomena near homoclinic systems: A two-parameters analysis
The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues (rho +- iω, lambda), where Vertical Barrho/lambdaVertical Bar<1 (Sil'nikov's condition), are studied in a two-parameters space. The perturbed homoclinic systems undergo a countable set of tangent bifurcation followed by period-doubling bifurcations leading to a periodic orbits which may be attractors if Vertical Barlambda/lVertical Bar<1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2πVertical Barrho/ωVertical Bar). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues rho +- iω of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected
Full system bifurcation analysis of endocrine bursting models.
Tsaneva-Atanasova, Krasimira; Osinga, Hinke M; Riess, Thorsten; Sherman, Arthur
2010-06-21
Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis. PMID:20307553
Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling Waves
Baldi, Pietro; Toland, John F.
2008-01-01
The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy elastic membrane is analyzed as a problem in bifurcation theory. The behaviour of the two-dimensional cross-section of the membrane is modelled as a thin (unshearable), heavy, hyperelastic Cosserat rod, following Antman's elasticity theory, and the fluid beneath...
EXPERIMENTAL STUDY ON SEDIMENT DISTRIBUTION AT CHANNEL BIFURCATION
G.M. Tarekul ISLAM; M.R. KABIR; Ainun NISHAT
2002-01-01
This paper presents the experimental results on the distribution of sediments at channel bifurcation.The experiments have been conducted in a physical model of channel bifurcation. It consists of a straight main channel which bifurcates into two branch channels of different widths. The test rig is a mobile bed with fixed bank. Four different noses have been used to study the phenomenon. For each nose, three upstream discharges viz. 20 l/s, 30 l/s and 40 l/s have been employed. From the measured data, discharges and sediment transport ratios per unit width are calculated in the downstream branches.These data have been set to the general nodal point relation and a set of equations has been developed to describe the distribution of sediments to the downstream branches for different nose angles.
Level of Work Related Stress among Teachers in Elementary Schools
Teuta Agai–Demjaha
2015-07-01
CONCLUSION: Our findings confirm that the majority of interviewed teachers perceived their work-related stress as high or very high. In terms of the relationship between the level of teachers’ stress and certain demographic and job characteristics, according to our results, the level of work-related stress has shown significantly high relation to gender, age, levels of grades taught as well as working experience, and significant relation to the level of education.
Bifurcation analysis of a forest-grassland ecosystem
Russo, Lucia; Spiliotis, Konstantinos G.
2016-06-01
The nonlinear analysis of a forest-grassland ecosystem is performed as the main system parameters are changed. The model consists of a couple of nonlinear ordinary differential equations which include dynamically the human perceptions of forest/grassland value. The system displays multiple steady states corresponding to different forest densities as well as periodic regimes characterized by oscillations in time. We performed the bifurcation analysis of the system as the parameter relative to the human opinions influence is changed. We found that the main mechanisms which regulate the transitions occurring between different states or the appearance of new steady and dynamic regimes are transcritical, saddle/node and Hopf bifurcations.
Tibial hemimelia and femoral bifurcation.
Ugras, Ali Akin; Sungur, Ibrahim; Akyildiz, Mustafa Fehmi; Ercin, Ersin
2010-02-01
Femoral bifurcation and tibial agenesis are rare anomalies and have been described in both the Gollop-Wolfgang complex and tibial agenesis-ectrodactyly syndrome. This article presents a case of Gollop-Wolfgang complex without hand ectrodactyly. Tibial agenesis-ectrodactyly syndrome and Gollop-Wolfgang complex are variants of tibial field defect, which includes distal femoral duplication, tibial aplasia, oligo-ectrodactylous toe defects, and preaxial polydactyly, occasionally associated with hand ectrodactyly.This article describes the case of a patient with bilateral tibial hemimelia and left femoral bifurcation. The proximal tibial anlage had not been identified in the patient's left leg. After failed fibular transfer procedure, the knee was disarticulated. The other leg was treated with tibiofibular synostosis and centralization of fibula to os calcis. At 7-year follow-up, the patient ambulates with an above-knee prosthesis and uses an orthopedic boot for ankle stability.In patients with a congenital absence of the tibia, accurate diagnosis is of the utmost importance in planning future treatment. In the absence of proximal tibial anlage, especially in patients with femoral bifurcation, the knee should be disarticulated. Tibiofibular synostosis is a good choice in the presence of a proximal tibial anlage and good quadriceps function. PMID:20192156
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...
Level of Work Related Stress among Teachers in Elementary Schools
Teuta Agai–Demjaha; Jovanka Karadzinska Bislimovska; Dragan Mijakoski
2015-01-01
BACKGROUND: Teaching is considered a highly stressful occupation, with work-related stress levels among teachers being among the highest compared to other professions. Unfortunately there are very few studies regarding the levels of work-related stress among teachers in the Republic of Macedonia. AIM: To identify the level of self-perceived work-related stress among teachers in elementary schools and its relationship to gender, age, position in the workplace, the level of education and wo...
BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW
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.
Bifurcation Structures in a Family of 1D Discontinuous Linear-Hyperbolic Invertible Maps
Makrooni, Roya; Gardini, Laura; Sushko, Iryna
2015-12-01
We consider a family of one-dimensional discontinuous invertible maps from an application in engineering. It is defined by a linear function and by a hyperbolic function with real exponent. The presence of vertical and horizontal asymptotes of the hyperbolic branch leads to particular codimension-two border collision bifurcation (BCB) such that if the parameter point approaches the bifurcation value from one side then the related cycle undergoes a regular BCB, while if the same bifurcation value is approached from the other side then a nonregular BCB occurs, involving periodic points at infinity, related to the asymptotes of the map. We investigate the bifurcation structure in the parameter space. Depending on the exponent of the hyperbolic branch, different period incrementing structures can be observed, where the boundaries of a periodicity region are related either to subcritical, or supercritical, or degenerate flip bifurcations of the related cycle, as well as to a regular or nonregular BCB. In particular, if the exponent is positive and smaller than one, then the period incrementing structure with bistability regions is observed and the corresponding flip bifurcations are subcritical, while if the exponent is larger than one, then the related flip bifurcations are supercritical and, thus, also the regions associated with cycles of double period are involved into the incrementing structure.
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.
This is the abstracts of the Mini-Symposium on Stability and Bifurcation in Fluid Motions held on September 9-10, 1994 at the Tokai Establishment of JAERI and the Tokai Kaikan. Sixteen talks were given on various important subjects related with stability and bifurcation phenomena in fluids. All of them are theoretical and numerical analyses involving linear stability analysis, weakly nonlinear analysis, bifurcation analysis, and direct computation of nonlinearly equilibrium solutions. (author)
Fujimura, Kaoru [ed.] [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1995-01-01
This is the abstracts of the Mini-Symposium on Stability and Bifurcation in Fluid Motions held on September 9-10, 1994 at the Tokai Establishment of JAERI and the Tokai Kaikan. Sixteen talks were given on various important subjects related with stability and bifurcation phenomena in fluids. All of them are theoretical and numerical analyses involving linear stability analysis, weakly nonlinear analysis, bifurcation analysis, and direct computation of nonlinearly equilibrium solutions. (author).
It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the 'coupled oscillators'-based signal processing paradigm with the good features of the 'cellular neural network (CNN)'-based one. The first paradigm in this combination is the 'master system' and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called 'van der Pol oscillator' and (b) the so-called 'Duffing oscillator'. It is then implemented or realized on top of a 'slave system' platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have been derived, which are capable of determining the various
Coronary bifurcation lesions treated with simple or complex stenting
Behan, Miles W; Holm, Niels R; de Belder, Adam J;
2016-01-01
from two large bifurcation coronary stenting trials with similar methodology: the Nordic Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study: old, new, and evolving strategies (BBC ONE). METHODS AND RESULTS: Both multicentre randomized trials compared simple (provisional T...
A theory of biological relativity: no privileged level of causation.
Noble, Denis
2012-02-01
Must higher level biological processes always be derivable from lower level data and mechanisms, as assumed by the idea that an organism is completely defined by its genome? Or are higher level properties necessarily also causes of lower level behaviour, involving actions and interactions both ways? This article uses modelling of the heart, and its experimental basis, to show that downward causation is necessary and that this form of causation can be represented as the influences of initial and boundary conditions on the solutions of the differential equations used to represent the lower level processes. These insights are then generalized. A priori, there is no privileged level of causation. The relations between this form of 'biological relativity' and forms of relativity in physics are discussed. Biological relativity can be seen as an extension of the relativity principle by avoiding the assumption that there is a privileged scale at which biological functions are determined. PMID:23386960
School Management Related Knowledge Levels of Primary School Teachers
Ugurlu, Celal Teyyar
2013-01-01
The knowledge levels of the teachers affect the qualifications of operations and transactions in schools. School management related knowledge of the teachers is an essential tool to reach the targets of the school. The objective of this study was to determine the school management related knowledge levels of the teachers. Qualitative and…
Bifurcation of the spin-wave equations
We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)
Voltage stability, bifurcation parameters and continuation methods
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.
Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
Stefan Liebscher
2011-05-01
Full Text Available We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. We provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.
Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations
The nonlinear problems related to the plasma magnetohydrodynamic instabilities are studied. A bifurcation theory is applied and a general magnetohydrodynamic equation is proposed. Scalar functions, a steady magnetic field and a new equation for the velocity field are taken into account. A method allowing the obtention of suitable reduced equations for the instabilities study is described. Toroidal and cylindrical configuration plasmas are studied. In the cylindrical configuration case, analytical calculations are performed and two steady bifurcated solutions are found. In the toroidal configuration case, a suitable reduced equation system is obtained; a qualitative approach of a steady solution bifurcation on a toroidal Kink type geometry is carried out
Effect of magnetized electron cooling on a Hopf bifurcation
We have observed longitudinal limit cycle oscillations of a proton beam when a critical threshold in the relative velocity between the proton beam and the cooling electrons has been exceeded. The threshold for the bifurcation of a fixed point into a limit cycle, also known as a Hopf bifurcation, was found to be asymmetric with respect to the relative velocity. Further experiments were performed to verify that the asymmetry was related to electron beam alignment with respect to the stored proton beam. The measured amplitudes of the ensuing limit cycle were used to determine the cooling drag force, which exhibits the essential characteristics of the magnetized cooling, where the limit cycle attractor can coexist with a damping-free region and/or a fixed point attractor. copyright 1996 The American Physical Society
Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance
Neurons in the brain utilize various firing trains to encode the input signals they have received. Firing behavior of one single neuron is thoroughly explained by using a bifurcation diagram from polarized resting to firing, and then to depolarized resting. This explanation provides an important theoretical principle for understanding neuronal biophysical behaviors. This paper reports the novel experimental and modeling results of the modification of such a bifurcation diagram by adjusting small conductance potassium (SK) channel. In experiments, changes in excitability and depolarization block in nucleus accumbens shell and medium-spiny projection neurons are explored by increasing the intensity of injected current and blocking the SK channels by apamin. A shift of bifurcation points is observed. Then, a Hodgkin—Huxley type model including the main electrophysiological processes of such neurons is developed to reproduce the experimental results. The reduction of SK channel conductance also shifts the bifurcations, which is in consistence with experiment. A global bifurcation paradigm of this shift is obtained by adjusting two parameters, intensity of injected current and SK channel conductance. This work reveals the dynamics underpinning modulation of neuronal firing behaviors by biologically important ionic conductance. The results indicate that small ionic conductance other than that responsible for spike generation can modify bifurcation points and shift the bifurcation diagram and, thus, change neuronal excitability and adaptation. (interdisciplinary physics and related areas of science and technology)
Nonlinear stability control and λ-bifurcation
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
Probabilistic surface reconstruction of relative sea-level rise
Choblet, Gael; Husson, Laurent; Bodin, Thomas; Capdeville, Yann
2013-04-01
Relative sea level is shaped by multiple processes (mantle dynamic topography, plate tectonics, glacio-isostatic adjustment, present day melting of continental ice, anthropogenic causes…), most of which induce spatial gradients in relative sea level fluctuations. The evaluation of the global mean sea level rise is a also a key variable to decipher sea level evolution. Tide gauges represent the only mean to monitor sea-level rise on the scale of the 20th century, while the high quality satellite altimetry era is too short to be immune from short-term fluctuations. Tide gauge data compiled by the Permanent Service for the Mean Sea Level (PSMSL) converts into local estimates of sea level rise. Classically, these in situ observations are averaged spatially in order to infer the global mean sea level trend. However, the strongly heterogeneous distribution of tide gauges (e.g. very sparse in the Southern hemisphere) makes this approach relatively prone to uncertainties, given that sea level rise strongly varies geographically. Last, the societal consequences for coastal communities raise the prominent need for local (rather than global) sea level estimates. An alternative is therefore to provide a global surface reconstruction of relative sea level leading to both local variations and a better constrained global average. Here, we propose such a model from tide gauge records using a probabilistic scheme based on the reversible jump Markov chain Monte Carlo algorithm (as described by Bodin et al., JGR, 2012 for the example of the Australian Moho). This method allows to infer both model and parameter space so that not only the functions within the model but also the number of functions itself are free to vary. This is particulalry relevant to the case of tide gauges that are unevenly distributed on the surface of the Earth and whose record lengths are strongly variable. In addition, Bayesian statistics leads to a probabilistic representation (rather than a best fitting
Learning Class-Level Bayes Nets for Relational Data
Schulte, Oliver; Khosravi, Hassan; Moser, Flavia; Ester, Martin
2008-01-01
Many databases store data in relational format, with different types of entities and information about links between the entities. The field of statistical-relational learning (SRL) has developed a number of new statistical models for such data. In this paper we focus on learning class-level or first-order dependencies, which model the general database statistics over attributes of linked objects and links (e.g., the percentage of A grades given in computer science classes). Class-level stati...
Bifurcations of non-smooth systems
Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.
2012-12-01
Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.
Backward Bifurcation in Simple SIS Model
Zhan-wei Wang
2009-01-01
We describe and analyze a simple SIS model with treatment.In particular,we give a completely qualitative analysis by means of the theory of asymptotically autonomous system.It is found that a backward bifurcation occurs if the adequate contact rate or the capacity is small.It is also found that there exists bistable endemic equilibria.In the case of disease-induced death,it is shown that the backward bifurcation also occurs.Moreover,there is no limit cycle under some conditions,and the subcritical Hopf bifurcation occurs under another conditions.
Bifurcations of Periodic Orbits and Uniform Approximations
Schomerus, H; Schomerus, Henning; Sieber, Martin
1997-01-01
We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller's type would diverge at the bifurcation. New results for the tangent, the period doubling and the period tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results.
Cellular Cell Bifurcation of Cylindrical Detonations
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.
Tree level relations in a composite electroweak theory
Fariborz, Amir H; Schechter, Joseph
2014-01-01
We work out simple tree level relations in a top condensate model with dynamical electroweak symmetry breaking. We find that in this picture the mass of the composite Higgs boson at tree level is given by $m_H^2=\\frac{m_t^2}{2}$ where $m_t$ is the mass of the top quark.
Bifurcations and Crises in a Shape Memory Oscillator
Luciano G. Machado
2004-01-01
Full Text Available The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.
WV Xiao-Bo; MO Juan; YANG Ming-Hao; ZHENG Qiao-Hua; GU Hua-Guang; HEN Wei
2008-01-01
@@ Two different bifurcation scenarios, one is novel and the other is relatively simpler, in the transition procedures of neural firing patterns are studied in biological experiments on a neural pacemaker by adjusting two parameters. The experimental observations are simulated with a relevant theoretical model neuron. The deterministic non-periodic firing pattern lying within the novel bifurcation scenario is suggested to be a new case of chaos, which has not been observed in previous neurodynamical experiments.
Coexistence of periods in a bifurcation
Highlights: ► The bifurcation of the Varley–Gradwell–Hassell population model is revisited. ► The structure of the attractor mediating the bifurcation to chaos is studied. ► Geometric arguments are given for the coexistence of periods in the attractor. ► An algebraic method for the localization of these bifurcations is provided. - Abstract: A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley–Gradwell–Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
Continuation and Bifurcation software in MATLAB
Ravnås, Eirik
2008-01-01
This article contains discussions of the algorithms used for the construction of the continuation software implemented in this thesis. The aim of the continuation was to be able to perform continuation of equilibria and periodic solutions originating from a Hopf bifurcation point. Algorithms for detection of simple branch points, folds, and Hopf bifurcation points have also been implemented. Some considerations are made with regard to optimization, and two schemes for mesh adaptation of perio...
Stability and bifurcation of mutual system with time delay
In this paper, we study the stability and bifurcation in a mutual model with a delay τ, where τ is regarded as a parameter. It is found that there are stability switches, and Hopf bifurcation occur when the delay τ passes through a sequence of critical values. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions in the first bifurcation value is given using the normal form method and center manifold theorem
Bifurcation Analysis of the Wound Rotor Induction Motor
Salas-Cabrera, R.; Hernandez-Colin, A.; Roman-Flores, J.; Salas-Cabrera, N.
This work deals with the bifurcation phenomena that occur during the open-loop operation of a single-fed three-phase wound rotor induction motor. This paper demonstrates the occurrence of saddle-node bifurcation, hysteresis, supercritical saddle-node bifurcation, cusp and Hopf bifurcation during the individual operation of this electromechanical system. Some experimental results associated with the bifurcation phenomena are presented.
JIA Bing; GU Hua-Guang; LI Yu-Ye
2011-01-01
@@ Excitability is an essential characteristic of excitable media such as nervous and cardiac systems.Different types of neuronal excitability are related to different bifurcation structures.We simulate the coherence resonance effect near a saddle-node and homoclinic bifurcation corresponding to type-I excitability in a theoretical neuron model,and recognize the obvious features of the corresponding firing pattern.Similar firing patterns are discovered in rat hippocampal CA1 pyramidal neurons.The results are not only helpful for understanding the dynamics of the saddle-node bifurcation and type-I excitability in a realistic nervous system,but also provide a practical indicator to identify types of excitability and bifurcation.%Excitability is an essential characteristic of excitable media such as nervous and cardiac systems. Different types of neuronal excitability are related to different bifurcation structures. We simulate the coherence resonance effect near a saddle-node and homoclinic bifurcation corresponding to type-I excitability in a theoretical neuron model, and recognize the obvious features of the corresponding firing pattern. Similar firing patterns are discovered in rat hippocampal CA1 pyramidal neurons. The results are not only helpful for understanding the dynamics of the saddle-node bifurcation and type-I excitability in a realistic nervous system, but also provide a practical indicator to identify types of excitability and bifurcation.
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 ...
Crystalline undulator radiation and sub-harmonic bifurcation of system
Luo Xiao-Hua; He Wei; Wu Mu-Ying; Shao Ming-Zhu; Luo Shi-Yu
2013-01-01
Looking for new light sources,especially short wavelength laser light sources has attracted widespread attention.This paper analytically describes the radiation of a crystalline undulator field by the sine-squared potential.In the classical mechanics and the dipole approximation,the motion equation of a particle is reduced to a generalized pendulum equation with a damping term and a forcing term.The bifurcation behavior of periodic orbits is analyzed by using the Melnikov method and the numerical method,and the stability of the system is discussed.The results show that,in principle,the stability of the system relates to its parameters,and only by adjusting these parameters appropriately can the occurrence of bifurcation be avoided or suppressed.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
The selection pressures induced non-smooth infectious disease model and bifurcation analysis
Highlights: • A non-smooth infectious disease model to describe selection pressure is developed. • The effect of selection pressure on infectious disease transmission is addressed. • The key factors which are related to the threshold value are determined. • The stabilities and bifurcations of model have been revealed in more detail. • Strategies for the prevention of emerging infectious disease are proposed. - Abstract: Mathematical models can assist in the design strategies to control emerging infectious disease. This paper deduces a non-smooth infectious disease model induced by selection pressures. Analysis of this model reveals rich dynamics including local, global stability of equilibria and local sliding bifurcations. Model solutions ultimately stabilize at either one real equilibrium or the pseudo-equilibrium on the switching surface of the present model, depending on the threshold value determined by some related parameters. Our main results show that reducing the threshold value to a appropriate level could contribute to the efficacy on prevention and treatment of emerging infectious disease, which indicates that the selection pressures can be beneficial to prevent the emerging infectious disease under medical resource limitation
McKinney, Alexander M.; Casey, Sean O.; Teksam, Mehmet; Truwit, Charles L.; Kieffer, Stephen [University of Minnesota Medical School, Departments of Radiology, Minneapolis, MN (United States); Lucato, Leandro T. [Clinics Hospital, University of Sao Paulo, Sao Paulo (Brazil); Smith, Maurice [Johns Hopkins University, Department of Biomedical Engineering, Baltimore, MD (United States)
2005-01-01
The aim of this paper was to determine the correlation between calcium burden (expressed as a volume) and extent of stenosis of the origin of the internal carotid artery (ICA) by CT angiography (CTA). Previous studies have shown that calcification in the coronary arteries correlates with significant vessel stenosis, and severe calcification (measured by CT) in the carotid siphon correlates with significant (greater than 50% stenosis) as determined angiographically. Sixty-one patients (age range 50-85 years) underwent CT of the neck with intravenous administration of iodinated contrast for a variety of conditions. Images were obtained with a helical multidetector array CT scanner and reviewed on a three-dimensional workstation. A single observer manipulated window and level to segment calcified plaque from vascular enhancement in order to quantify vascular calcium volume (cc) in the region of the bifurcation of the common carotid artery/ICA origin, and to measure the extent of ICA stenosis near the origin. A total of 117 common carotid artery bifurcations were reviewed. A ''significant'' stenosis was defined arbitrarily as >40% (to detect lesions before they become hemodynamically significant) of luminal diameter on CTA using NASCET-like criteria. All ''significant'' stenoses (21 out of 117 carotid bifurcations) had measurable calcium. We found a relatively strong correlation between percent stenosis and the calcium volume (Pearson's r= 0.65, P<0.0001). We also found that there was an even stronger correlation between the square root of the calcium volume and the percent stenosis as measured by CTA (r= 0.77, P<0.0001). Calcium volumes of 0.01, 0.03, 0.06, 0.09 and 0.12 cc were used as thresholds to evaluate for a ''significant'' stenosis. A receiver operating characteristic (ROC) curve demonstrated that thresholds of 0.06 cc (sensitivity 88%, specificity 87%) and 0.03 cc (sensitivity 94%, specificity
The aim of this paper was to determine the correlation between calcium burden (expressed as a volume) and extent of stenosis of the origin of the internal carotid artery (ICA) by CT angiography (CTA). Previous studies have shown that calcification in the coronary arteries correlates with significant vessel stenosis, and severe calcification (measured by CT) in the carotid siphon correlates with significant (greater than 50% stenosis) as determined angiographically. Sixty-one patients (age range 50-85 years) underwent CT of the neck with intravenous administration of iodinated contrast for a variety of conditions. Images were obtained with a helical multidetector array CT scanner and reviewed on a three-dimensional workstation. A single observer manipulated window and level to segment calcified plaque from vascular enhancement in order to quantify vascular calcium volume (cc) in the region of the bifurcation of the common carotid artery/ICA origin, and to measure the extent of ICA stenosis near the origin. A total of 117 common carotid artery bifurcations were reviewed. A ''significant'' stenosis was defined arbitrarily as >40% (to detect lesions before they become hemodynamically significant) of luminal diameter on CTA using NASCET-like criteria. All ''significant'' stenoses (21 out of 117 carotid bifurcations) had measurable calcium. We found a relatively strong correlation between percent stenosis and the calcium volume (Pearson's r= 0.65, P<0.0001). We also found that there was an even stronger correlation between the square root of the calcium volume and the percent stenosis as measured by CTA (r= 0.77, P<0.0001). Calcium volumes of 0.01, 0.03, 0.06, 0.09 and 0.12 cc were used as thresholds to evaluate for a ''significant'' stenosis. A receiver operating characteristic (ROC) curve demonstrated that thresholds of 0.06 cc (sensitivity 88%, specificity 87%) and 0.03 cc (sensitivity 94%, specificity 76%) generated the best combinations of sensitivity and
Agliari, Anna [Dipartimento di Scienze Economiche e Sociali, Universita Cattolica del Sacro Cuore, Via Emilia Parmense, 84, 29100 Piacenza (Italy)]. E-mail: anna.agliari@unicatt.it
2006-08-15
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed.
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed
Explaining trends and variability in coastal relative sea level
Frederikse, Thomas; Riva, Riccardo
2016-04-01
Comprehensive understanding of trends and variability in coastal mean sea level is vital for protecting shores under a changing climate. To understand the behavior of coastal relative sea level (RSL), it is crucial to identify all relevant processes. We combine data from various geophysical models and observations to determine whether the trends and decadal variability observed in relative sea level at tide gauges can be explained by the sum of all known contributors. A key contributor to RSL is vertical land motion, which is caused by glacial isostatic adjustment (GIA), solid earth response to surface loading, tectonics, and local effects. We explicitly model low-frequency loading effects to correct GPS records, which leads to a more consistent trend than only using GIA models. Secondly, we create sea level fingerprints based on estimates of ice melt and changes in land hydrology, which provide the RSL contribution due to large-scale mass transport. Since coastal areas are often located on shallow continental shelves, steric effects will generally be small, and a large fraction of the decadal sea level variability will have a remote steric origin. Therefore, we determine a relation between coastal sea level and deep sea steric variability. For the period 1950-2012, we find that for many locations, including the European coast, the observed and modeled RSL time series agree well on decadal and secular scales.
University students' understanding level about words related to nuclear power
The authors conducted a survey of university students' understanding level about words related to nuclear power before and after Fukushima Daiichi Power Plant accident, and analyzed the difference between before and after the accident. The results show that university students' understanding level improved after the accident, especially in the case of reported words by mass media. Understanding level of some nuclear power security words which were not reported so much by mass media also improved. That may be caused by rising of people's concern about nuclear power generation after the accident, and there is a possibility that the accident motivated people to access such words via internet, journals, etc. (author)
Extraction of Children's Friendship Relation from Activity Level
Kono, Aki; Shintani, Kimio; Katsuki, Takuya; Kihara, Shin'ya; Ueda, Mari; Kaneda, Shigeo; Haga, Hirohide
Children learn to fit into society through living in a group, and it's greatly influenced by their friend relations. Although preschool teachers need to observe them to assist in the growth of children's social progress and support the development each child's personality, only experienced teachers can watch over children while providing high-quality guidance. To resolve the problem, this paper proposes a mathematical and objective method that assists teachers with observation. It uses numerical data of activity level recorded by pedometers, and we make tree diagram called dendrogram based on hierarchical clustering with recorded activity level. Also, we calculate children's ``breadth'' and ``depth'' of friend relations by using more than one dendrogram. When we record children's activity level in a certain kindergarten for two months and evaluated the proposed method, the results usually coincide with remarks of teachers about the children.
Yan Zhang
2014-01-01
Full Text Available We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and nonhomogeneous periodic solutions of this particular system. In particular, we also prove that the spatial homogeneous periodic solutions bifurcating from the smallest Hopf bifurcation point of the system are always unstable. This together with the instability results of the spatially nonhomogeneous periodic solutions by Yi et al., 2009, indicates that, in this model, all the oscillatory patterns from Hopf bifurcations are unstable.
Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model
Xie, Yong; Chen, Luonan; Kang, Yan Mei; Aihara, Kazuyuki
2008-06-01
It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer’s disease, and Parkinson’s disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases. In this study, we employ a washout filter-aided dynamic feedback controller to control the onset of Hopf bifurcation in the Hodgkin-Huxley (HH) model. Specifically, by the control scheme, we can move the Hopf bifurcation to a desired point irrespective of whether the corresponding steady state is stable or unstable. In other words, we are able to advance or delay the Hopf bifurcation, so as to prevent it from occurring in a certain range of the externally applied current. Moreover, we can control the criticality of the bifurcation and regulate the oscillation amplitude of the bifurcated limit cycle. In the controller, there are only two terms: the linear term and the nonlinear cubic term. We show that while the former determines the location of the Hopf bifurcation, the latter regulates the criticality of the Hopf bifurcation. According to the conditions of the occurrence of Hopf bifurcation and the bifurcation stability coefficient, we can analytically deduce the linear term and the nonlinear cubic term, respectively. In addition, we also show that mixed-mode oscillations (MMOs), featuring slow action potential generation, which are frequently observed in both experiments and models of chemical and biological systems, appear in the controlled HH model. It is well known that slow firing rates in single neuron models could be achieved only by type-I neurons. However, the controlled HH model is still classified as a type
Bifurcation readout of a Josephson phase qubit
The standard method to read out a Josephson phase qubit is using a dc-SQUID to measure the state-dependent magnetic flux of the qubit by switching to the non-superconducting state. This process generates heat directly on the qubit chip and quasi-particles in the circuitry. Both effects require a relatively long cool-down time after each switching event. This, together with the time needed to ramp up the bias current of the SQUID limits the repetition rate of the experiment. In our ongoing experiments we replace the standard readout scheme by a SQUID shunted by a capacitor. This nonlinear resonator is operated close to its bifurcation point between two oscillating states which depend on the qubit flux. The measurement is done by detecting either the resonance amplitude or phase shift of the reflected probe signal. We verified that our SQUID resonator works as linear resonator for low excitation powers and observed the periodic dependence of the resonance frequency on the externally applied magnetic flux. For higher excitation powers the device shows a hysteretic behavior between the two oscillating states. Current experiments are focused on a pulsed rf-readout to measure coherent evolution of the qubit states. We hope to achieve longer coherence times, perform faster measurements, and test non-destructive measurement schemes with Josephson phase qubits.
Lung cancer in relation to airborne radiation levels
A 1986 aeroradiometric survey of the eastern two-thirds of Washington County, Maryland provided and opportunity to study lung cancers in relation to gamma radiation levels. In the first approach, lung cancer deaths between 1963 and 1975 in four areas of the county categorized as low, moderately low, moderately high, and high showed relative risks of 1.00, 0.93, 1.01, and 1.43, respectively, after adjustment of sex, age, and smoking. A second approach used lung cancer cases diagnosed between 1975 and 1989, controls matched to cases by race, sex, and age, and aerometric radiation readings above the individual residences. In four levels of increasing gamma radiation, odds ratios adjusted for smoking were 1.00, 0.84, 0.90, and 0.92, respectively. No differences were statistically significant
TAXONOMIC FINANCIAL ANALYSIS OF FINANCIAL RELATIONS OF SUBJECTS MAKRO LEVEL
Kuzenko, A.
2014-01-01
This paper presents the results of the taxonomic analysis of the financial security of financial relations macro level. In economics sometimes difficult to conduct research statistical methods, which are based on the distribution of the multidimensional space of random variables, as the number of available observations, which are in the data set, not great. This problem can solve application taxonomic analysis in diagnosing the state of financial security.Rozrahunky carried out in accordance ...
COLLEGE-LEVEL INSTRUCTION: DERIVED RELATIONS AND PROGRAMMED INSTRUCTION
Fienup, Daniel M; Hamelin, Jeffery; Reyes-Giordano, Kimberly; Falcomata, Terry S
2011-01-01
Recent research has demonstrated the effectiveness of programmed instruction that integrates derived relations to teach college-level academic material. This method has been demonstrated to be effective and economical in the teaching of complex mathematics and biology concepts. Although this approach may have potential applications with other domains of college learning, more studies are needed to evaluate important technological variables. Studies that employ programmed instruction are discu...
Changes in Holocene relative sea-level and coastal morphology
Hede, Mikkel Ulfeldt; Sander, Lasse; Clemmensen, Lars B;
2015-01-01
Changes in relative sea-level (RSL) during the Holocene are reconstructed based on ground-penetrating radar (GPR) data collected across a raised beach ridge system on the island of Samsø, Denmark. The internal architecture of the beach ridge and swale deposits is divided into characteristic radar...... facies. We identify downlap points interpreted to mark the transition from the beachface to the upper shoreface and, thus, sea-level at the time of deposition. This new data set shows that beach steps can be preserved and resolved in GPR reflection data. This is important, as downlap points identified at...... the base of the beach steps should be corrected for beach step height in order to be used as a marker of sea-level. Identification of beach steps in combination with observed changes in dips of the interpreted beachface reflections can give information about changes in the morphodynamic conditions of...
Oxygen transfer in human carotid artery bifurcation
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.
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.
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 ...
Mangrove sedimentation and response to relative sea-level rise
Woodroffe, CD; Rogers, K.; Mckee, Karen L.; Lovelock, CE; Mendelssohn, IA; Saintilan, N.
2016-01-01
Mangroves occur on upper intertidal shorelines in the tropics and subtropics. Complex hydrodynamic and salinity conditions influence mangrove distributions, primarily related to elevation and hydroperiod; this review considers how these adjust through time. Accumulation rates of allochthonous and autochthonous sediment, both inorganic and organic, vary between and within different settings. Abundant terrigenous sediment can form dynamic mudbanks; tides redistribute sediment, contrasting with mangrove peat in sediment-starved carbonate settings. Sediments underlying mangroves sequester carbon, but also contain paleoenvironmental records of adjustments to past sea-level changes. Radiometric dating indicates long-term sedimentation, whereas Surface Elevation Table-Marker Horizon measurements (SET-MH) provide shorter perspectives, indicating shallow subsurface processes of root growth and substrate autocompaction. Many tropical deltas also experience deep subsidence, which augments relative sea-level rise. The persistence of mangroves implies an ability to cope with moderately high rates of relative sea-level rise. However, many human pressures threaten mangroves, resulting in continuing decline in their extent throughout the tropics.
Mangrove Sedimentation and Response to Relative Sea-Level Rise
Woodroffe, C. D.; Rogers, K.; McKee, K. L.; Lovelock, C. E.; Mendelssohn, I. A.; Saintilan, N.
2016-01-01
Mangroves occur on upper intertidal shorelines in the tropics and subtropics. Complex hydrodynamic and salinity conditions, related primarily to elevation and hydroperiod, influence mangrove distributions; this review considers how these distributions change over time. Accumulation rates of allochthonous and autochthonous sediment, both inorganic and organic, vary between and within different settings. Abundant terrigenous sediment can form dynamic mudbanks, and tides redistribute sediment, contrasting with mangrove peat in sediment-starved carbonate settings. Sediments underlying mangroves sequester carbon but also contain paleoenvironmental records of adjustments to past sea-level changes. Radiometric dating indicates long-term sedimentation, whereas measurements made using surface elevation tables and marker horizons provide shorter perspectives, indicating shallow subsurface processes of root growth and substrate autocompaction. Many tropical deltas also experience deep subsidence, which augments relative sea-level rise. The persistence of mangroves implies an ability to cope with moderately high rates of relative sea-level rise. However, many human pressures threaten mangroves, resulting in a continuing decline in their extent throughout the tropics. *
Lassen, Jens Flensted; Holm, Niels Ramsing; Banning, Adrian; Burzotta, Francesco; Lefèvre, Thierry; Chieffo, Alaide; Hildick-Smith, David; Louvard, Yves; Stankovic, Goran
2016-05-17
Coronary bifurcations are involved in 15-20% of all percutaneous coronary interventions (PCI) and remain one of the most challenging lesions in interventional cardiology in terms of procedural success rate as well as long-term cardiac events. The optimal management of bifurcation lesions is, despite a fast growing body of scientific literature, the subject of considerable debate. The European Bifurcation Club (EBC) was initiated in 2004 to support a continuous overview of the field, and aims to facilitate a scientific discussion and an exchange of ideas on the management of bifurcation disease. The EBC hosts an annual, compact meeting, dedicated to bifurcations, which brings together physicians, engineers, biologists, physicists, epidemiologists and statisticians for detailed discussions. Every meeting is finalised with a consensus statement which reflects the unique opportunity of combining the opinions of interventional cardiologists with the opinions of a large variety of other scientists on bifurcation management. The present 11th EBC consensus document represents the summary of the up-to-date EBC consensus and recommendations. It points to the fact that there is a multitude of strategies and approaches to bifurcation stenting within the provisional strategy and in the different two-stent strategies. The main EBC recommendation for PCI of bifurcation lesions remains to use main vessel (MV) stenting with a proximal optimisation technique (POT) and provisional side branch (SB) stenting as a preferred approach. The consensus document covers a moving target. Much more scientific work is needed in non-left main (LM) and LM bifurcation lesions for continuous improvement of the outcome of our patients. PMID:27173860
Linking the levels: network and relational perspectives for community psychology.
Neal, Jennifer Watling; Christens, Brian D
2014-06-01
In this article, we assert that relationships and networks are of paramount importance for understanding and improving settings, neighborhoods, communities, and larger social systems. Despite previous acknowledgements of their relevance, relational and social network perspectives and analyses remain underrepresented in community psychological research and action. Here, we claim that network and relational perspectives can provide conceptual and empirical 'links' between levels of analysis, more fully reflecting a transactional view. We also describe some of the sophisticated methodologies that can be employed in empirical studies drawing on these perspectives. Additionally, we contend that core concepts in community psychology such as health promotion, empowerment, coalition building, and dissemination and implementation can be better understood when employing relational and network perspectives. As an introduction to this special issue of American Journal of Community Psychology, we draw out themes and key points from the articles in the issue, and offer recommendations for future advancement of these perspectives in the field. PMID:24752731
CAVITATION BIFURCATION FOR COMPRESSIBLE ANISOTROPIC HYPERELASTIC MATERIALS
ChengChangjun; RenJiusheng
2004-01-01
The effect of material anisotropy on the bifurcation for void tormation in anisotropic compressible hyperelastic materials is examined. Numerical solutions are obtained in an anisotropic sphere, whose material is transversely isotropic in the radial direction. It is shown that the bifurcation may occur either to the right or to the left, depending on the degree of material anisotropy. The deformation and stress contribution in the sphere before cavitation are different from those after cavitation. The stability of solutions is discussed through a comparison of energy.
Bifurcation of Jovian magnetotail current sheet
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the B_{x}-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Hopf Bifurcation in a Nonlinear Wave System
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.
Physical exercise intensity can be related to plasma glutathione levels.
Gambelunghe, C; Rossi, R; Micheletti, A; Mariucci, G; Rufini, S
2001-03-01
The aim of the present study was to examine the effect of different kinds of physical exercise on plasma glutathione levels. Male Wistar rats were randomly divided into four groups: In walking group (W; n=6), rats were trained to walk 0.8 m/min for 45 min; slow running group (SR; n=6) were trained to run 4 m/min for 45 min; fast running group (FR; n=6) ran 8m/min for 60 min and control rats (C; n=6) remained in their home cages. All animals were sacrificed after exercise and the levels of reduced glutathione (GSH) in plasma samples determined by high performance liquid chromatography (HPLC) with a fluorescent detector. Compared to controls, exercise did not change GSH plasma levels of the W group. A tendency to decrease blood GSH was observed in plasma samples of the SR group and in the FR group, physical exercise resulted in a dramatic decrease in GSH plasma levels. These data suggest that during light physical exercise there is a low production of reactive oxygen species (ROS) with a low request for antioxidant defence such as oxidation of GSH. The dramatic decrease observed in GSH levels in FR rats would indicate the presence of oxidative stress able to modify blood antioxidant profiles. Our results suggest that GSH plays a central antioxidant role in blood during intensive physical exercise and that its modifications are closely related to exercise intensity. PMID:11579999
Bifurcations of a class of singular biological economic models
This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.
Codimension-2 bifurcations of the Kaldor model of business cycle
Research highlights: → The conditions are given such that the characteristic equation may have purely imaginary roots and double zero roots. → Purely imaginary roots lead us to study Hopf and Bautin bifurcations and to calculate the first and second Lyapunov coefficients. → Double zero roots lead us to study Bogdanov-Takens (BT) bifurcation. → Bifurcation diagrams for Bautin and BT bifurcations are obtained by using the normal form theory. - Abstract: In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov-Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.
Bifurcation Analysis of a Discrete Logistic System with Feedback Control
WU Dai-yong
2015-01-01
The paper studies the dynamical behaviors of a discrete Logistic system with feedback control. The system undergoes Flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors of the system, such as the period-doubling bifurcation in periods 2, 4, 8 and 16, and quasi-periodic orbits and chaotic sets.
Delay-induced multistability near a global bifurcation
Hizanidis, J.; Aust, R.; Schoell, E.
2007-01-01
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit cycles are found in accordance with Shilnikov's theorems.
Symmetry breaking and bifurcations in the periodic orbit theory. 2. Spheroidal cavity
We derive a semiclassical trace formula for the level density of a three-dimensional spheroidal cavity. To overcome the divergences and discontinuities occurring at bifurcation points and in the spherical limit, the trace integrals over the action-angle variables are performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell energies are in good agreement with quantum-mechanical results. We find that the births of three-dimensional orbits through the bifurcations of planar orbits in the equatorial plane lead to considerable enhancement of the shell effect for superdeformed shapes. (author)
Stability and Hopf Bifurcation in the Watt Governor System
Sotomayor, Jorge; Mello, Luis Fernando; Braga, Denis de Carvalho
2006-01-01
In this paper we study the Lyapunov stability and Hopf bifurcation in a system coupling a Watt-centrifugal-governor with a steam-engine. Sufficient conditions for the stability of the equilibrium state in terms of the physical parameters and of the bifurcating periodic orbit at most critical parameters on the bifurcation surface are given.
The Bifurcations of Traveling Wave Solutions of the Kundu Equation
Yating Yi; Zhengrong Liu
2013-01-01
We use the bifurcation method of dynamical systems to study the bifurcations of traveling wave solutions for the Kundu equation. Various explicit traveling wave solutions and their bifurcations are obtained. Via some special phase orbits, we obtain some new explicit traveling wave solutions. Our work extends some previous results.
Bifurcation structure of a model of bursting pancreatic cells
Mosekilde, Erik; Lading, B.; Yanchuk, S.; Maistrenko, Y.
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...
Singular limit cycle bifurcations to closed orbits and invariant tori
This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed
Singular limit cycle bifurcations to closed orbits and invariant tori
Ye Zhiyong [Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240 (China); Department of Mathematics, Chongqing Institute of Technology, Chongqing 400050 (China); E-mail: yezhiyong@sjtu.edu.cn; Han Maoan [Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240 (China); E-mail: mahan@sjtu.edu.cn
2006-02-01
This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed.
NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS
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).
Nomura, Yasuyuki; Saito, Satoshi; Ishiwata, Ryosuke; Sugiyama, Yuki
2016-01-01
A dissipative system with asymmetric interaction, the optimal velocity model, shows a Hopf bifurcation concerned with the transition from a homogeneous motion to the formation of a moving cluster, such as the emergence of a traffic jam. We investigate the properties of Hopf bifurcation depending on the particle density, using the dynamical system for the traveling cluster solution of the continuum system derived from the original discrete system of particles. The Hopf bifurcation is revealed as a subcritical one, and the property explains well the specific phenomena in highway traffic: the metastability of jamming transition and the hysteresis effect in the relation of car density and flow rate. PMID:26871081
Digital subtraction angiography of carotid bifurcation
This study demonstrates the reliability of digital subtraction angiography (DSA) by means of intra- and interobserver investigations as well as indicating the possibility of substituting catheterangiography by DSA in the diagnosis of carotid bifurcation. Whenever insufficient information is obtained from the combination of non-invasive investigation and DSA, a catheterangiogram will be necessary. (Auth.)
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 successive torus doubling
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.
Stability and Hopf bifurcation for a business cycle model with expectation and delay
Liu, Xiangdong; Cai, Wenli; Lu, Jiajun; Wang, Yangyang
2015-08-01
According to rational expectation hypothesis, the government will take into account the future capital stock in the process of investment decision. By introducing anticipated capital stock into an economic model with investment delay, we construct a mixed functional differential system including delay and advanced variables. The system is converted to the one containing only delay by variable substitution. The equilibrium point of the system is obtained and its dynamical characteristics such as stability, Hopf bifurcation and its stability and direction are investigated by using the related theories of nonlinear dynamics. We carry out some numerical simulations to confirm these theoretical conclusions. The results indicate that both capital stock's anticipation and investment lag are the certain factors leading to the occurrence of cyclical fluctuations in the macroeconomic system. Moreover, the level of economic fluctuation can be dampened to some extent if investment decisions are made by the reasonable short-term forecast on capital stock.
Hyperhomocysteinemia in ulcerative colitis is related to folate levels
Petros Zezos; Georgia Papaioannou; Nikolaos Nikolaidis; Themistoclis Vasiliadis; Olga Giouleme; Nikolaos Evgenidis
2005-01-01
AIM: To study the prevalence and clinical significance of hyperhomocysteinemia (hHcys), an independent factor for arterial and venous thrombosis, in a group of patients with ulcerative colitis (UC).METHODS: Fasting homocysteine (Hcys), folate, and vitamin B12 serum levels were measured in 40 UC patients and 50 healthy controls. Clinical data regarding UC were gathered.RESULTS: Median serum Hcys levels in UC patients were similar to those in controls (12.26 μmol/L vs 12.32 μmol/L), but the prevalence of hHcys was higher in UC patients than in controls (30% vs 10%, P= 0.028). UC significantly increased the risk of hHcys (adjusted odds ratio: 4.125;95% CI: 1.26-13.44). Multivariate regression analysis showed that male sex, folate and vitamin B12 deficiency or lower serum values were significant independent predictors of higher Hcys levels in UC patients (r2 = 0.4; P＜0.001).CONCLUSION: hHcys is common in UC patients and it is related to folate and vitamin B12 deficiency or lower serum values. It would be reasonable for patients with UC to receive folate and vitamin B complex supplements as a prophylactic measure.
Rothenstein, Bernhard; Nafornita, Corina
2004-01-01
We present a way of teaching Einstein's special relativity. It starts with Galileo's relativity, the learners know from previous lectures. The lecture underlines that we can have three transformation equations for the space-time coordinates of the same event, which lead to absolute clock readings, time intervals and lengths (Galileo's relativity), to absolute clock readings but to relative time intervals and lengths (up-to-date Galileo transformations) and to relative clock readings time inte...
Bifurcation of a nonlinear Schrödinger equation with a symmetrical double well
The bifurcation of a one-dimensional Gross–Pitaevskii-type equation with a symmetrical double well is investigated. A general relation for the critical power, above which a kind of bifurcation transition from a supercritical pitchfork to a subcritical pitchfork occurs, is presented in terms of the ratio of the nonlinear tunneling to the nonlinear interaction. When the nonlinearity is very weak, our relation reduces to a universal power law; when the nonlinearity is strong, this universal critical power depends on the nonlinearity, the shape of the trap and even the dimension. By means of a numerical calculation, a possible bifurcation transition induced by nonlinearity is predicted for both the ground state and the first excited state. (paper)
William H Barnett
Full Text Available The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator
Stable 3-level leapfrog integration in numerical relativity
New, K C B; Misner, Charles William; Centrella, J M; New, Kimberly C. B.; Watt, Keith; Misner, Charles W.; Centrella, Joan M.
1998-01-01
The 3-level leapfrog time integration algorithm is an attractive choice for numerical relativity simulations since it is time-symmetric and avoids non-physical damping. In Newtonian problems without velocity dependent forces, this method enjoys the advantage of long term stability. However, for more general differential equations, whether ordinary or partial, delayed onset numerical instabilities can arise and destroy the solution. A known cure for such instabilities appears to have been overlooked in many application areas. We give an improved cure ("deloused leapfrog") that both reduces memory demands (important for 3+1 dimensional wave equations) and allows for the use of adaptive timesteps without a loss in accuracy. We show both that the instability arises and that the cure we propose works in highly relativistic problems such as tightly bound geodesics, spatially homogeneous spacetimes, and strong gravitational waves. In the gravitational wave test case (polarized waves in a Gowdy spacetime) the delouse...
BIFURCATION ANALYSIS OF EQUILIBRIUM POINT IN TWO NODE POWER SYSTEM
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.
Correlation analysis of the North Equatorial Current bifurcation and the Indonesian Throughflow
ZHAO Yunxia; WEI Zexun; WANG Yonggang; XU Tengfei; FENG Ying
2015-01-01
Based on monthly mean Simple Ocean Data Assimilation (SODA) products from 1958 to 2007, this study analyzes the seasonal and interannual variability of the North Equatorial Current (NEC) bifurcation latitude and the Indonesian Throughflow (ITF) volume transport. Further, Empirical Mode Decomposition (EMD) method and lag-correlation analysis are employed to reveal the relationships between the NEC bifurcation location, NEC and ITF volume transport and ENSO events. The analysis results of the seasonal variability show that the annual mean location of NEC bifurcation in upper layer occurs at 14.33°N and ITF volume transport has a maximum value in summer, a minimum value in winter and an annual mean transport of 7.75×106 m3/s. The interannual variability analysis indicates that the variability of NEC bifurcation location can be treated as a precursor of El Niño. The correlation coefficient between the two reaches the maximum of 0.53 with a time lag of 2 months. The ITF volume transport is positively related with El Niño events with a maximum coefficient of 0.60 by 3 months. The NEC bifurcation location is positively correlated with the ITF volume transport with a correlation coefficient of 0.43.
Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study
There is recent interest in the role of carotid bifurcation anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis. Certain anatomical and geometric configurations at the carotid bifurcation have been linked to disturbed flow. It has been proposed that vascular dimensions are selected to minimize energy required to maintain blood flow, and that this occurs when an exponent of 3 relates the radii of parent and daughter arteries. We evaluate whether the dimensions of bifurcation of the extracranial carotid artery follow this principle of minimum work. This study involved subjects who had computed tomographic angiography (CTA) at our institution between 2006 and 2007. Radii of the common, internal and external carotid arteries were determined. The exponent was determined for individual bifurcations using numerical methods and for the sample using nonlinear regression. Mean age for 45 participants was 56.9 ± 16.5 years with 26 males. Prevalence of vascular risk factors was: hypertension-48%, smoking-23%, diabetes-16.7%, hyperlipidemia-51%, ischemic heart disease-18.7%. The value of the exponent ranged from 1.3 to 1.6, depending on estimation methodology. The principle of minimum work (defined by an exponent of 3) may not apply at the carotid bifurcation. Additional factors may play a role in the relationship between the radii of the parent and daughter vessels
Overcoming Bifurcation Instability in High-Repetition-Rate Ho:YLF Regenerative Amplifiers
Kroetz, Peter; Ruehl, Axel; Chatterjee, Gourab; Calendron, Anne-Laure; Murari, Krishna; Cankaya, Huseyin; LI Peng; Kaertner, Franz X.; Hartl, Ingmar; Miller, R. J. Dwayne
2015-01-01
We demonstrate a Ho:YLF regenerative amplifier (RA) overcoming bifurcation instability and consequently achieving high extraction energies of 6.9 mJ at a repetition rate of 1 kHz with pulse-to-pulse fluctuations of 1.1%. Measurements of the output pulse energy, corroborated by numerical simulations, identify an operation point that allows high-energy pulse extraction at a minimum noise level. Complete suppression of the onset of bifurcation was achieved by gain saturation after each pumping c...
Bifurcation and neck formation as a precursor to ductile fracture during high rate extension
Freund, L.B.; Soerensen, N.J. [Brown Univ., Providence, RI (United States)
1997-12-31
A block of ductile material, typically a segment of a plate or shell, being deformed homogeneously in simple plane strain extension commonly undergoes a bifurcation in deformation mode to nonuniform straining in the advanced stages of plastic flow. The focus here is on the influence of material inertia on the bifurcation process, particularly on the formation of diffuse necks as precursors to dynamic ductile fracture. The issue is considered from two points of view, first within the context of the theory of bifurcation of rate-independent, incrementally linear materials and then in terms of the complete numerical solution of a boundary value problem for an elastic-viscoplastic material. It is found that inertia favors the formation of relatively short wavelength necks as observed in shaped charge break-up and dynamic fragmentation.
Quelques problèmes de stabilité et de bifurcation des solides visqueux
ABED-MERAIM, Farid
1999-01-01
This PhD thesis is composed essentially of two main parts, of unequal sizes, which are summarized as follows: Part I: It is concerned with stability and bifurcation issues relating to strain-rate-independent solids and structures (i.e., elastic or elasto-plastic). A thorough and comprehensive review of the various investigations in this field allowed us to propose an original and compact presentation of the theory of stability and bifurcation. An illustration of this theory is then shown thro...
Parametric Controller Design of Hopf Bifurcation System
Jinbo Lu
2015-01-01
Full Text Available A general parametric controller design method is proposed for Hopf bifurcation of nonlinear dynamic system. This method does not increase the dimension of the system. Compared with the existing methods, the controller designed by this method has a lower controller order and a simpler structure, and it does not contain equilibrium points. The method keeps equilibrium of the origin system unchanged. Symbolic computation is used to deduce the constraints of controller, and cylindrical algebraic decomposition is used to find the stability parameter regions in parameter space of controller. The method is then employed for Hopf bifurcation control. Taking Lorenz system as an example, the controller design steps of the method and numerical simulations are discussed. Computer simulation results are presented to confirm the analytical predictions.
Periodic orbits near a bifurcating slow manifold
Kristiansen, Kristian Uldall
2015-01-01
This paper studies a class of $1\\frac12$-degree-of-freedom Hamiltonian systems with a slowly varying phase that unfolds a Hamiltonian pitchfork bifurcation. The main result of the paper is that there exists an order of $\\ln^2\\epsilon^{-1}$-many periodic orbits that all stay within an $\\mathcal O......(\\epsilon^{1/3})$-distance from the union of the normally elliptic slow manifolds that occur as a result of the bifurcation. Here $\\epsilon\\ll 1$ measures the time scale separation. These periodic orbits are predominantly unstable. The proof is based on averaging of two blowup systems, allowing one to estimate...... the effect of the singularity, combined with results on asymptotics of the second Painleve equation. The stable orbits of smallest amplitude that are {persistently} obtained by these methods remain slightly further away from the slow manifold being distant by an order $\\mathcal O(\\epsilon^{1/3}\\ln^{1...
Sex differences in intracranial arterial bifurcations
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K; Mardal, Kent-Andre; Faulder, Kenneth; Magnus, Jeanette H; Waterloo, Knut; Romner, Bertil; Ingebrigtsen, Tor
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...... 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....
Shape optimization of the carotid artery bifurcation
Bressloff, N. W.; Forrester, A.I.J.; Banks, J.; Bhaskar, K.V.
2004-01-01
A parametric CAD model of the human carotid artery bifurcation is employed in an initial exploration of the response of shear stress to the variation of the angle of the internal carotid artery and the width of the sinus bulb. Design of experiment and response surface technologies are harnessed for the first time in such an application with the aim of developing a better understanding of the relationship between geometry (anatomy) and sites of arterial disease.
Bifurcated Helical Core Equilibrium States in Tokamaks
Full text: Tokamaks with weak to moderate reversed central magnetic shear in which the minimum of the inverse rotational transform qmin is in the neighbourhood of unity can trigger bifurcated MagnetoHydroDynamic (MHD) equilibrium states. In addition to the standard axisymmetric branch that can be obtained with standard Grad-Shafranov solvers, a novel branch with a three-dimensional (3D) helical core has been computed with the ANIMEC code, an anisotropic pressure extension of the VMEC code. The solutions have imposed nested magnetic flux surfaces and are similar to saturated ideal internal kink modes. The difference in energy between both possible branches is very small. Plasma elongation, current and β enhance the susceptibility for bifurcations to occur. An initial value nonlinear ideal MHD evolution of the axisymmetric branch compares favourably with the helical core equilibrium structures calculated. Peaked prescribed pressure profiles reproduce the 'snake' structures observed in many tokamaks which has led to a new explanation of the snake as a bifurcated helical equilibrium state that results from a saturated ideal internal kink in which pellets or impurities induce a hollow current profile. Snake equilibrium structures are computed in free boundary TCV tokamak simulations. Magnetic field ripple and resonant magnetic perturbations in MAST free boundary calculations do not alter the helical core deformation in a significant manner when qmin is near unity. These bifurcated solutions constitute a paradigm shift that motivates the application of tools developed for stellarator research in tokamak physics investigations. The examination of fast ion confinement in this class of equilibria is performed with the VENUS code in which a coordinate independent noncanonical phase-space Lagrangian formulation of guiding centre drift orbit theory has been implemented. (author)
Torus bifurcations in multilevel converter systems
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....
Perturbed period-doubling bifurcation. I. Theory
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 and the...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
The relation between oxygen saturation level and retionopathy of prematurity
Mohammad Gharavi Fard
2016-03-01
Full Text Available Introduction: Oxygen therapy used for preterm infant disease might be associated with oxygen toxicity or oxidative stress. The exact oxygen concentration to control and maintain the arterial oxygen saturation balance is not certainly clear. We aimed to compare the efficacy of higher or lower oxygen saturations on the development of severe retinopathy of prematurity which is a major cause of blindness in preterm neonates. Methods: PubMed was searched for obtaining the relevant articles. A total of seven articles were included after studying the titles, abstracts, and the full text of retrieved articles at initial search. Inclusion criteria were all the English language human clinical randomized controlled trials with no time limitation, which studied the efficacy of low versus high oxygen saturation measured by pulse oximetry in preterm infants.Result: It can be suggested that lower limits of oxygen saturations have higher efficacy at postmesetural age of ≤28 weeks in preterm neonates. This relation has been demonstrated in five large clinical trials including three Boost trials, COT, and Support.Discussion: Applying higher concentrations of oxygen supplementations at mesentural age ≥32 weeks reduced the development of retinopathy of prematurity. Lower concentrations of oxygen saturation decreased the incidence and the development of retinopathy of prematurity in preterm neonates while applied soon after the birth.Conclusions: Targeting levels of oxygen saturation in the low or high range should be performed cautiously with attention to the postmesentural age in preterm infants at the time of starting the procedures.
Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model
Thies, J.; Wubs, F.W.; Dijkstra, H.A.
2009-01-01
To understand the physics and dynamics of the ocean circulation, techniques of numerical bifurcation theory such as continuation methods have proved to be useful. Up to now these techniques have been applied to models with relatively few degrees of freedom such as multi-layer quasi-geostrophic and s
Bifurcations of Eigenvalues of Gyroscopic Systems with Parameters Near Stability Boundaries
Seyranian, Alexander P.; Kliem, Wolfhard
1999-01-01
shown that the bifurcation (splitting) of double eigenvalues is closely related to the stability, flutter and divergence boundaries in the parameter space. Normal vectors to these boundaries are derived using only information at a boundary point: eigenvalues, eigenvectors and generalized eigenvectors...
(r,s)-STABILITY OF UNFOLDING OF Γ-EQUIVARIANT BIFURCATION PROBLEM
Liu Hengxing; Zhang Dunmu
2005-01-01
In this paper,the Γ-equivariant (s, t)-equivalence relation and Γ-equivariant infinitesimally (r, s)-stability of Γ-equivariant bifurcation problem are defined. The criterion for Γ-equivariant infinitesimally (r, s)-stability is proven when Γ is a compact finite Lie group . Transversality condition is used to characterize the stability.
First-passage times, mobile traps, and Hopf bifurcations.
Tzou, Justin C; Xie, Shuangquan; Kolokolnikov, Theodore
2014-12-01
For a random walk on a confined one-dimensional domain, we consider mean first-passage times (MFPT) in the presence of a mobile trap. The question we address is whether a mobile trap can improve capture times over a stationary trap. We consider two scenarios: a randomly moving trap and an oscillating trap. In both cases, we find that a stationary trap actually performs better (in terms of reducing expected capture time) than a very slowly moving trap; however, a trap moving sufficiently fast performs better than a stationary trap. We explicitly compute the thresholds that separate the two regimes. In addition, we find a surprising relation between the oscillating trap problem and a moving-sink problem that describes reduced dynamics of a single spike in a certain regime of the Gray-Scott model. Namely, the above-mentioned threshold corresponds precisely to a Hopf bifurcation that induces oscillatory motion in the location of the spike. We use this correspondence to prove the uniqueness of the Hopf bifurcation. PMID:25615075
Resonances and bifurcations in systems with elliptical equipotentials
Marchesiello, Antonella
2012-01-01
We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find that the 1:1 resonance is associated only to the appearance of the loops and leads to the destabilization of either one or the other normal modes, depending on the ellipticity of equipotentials. Inclined orbits are never present and may appear only when the equipotentials are heavily deformed. The 1:2 resonance determines the appearance of bananas and anti-banana orbits: the first family is stable and always appears at a lower energy than the second, which is unstable. The bifurcation sequence also produces the variations in the stability character of the major axis orbit and is modified only by very large deformations of the equipotentials. Higher-order resonances appear at intermediate or higher energies and can be described with good accuracy.
Salt marsh stability modelled in relation to sea level rise
Bartholdy, Jesper; Bartholdy, Anders; Kroon, Aart
2010-01-01
the model with a constant sea level revealed that balance between the inner and the outer salt marsh deposition can not be achieved within a reasonable time scale. Likewise it is shown that only one specific sea level rise provides equilibrium for a given location on the salt marsh. With a higher sea...... level rise, the marsh at the specific location will eventually drown, whereas - with a sea level rise below this level – it will grow towards the top of the rising tidal frame. The short term variation of salt marsh accretion was found to correlate well with variations in the North Atlantic Oscillation...
Classification of solitary wave bifurcations in generalized nonlinear Schr\\"odinger equations
Yang, Jianke
2012-01-01
Bifurcations of solitary waves are classified for the generalized nonlinear Schr\\"odinger equations with arbitrary nonlinearities and external potentials in arbitrary spatial dimensions. Analytical conditions are derived for three major types of solitary wave bifurcations, namely saddle-node bifurcations, pitchfork bifurcations and transcritical bifurcations. Shapes of power diagrams near these bifurcations are also obtained. It is shown that for pitchfork and transcritical bifurcations, their power diagrams look differently from their familiar solution-bifurcation diagrams. Numerical examples for these three types of bifurcations are given as well. Of these numerical examples, one shows a transcritical bifurcation, which is the first report of transcritical bifurcations in the generalized nonlinear Schr\\"odinger equations. Another shows a power loop phenomenon which contains several saddle-node bifurcations, and a third example shows double pitchfork bifurcations. These numerical examples are in good agreeme...
The significance of enhanced radionuclide deposition at bronchial bifurcations
Experiments were conducted to quantitate deposition patterns of monodisperse aerosols in surrogates of the human upper respiratory tract. Laryngeal casts and most upper airway bifurcations were sites of preferential particle deposition. Highly concentrated deposits were detected at carinal ridges within bifurcation zones. Together with impaired mucociliary clearance at branching sites, this initial deposition pattern results in localized accumulations of radionuclides within bifurcation zones. For inhaled radon progeny radiation doses are calculated for 3 regions of bronchial airways: tubular airway segments, bifurcation zones (including the carina), and carinal ridges. These calculations indicated that enhanced deposition at branching sites leads to significantly higher doses to epithelial cells located at bifurcations than along tubular airway segments. If cell killing is included in the analysis of lung cancer risk, it reduces carcinogenic potential at bifurcation sites, particularly at high doses. (author)
Codimension 2 reversible heteroclinic bifurcations with inclination flips
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.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
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.
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
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.
Bifurcation Analysis for Neural Networks in Neutral Form
Chen, Hong-Bing; Sun, Xiao-Ke
2016-06-01
In this paper, a system of neural networks in neutral form with time delay is investigated. Further, by introducing delay τ as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ is across some critical values. The direction of the Hopf bifurcations and the stability are determined by using normal form method and center manifold theory. Next, the global existence of periodic solution is established by using a global Hopf bifurcation result. Finally, an example is given to support the theoretical predictions.
Periodic solutions and flip bifurcation in a linear impulsive system
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
Housing Electrons: Relating Quantum Numbers, Energy Levels, and Electron Configurations.
Garofalo, Anthony
1997-01-01
Presents an activity that combines the concepts of quantum numbers and probability locations, energy levels, and electron configurations in a concrete, hands-on way. Uses model houses constructed out of foam board and colored beads to represent electrons. (JRH)
Factors Relating to EFL Writers' Discourse Level Revision Skills
Carol Rinnert; Hiroe Kobayashi
2001-01-01
This study investigated discourse level revising skills among three groups of Japanese EFL writers and the relationship between these skills and the two factors of English proficiency and writing experience. The three groups of university students (N = 53) differed in terms of their educational level and the amount of writing instruction they had received. Group 1, undergraduates with no writing instruction; Group 2, undergraduates with one year of English writing instruction; and Group 3, gr...
Bifurcation structure of an optical ring cavity
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...... the individual family, the organization of the solutions exhibit an infinite number of regulatory arranged domains, the so-called swallow tails. We discuss the origin of this structure which has recently been observed in a variety of other systems as well....
Longitudinal stent deformation during coronary bifurcation stenting.
Vijayvergiya, Rajesh; Sharma, Prafull; Gupta, Ankush; Goyal, Praveg; Panda, Prashant
2016-03-01
A distortion of implanted coronary stent along its longitudinal axis during coronary intervention is known as longitudinal stent deformation (LSD). LSD is frequently seen with newer drug eluting stents (DES), specifically with PROMUS Element stent. It is usually caused by impact of guide catheter tip, or following passage of catheters like balloon catheter, IVUS catheter, guideliner, etc. We hereby report a case of LSD during coronary bifurcation lesion intervention, using two-stents technique. Patient had acute stent thrombosis as a complication of LSD, which was successfully managed. PMID:26811144
Bifurcation analysis of a preloaded Jeffcott rotor
A model of two-degrees-of-freedom Jeffcott rotor system with bearing clearance subjected of an out-of-balance excitation is considered. The influence of preloading and viscous damping of the snubber ring is introduced in the mathematical description. A programme of numerical simulations is conducted to show how the preloading and viscous damping change the dynamics of the rotor system. Bifurcation diagrams and Lyapunov exponents are constructed to explore stability. It is shown that dynamics of the rotor system can be effectively controlled by varying the preloading and the damping both of the rotor and the snubber ring. In the most considered cases preloading stabilises the dynamic responses
Bifurcation analysis of a preloaded Jeffcott rotor
Karpenko, Evgueni V.; Pavlovskaia, Ekaterina E.; Wiercigroch, Marian E-mail: m.wiercigroch@eng.abdn.ac.uk
2003-01-01
A model of two-degrees-of-freedom Jeffcott rotor system with bearing clearance subjected of an out-of-balance excitation is considered. The influence of preloading and viscous damping of the snubber ring is introduced in the mathematical description. A programme of numerical simulations is conducted to show how the preloading and viscous damping change the dynamics of the rotor system. Bifurcation diagrams and Lyapunov exponents are constructed to explore stability. It is shown that dynamics of the rotor system can be effectively controlled by varying the preloading and the damping both of the rotor and the snubber ring. In the most considered cases preloading stabilises the dynamic responses.
Uniformity pattern and related criteria for two-level factorials
FANG; Kaitai; QIN; Hong
2005-01-01
In this paper,the study of projection properties of two-level factorials in view of geometry is reported.The concept of uniformity pattern is defined.Based on this new concept,criteria of uniformity resolution and minimum projection uniformity are proposed for comparing two-level factorials.Relationship between minimum projection uniformity and other criteria such as minimum aberration,generalized minimum aberration and orthogonality is made explict.This close relationship raises the hope of improving the connection between uniform design theory and factorial design theory.Our results provide a justification of orthogonality,minimum aberration,and generalized minimum aberration from a natural geometrical interpretation.
Enhancing Sentence Relation Modeling with Auxiliary Character-level Embedding
Li, Peng; Huang, Heng
2016-01-01
Neural network based approaches for sentence relation modeling automatically generate hidden matching features from raw sentence pairs. However, the quality of matching feature representation may not be satisfied due to complex semantic relations such as entailment or contradiction. To address this challenge, we propose a new deep neural network architecture that jointly leverage pre-trained word embedding and auxiliary character embedding to learn sentence meanings. The two kinds of word seq...
Swept-parameter-induced postponements and noise on the Hopf bifurcation.
Fronzoni, L.; Moss, F; McClintock, Peter V. E.
1987-01-01
The postponement of Hopf bifurcations driven by a swept bifurcation parameter is demonstrated with an electronic Brusselator. Noise on the swept parameter destroys the postponement and the bifurcation as it is usually defined.
On the application of Newton's and Chord methods to bifurcation problems
M. B. M. Elgindi
1994-01-01
Full Text Available This paper is concerned with the applications of Newton's and chord methods in the computations of the bifurcation solutions in a neighborhood of a simple bifurcation point for prescribed values of the bifurcation parameter.
The Relation between Bullying, Victimization, and Adolescents' Level of Hopelessness
Siyahhan, Sinem; Aricak, O. Tolga; Cayirdag-Acar, Nur
2012-01-01
In this study, 419 Turkish middle school students (203 girls, 216 boys) were surveyed on their exposure to and engagement in bullying, and their level of hopelessness. Our findings suggest that girls were victims of indirect (e.g. gossiping) bullying more than boys. Boys reported being victims of physical (e.g. damaging property) and verbal (e.g.…
Quaternions in University-Level Physics Considering Special Relativity
Horn, M E
2003-01-01
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly regarded in the current physics curriculum. In particular, many approaches emerge that are useful in conveying the unity of seemingly distinct theories in a didactically convincing manner. This will be exemplified with the help of special relativity. The diverse examples of spatial and space-time rotations are merged into a didactic whole by introducing quaternion transformations and comparing them to the representation using rotation matrices common in physics books.
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.
Factors Related to Low Research Productivity at Higher Education Level
Muhammad Zafar Iqbal; Azhar Mahmood
2011-01-01
Research is vital and necessary part of modern university education; universities are producers of new knowledge. Role of universities is different from the 19th century; demands of the 21st century are enormously higher. The purpose of study was to find out the causes of low research productivity at university level. Population of the study was faculty members working at University. Sample consisting of 232 male and female faculty members was selected through the stratified sampling techniqu...
Free market in practice. Customer loyalty related to service level
Sixty percent of the bulk consumers of energy have changed to a different supplier since the liberalization of the market. Newcomers like Vattenfall and EnBW are doing reasonably well, while small (gas) companies like Cogas and Rendo are also performing a lot better than the known big players, especially where it concerns the level of service. These are some of the remarkable results of research conducted by the market research agency Datamonitor
Objective: to evaluate the efficacy and safety of percutaneous endovascular management with single stent in treating symptomatic series stenosis located at subclavian-vertebral artery bifurcation. Methods: Between February 2009 and April 2010, percutaneous single-stent endovascular treatment was carried out in 7 consecutive patients with symptomatic series stenosis located at subclavian-vertebral artery bifurcation. After implantation of cerebral protection device, percutaneous single-stent endovascular procedure was performed to treat two stenoses at subclavian-vertebral artery bifurcation. All patients were followed up for 3∼15 months. The therapeutic efficacy was evaluated with the observation of clinical symptoms and Doppler ultrasonic examination, the possible occurrence of re-stenosis was checked. Results: Technical success was achieved in all seven patients. After the implantation the residual stenosis of both subclavian and vertebral arteries was less than 10%. No procedure-related complications occurred. During the follow-up period no re-stenosis was observed on Doppler ultrasonography, the clinical symptoms were markedly improved, and no cerebrovascular accident or new cerebral infarction occurred. Conclusion: For the treatment of series stenosis located at subclavian-vertebral artery bifurcation percutaneous single-stent endovascular implantation is a feasible technique. Compared with other methods, this technique carries the advantages of easier manipulation and higher safety for patient although long-term efficacy needs to be further observed. (authors)
Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics
Toichiro Asada
2011-01-01
Full Text Available Complex dynamical features are explored in a discrete interregional macrodynamic model proposed by Asada et al., using numerical methods. The model is five-dimensional with four parameters. The results demonstrate patterns of dynamical behaviour, such as bifurcation processes and coexistence of attractors, generated by high-dimensional discrete systems. In three cases of two-dimensional parameter subspaces the stability of equilibrium region is determined and its boundaries, the flip and Neimark-Hopf bifurcation curves, are identified by means of necessary coefficient criteria. In the first case closed invariant curves (CICs are found to occur through 5D-crater-type bifurcations, and for certain ranges of parameter values a stable equilibrium coexists with an unstable CIC associated with the subcritical bifurcation, as well as with an outer stable CIC. A remarkable feature of the second case is the coexistence of two attracting CICs outside the stability region. In both these cases the related hysteresis effects are illustrated by numerical simulations. In the third case a remarkable feature is the apparent unfolding of an attracting CIC before it evolves to a chaotic attractor. Examples of CICs and chaotic attractors are given in subspaces of phase space.
Fast-scale border collision bifurcation in SEPIC power factor pre-regulators
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. (general)
Fast-scale border collision bifurcation in SEPIC power factor pre-regulators
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.
Bifurcation of the femur with tibial agenesis and additional anomalies
van der Smagt, JJ; Bos, CFA; van Haeringen, A; Hogendoorn, PCW; Breuning, MH
2005-01-01
Bifurcation of the femur and tibial agenesis are rare anomalies and have been described in both the Gollop-Wolfgang Complex and the tibial agenesis-ectrodactyly syndrome. We report on two patients with bifurcation of the femur and tibial agenesis. Hand ectrodactyly was seen in one of these patients.
Bifurcation Analysis in a Delayed Diffusive Leslie-Gower Model
Shuling Yan
2013-01-01
Full Text Available We investigate a modified delayed Leslie-Gower model under homogeneous Neumann boundary conditions. We give the stability analysis of the equilibria of the model and show the existence of Hopf bifurcation at the positive equilibrium under some conditions. Furthermore, we investigate the stability and direction of bifurcating periodic orbits by using normal form theorem and the center manifold theorem.
Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions
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.
Hopf Bifurcation in a New Four-Dimensional Hyperchaotic System
Li, Xin; Yan, Zhen-Ya
2015-08-01
In this paper, the Hopf bifurcation in a new hyperchaotic system is studied. Based on the first Lyapunov coefficient theory and symbolic computation, the conditions of supercritical and subcritical bifurcation in the new hyperchaotic system are obtained. Numerical simulations are used to illustrate some main results. Supported by National Key Bsic Research Program of China under Grant No. 2011CB302400
Sediment discharge division at two tidally influenced river bifurcations
Sassi, M.G.; Hoitink, A.J.F.; Vermeulen, B.; Hidayat, H.
2013-01-01
[1] We characterize and quantify the sediment discharge division at two tidally influenced river bifurcations in response to mean flow and secondary circulation by employing a boat-mounted acoustic Doppler current profiler (ADCP), to survey transects at bifurcating branches during a semidiurnal tida
Non-Gaussian bifurcating models and quasi-likelihood estimation
Basawa, I. V.; J. Zhou
2004-01-01
A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasi-likelihood estimation for the model parameters and large-sample properties of the estimates are discussed.
Identification of Bifurcations from Observations of Noisy Biological Oscillators.
Salvi, Joshua D; Ó Maoiléidigh, Dáibhid; Hudspeth, A J
2016-08-23
Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise. Using an improved mechanical-load clamp to coerce a hair bundle to traverse different bifurcations, we find that a bundle operates within at least two functional regimes. When coupled to a high-stiffness load, a bundle functions near a supercritical Hopf bifurcation, in which case it responds best to sinusoidal stimuli such as those detected by an auditory organ. When the load stiffness is low, a bundle instead resides close to a subcritical Hopf bifurcation and achieves a graded frequency response-a continuous change in the rate, but not the amplitude, of spiking in response to changes in the offset force-a behavior that is useful in a vestibular organ. The mechanical load in vivo might therefore control a hair bundle's responsiveness for effective operation in a particular receptor organ. Our results provide direct experimental evidence for the existence of distinct bifurcations associated with a noisy biological oscillator, and demonstrate a general strategy for bifurcation analysis based on observations of any noisy system. PMID:27558723
Critical bifurcation surfaces of 3D discrete dynamics
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.
Online Activity Levels Are Related to Caffeine Dependency.
Phillips, James G; Landhuis, C Erik; Shepherd, Daniel; Ogeil, Rowan P
2016-05-01
Online activity could serve in the future as behavioral markers of emotional states for computer systems (i.e., affective computing). Hence, this study considered relationships between self-reported stimulant use and online study patterns. Sixty-two undergraduate psychology students estimated their daily caffeine use, and this was related to study patterns as tracked by their use of a Learning Management System (Blackboard). Caffeine dependency was associated with less time spent online, lower rates of file access, and fewer online activities completed. Reduced breadth or depth of processing during work/study could be used as a behavioral marker of stimulant use. PMID:27096737
Fat free mass and obesity in relation to educational level
Rissanen Harri; Knekt Paul; Männistö Satu; Lahti-Koski Marjaana; Seppänen-Nuijten Elina; Aromaa Arpo; Heliövaara Markku
2009-01-01
Abstract Background The aim of the study was to describe the body composition of Finnish adults, especially by education, and to investigate whether fat-free mass (FFM) can explain educational gradients relating to body mass index (BMI) and waist-to-hip ratio (WHR). Methods Data for this cross-sectional study were based on data collected in 2000-2001 for the Health 2000 Survey. Of the nationally representative sample of 8,028 Finnish men and women aged 30 years and older, 6,300 (78.5%) were i...
Climate bifurcation during the last deglaciation?
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
Improved tropical cyclone intensity and intensity spread prediction in bifurcation situations
Tsai, Hsiao-Chung; Elsberry, Russell L.
2014-11-01
Bifurcation or bi-modal tropical cyclone intensity forecasts may arise due to uncertainty in the timing of formation, timing and magnitude of rapid intensification periods, or track forecast uncertainty leading to landfall or non-landfall or leading to interaction with warm- or cold-ocean eddies. An objective technique is developed and tested to detect these intensity bifurcation situations in our weighted-analog intensity (WANI) forecasts that are based on the 10 best historical analogs to the Joint Typhoon Warning Center (JTWC) official track forecasts. About 19% of the overall sample of 1136 WANI forecasts in the western North Pacific during the 2010-2012 seasons met the criteria for a substantial intensity bifurcation situation. Using a hierarchical clustering technique, two clusters of the 10 best analogs are defined and separate WANI forecasts and intensity spreads are calculated for the two clusters. If an always perfect selection of the correct cluster WANI forecast of each bifurcation situation is made, a substantial improvement in the intensity mean absolute errors is achieved relative to the original WANI forecasts based on all 10 of the best analogs. These perfect-cluster selection WANI forecasts have smaller bias errors and are more highly correlated with the verifying intensities at all forecast intervals through 120 h. Without further bias correction and calibration, the cluster WANI intensity spreads are under-determined as the Probability of Detections are smaller than the desired 68%. Four examples of WANI cluster predictions of intensity bifurcation situations are provided to illustrate how a correct choice of the intensity forecast and the intensity spread can be the basis for improved warnings of the threat from western North Pacific tropical cyclones.
The simplest normal form of Hopf bifurcation
Yu, P.; Leung, A. Y. T.
2003-01-01
Recently, further reduction on normal forms of differential equations leading to the simplest normal forms (SNFs) has received considerable attention. However, the computation of the SNF has been mainly restricted to systems which do not contain perturbation parameters (unfolding), since the computation of the SNF with unfolding is much more complicated than that of the SNF without unfolding. From the practical point of view, only the SNF with perturbation (bifurcation) parameters is useful in analysing physical or engineering problems. It is shown that the SNF with unfolding cannot be obtained using only near-identity transformation. Additional transformations such as time and parameter rescaling need to be introduced. An efficient computational method is presented for computing the algebraic equations that can be used to find the SNF. A physical example is given to show the applicability of the new method.
Chua Corsage Memristor Oscillator via Hopf Bifurcation
Mannan, Zubaer Ibna; Choi, Hyuncheol; Kim, Hyongsuk
This paper demonstrates that the Chua Corsage Memristor, when connected in series with an inductor and a battery, oscillates about a locally-active operating point located on the memristor’s DC V-I curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance Y (s,V ) is derived from the small-signal equivalent circuit and the value of inductance is determined at a frequency where the real part of the admittance ReY (iω) of the small-signal equivalent circuit of Chua Corsage Memristor is zero. Oscillation of the circuit is analyzed via an in-depth application of the theory of Local Activity, Edge of Chaos and the Hopf-bifurcation.
Bifurcated SEN with Fluid Flow Conditioners
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.
Smith, D. E.; Davies, M. H.; Brooks, C. L.; Mighall, T. M.; Dawson, S.; Rea, B. R.; Jordan, J. T.; Holloway, L. K.
2010-08-01
Changes in relative sea level (RSL) and their effect on the distribution of human activity in the Forth lowland, Scotland, UK between ca 11,700 and ca 2000 calibrated years before present (BP) are examined. Block uplift of shorelines occurred over a longer period than previously thought, continuing to at least around 4700 BP. New graphs of RSL change, based upon an analysis of previous work and evidence from new sites using standard morphological and stratigraphical analyses, support a fall in RSL in the early Holocene during which buried estuarine surfaces were formed, followed by a marked reversal on a centennial, perhaps even decadal, scale sometime around 9900-9500 BP from a falling sequence to a rising one. There may have been a short-lived fluctuation in the rising RSL ca 8300 BP, and the Holocene Storegga Slide tsunami of ca 8100 BP was widespread in the lowland. The rising RSL culminated at the Main Postglacial Shoreline, reached ca 7800 BP, when Mean High Water Spring Tides (MHWS) lay within the range 14.6-16.5 m British Ordnance Datum (OD) in the western lowland. This is the highest published Holocene RSL in Britain and Ireland. The subsequent fall in RSL stabilised at a second shoreline, the Blairdrummond Shoreline, from which regression was occurring at ca 4700 BP. RSL later fell to a lower shoreline at ca 3900 BP before reaching present levels within the last three millennia. Comparison between the empirical evidence for RSL change in this area and glacial isostatic adjustment models indicates both similarities and differences. Records of archaeological sites and artefacts in the lowland and surrounding areas are discussed. Maps showing the evolution of the estuary are compared with the distribution of Mesolithic, Neolithic, Bronze Age and Iron Age activity. Evidence for Mesolithic people indicates the opportunistic use of available resources as RSL rose and the estuary expanded to its maximum extent. Neolithic people were also attracted to the estuary
Saho, Tatsunori; Onishi, Hideo
2016-07-01
In this study, we evaluated the hemodynamics of carotid artery bifurcation with various geometries using simulated and volunteer models based on magnetic resonance imaging (MRI). Computational fluid dynamics (CFD) was analyzed by use of OpenFOAM. The velocity distribution, streamline, and wall shear stress (WSS) were evaluated in a simulated model with known bifurcation angles (30°, 40°, 50°, 60°, derived from patients' data) and in three-dimensional (3D) healthy volunteer models. Separated flow was observed at the outer side of the bifurcation, and large bifurcation models represented upstream transfer of the point. Local WSS values at the outer bifurcation [both simulated (100 Pa). The bifurcation angle had a significant negative correlation with the WSS value (p<0.05). The results of this study show that the carotid artery bifurcation angle is related to the WSS value. This suggests that hemodynamic stress can be estimated based on the carotid artery geometry. The construction of a clinical database for estimation of developing atherosclerosis is warranted. PMID:27255300
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
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.
Statistical multimoment bifurcations in random-delay coupled swarms
Mier-y-Teran-Romero, Luis; Lindley, Brandon; Schwartz, Ira B.
2012-11-01
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.
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.
Bifurcations of a parametrically excited oscillator with strong nonlinearity
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.
Bifurcation control of nonlinear oscillator in primary and secondary resonance
无
2007-01-01
A weakly nonlinear oscillator was modeled by a sort of differential equation, a saddle-node bifurcation was found in case of primary and secondary resonance. To control the jumping phenomena and the unstable region of the nonlinear oscillator, feedback controllers were designed. Bifurcation control equations were obtained by using the multiple scales method. And through the numerical analysis, good controller could be obtained by changing the feedback control gain. Then a feasible way of further research of saddle-node bifurcation was provided. Finally, an example shows that the feedback control method applied to the hanging bridge system of gas turbine is doable.
Civan, Adem
2015-01-01
This research was carried out to determine the self-esteem and life quality levels of disabled and non-disabled tennis sportsmen; and also to set forth the relation between their self-esteem and life quality levels. The research group consists of total 44 sportsmen including 22 disabled tennis sportsmen (n[subscript (female)]=9, n[subscript…
G. Vilalta
2008-05-01
section of the arteries as a result of lipid deposit in the inner layer of the vessel. Thepresent paper studies the influence of the blood viscosity in the flow at the carotid bifurcation through the numericalmodeling. The study was carried out for three stenosis levels, (SS=30, 60 and 75 % and five viscosity values, (3,5 cP, 7 cP,20 cP, 35 cP, 50 cP.The results obtained show a significant reduction in the blood flow for viscosities increasing up to 7cP. For greater viscosities values the system flow remains constant, which is consistent with the medical practice.Key words: Fluid dynamic, polymer addition, finite element formulation, carotid bifurcation.
Codimension-Two Bifurcation Analysis in Hindmarsh-Rose Model with Two Parameters
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.
An overview of intrinsic torque and momentum transport bifurcations in toroidal plasmas
An overview of the physics of intrinsic torque is presented, with special emphasis on the phenomenology of intrinsic toroidal rotation in tokamaks, its theoretical understanding, and the variety of momentum transport bifurcation dynamics. Ohmic reversals and electron cyclotron heating-driven counter torque are discussed in some detail. Symmetry breaking by lower single null versus upper single null asymmetry is related to the origin of intrinsic torque at the separatrix. (paper)
Vertical distance between umbilicus to aortic bifurcation on coronal view in Korean women
Jeong, Joo Yeon; Kim, Yeo Rang; Kim, Ju Yeong; Jee, Byung Chul; Kim, Seok Hyun
2014-01-01
Objective To evaluate the vertical distance between umbilicus to aortic bifurcation on coronal view in Korean women and their relation with body mass index (BMI) and woman's age. Methods This retrospective study included 257 women who visited emergency center at university-based hospital from January to December 2011. All women underwent abdomino-pelvic computerized tomography (CT) due to various symptoms in a supine position. By using the electronic coronal CT images, the vertical distance b...
Dynamical Analysis of Nonlinear Bifurcation in Current-Controlled Boost Converter
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.
Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems
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.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
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.
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.
Cardiac Alternans Arising from an Unfolded Border-Collision Bifurcation
Zhao, Xiaopeng; Berger, Carolyn M; Krassowska, Wanda; Gauthier, Daniel J
2007-01-01
Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. Existing cardiac models treat alternans either as a smooth or as a border-collision bifurcation. However, recent experiments in paced cardiac tissue reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which can be qualitatively described by a model of so-called unfolded border-collision bifurcation. In this paper, we obtain analytical solutions of the unfolded border-collision model and use it to explore the crossover between smooth and nonsmooth behaviors. Our analysis shows that the hybrid smooth/nonsmooth behavi...
Hopf bifurcation in doubly fed induction generator under vector control
This paper first presents the Hopf bifurcation phenomena of a vector-controlled doubly fed induction generator (DFIG) which is a competitive choice in wind power industry. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable rotor speed and provide independent control of active and reactive power output. Main results are illustrated by 'exact' cycle-by-cycle simulations. The detailed mathematical model of the closed-loop system is derived and used to analyze the observed bifurcation phenomena. The loci of the Jacobian's eigenvalues are computed and the analysis shows that the system loses stability via a Hopf bifurcation. Moreover, the boundaries of Hopf bifurcation are also given to facilitate the selection of practical parameters for guaranteeing stable operation.
Grazing bifurcation and chaos in response of rubbing rotor
This paper investigates the grazing bifurcation in the nonlinear response of a complex rotor system. For a rotor with overhung disc, step diameter shaft and elastic supports, the motion equations are derived based on the Transition Matrix Method. When the rotor speed increases, the disc will touch the case and lead to rubbing of rotor. When the disc rubs with the case, the elastic force and friction force of the case will make the rotor exhibit nonlinear characteristics. For the piecewise ODEs, the numerical method is applied to obtain its nonlinear response. From the results, the grazing bifurcation, which happens at the moment of touching between disc and case, can be observed frequently. The grazing bifurcation can lead to the jump between periodic orbits. The response can go to chaos from periodic motion under grazing bifurcation. When grazing occurs, response can become quasi-period from period
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings. PMID:27586627
Bifurcation control of the Hodgkin-Huxley equations
Wang Jiang [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China)]. E-mail: jiangwang@tju.edu.cn; Chen Liangquan [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China); Fei Xianyang [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China)
2007-07-15
The Hodgkin-Huxley equations (HH) are parameterized by a number of parameters and show a variety of qualitatively different behaviors. This paper finds that when the externally applied current I {sub ext} varies the bifurcation would occur in the HH equations. The HH model's Hopf bifurcation is controlled by permanent or interval Washout filters (WF), which can transform the subcritical bifurcations into supercritical bifurcations, and can make the HH equations stable directly. Simulation results show the validity of those controllers. We choose the membrane voltage V as an input to the washout filter because V can be readily measured, and the controller can be realized easily. The controller designs described here may boost the development of electrical stimulation systems for patients suffering from different neuron-system dysfunctions.
Hopf bifurcation and multistability in a system of phase oscillators
Astakhov, Sergey; Fujiwara, Naoya; Gulay, Artem; Tsukamoto, Naofumi; Kurths, Jürgen
2013-09-01
We study the phase reduction of two coupled van der Pol oscillators with asymmetric repulsive coupling under an external harmonic force. We show that the system of two phase oscillators undergoes a Hopf bifurcation and possesses multistability on a 2π-periodic phase plane. We describe the bifurcation mechanisms of formation of multistability in the phase-reduced system and show that the Andronov-Hopf bifurcation in the phase-reduced system is not an artifact of the reduction approach but, indeed, has its prototype in the nonreduced system. The bifurcational mechanisms presented in the paper enable one to describe synchronization effects in a wide class of interacting systems with repulsive coupling e.g., genetic oscillators.
2D bifurcations and Newtonian properties of memristive Chua's circuits
Marszalek, W.; Podhaisky, H.
2016-01-01
Two interesting properties of Chua's circuits are presented. First, two-parameter bifurcation diagrams of Chua's oscillatory circuits with memristors are presented. To obtain various 2D bifurcation images a substantial numerical effort, possibly with parallel computations, is needed. The numerical algorithm is described first and its numerical code for 2D bifurcation image creation is available for free downloading. Several color 2D images and the corresponding 1D greyscale bifurcation diagrams are included. Secondly, Chua's circuits are linked to Newton's law φ ''= F(t,φ,φ')/m with φ=\\text{flux} , constant m > 0, and the force term F(t,φ,φ') containing memory terms. Finally, the jounce scalar equations for Chua's circuits are also discussed.
Multiple bifurcations and periodic 'bubbling' in a delay population model
In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc
Overcoming bifurcation instability in high-repetition-rate Ho:YLF regenerative amplifiers.
Kroetz, Peter; Ruehl, Axel; Chatterjee, Gourab; Calendron, Anne-Laure; Murari, Krishna; Cankaya, Huseyin; Li, Peng; Kärtner, Franz X; Hartl, Ingmar; Miller, R J Dwayne
2015-12-01
We demonstrate a Ho:YLF regenerative amplifier (RA) overcoming bifurcation instability and consequently achieving high extraction energies of 6.9 mJ at a repetition rate of 1 kHz with pulse-to-pulse fluctuations of 1.1%. Measurements of the output pulse energy, corroborated by numerical simulations, identify an operation point (OP) that allows high-energy pulse extraction at a minimum noise level. Complete suppression of the onset of bifurcation was achieved by gain saturation after each pumping cycle in the Ho:YLF crystal via lowering the repetition rate and cooling the crystal. Even for moderate cooling, a significant temperature dependence of the Ho:YLF RA performance was observed. PMID:26625017
Overcoming Bifurcation Instability in High-Repetition-Rate Ho:YLF Regenerative Amplifiers
Kroetz, Peter; Chatterjee, Gourab; Calendron, Anne-Laure; Murari, Krishna; Cankaya, Huseyin; Li, Peng; Kaertner, Franz X; Hartl, Ingmar; Miller, R J Dwayne
2015-01-01
We demonstrate a Ho:YLF regenerative amplifier (RA) overcoming bifurcation instability and consequently achieving high extraction energies of 6.9 mJ at a repetition rate of 1 kHz with pulse-to-pulse fluctuations of 1.1%. Measurements of the output pulse energy, corroborated by numerical simulations, identify an operation point that allows high-energy pulse extraction at a minimum noise level. Complete suppression of the onset of bifurcation was achieved by gain saturation after each pumping cycle in the Ho:YLF crystal via lowering the repetition rate and cooling the crystal. Even for moderate cooling, a significant temperature dependence of the Ho:YLF RA performance was observed.
Relative outcomes of climate change mitigation related to global temperature versus sea-level rise
Meehl, Gerald A.; Hu, Aixue; Tebaldi, Claudia; Arblaster, Julie M.; Washington, Warren M.; Teng, Haiyan; Sanderson, Benjamin M.; Ault, Toby; Strand, Warren G.; White, James B.
2012-08-01
There is a common perception that, if human societies make the significant adjustments necessary to substantively cut emissions of greenhouse gases, global temperature increases could be stabilized, and the most dangerous consequences of climate change could be avoided. Here we show results from global coupled climate model simulations with the new representative concentration pathway mitigation scenarios to 2300 to illustrate that, with aggressive mitigation in two of the scenarios, globally averaged temperature increase indeed could be stabilized either below 2 °C or near 3 °C above pre-industrial values. However, even as temperatures stabilize, sea level would continue to rise. With little mitigation, future sea-level rise would be large and continue unabated for centuries. Though sea-level rise cannot be stopped for at least the next several hundred years, with aggressive mitigation it can be slowed down, and this would buy time for adaptation measures to be adopted.
Wilhelm, Miriam M.
2011-01-01
A growing research stream has expanded the level of analysis beyond single buyer-supplier relations to the network, including supplier-supplier relations. These supplier-supplier relations may constitute a missing link between the traditional analysis of the dyadic and the network level of analysis
Subcritical dynamo bifurcation in the Taylor Green flow
Ponty, Yannick; Dubrulle, Berengere; Daviaud, François; Pinton, Jean-François
2007-01-01
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.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Chao Su; Zhenxue Zhu; Yangyang Zhang; Niantang Jiang
2015-01-01
Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimiza...
Bunch lengthening with bifurcation in electron storage rings
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 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.