DEFF Research Database (Denmark)
Yang, Li Hui; Xu, Zhao; Østergaard, Jacob
2010-01-01
This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable...
DEFF Research Database (Denmark)
Yang, Lihui; Xu, Zhao; Østergaard, Jacob
2009-01-01
This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable...
On a quasi-periodic Hopf bifurcation
Braaksma, B.L.J.; Broer, H.W.
1987-01-01
In this paper we study quasi-periodic Hopf bifurcations for the model problem of a quasi-periodically forced oscillator, where the frequencies remain fixed. For this purpose we first consider Stoker's problem for small damping.
Hopf bifurcation for tumor-immune competition systems with delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available In this article, a immune response system with delay is considered, which consists of two-dimensional nonlinear differential equations. The main purpose of this paper is to explore the Hopf bifurcation of a immune response system with delay. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solution are also given. Especially, the conditions of the global existence of periodic solutions bifurcating from Hopf bifurcations are given. Numerical simulations are carried out to illustrate the the theoretical analysis and the obtained results.
Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System
Ma, Junhai; Ren, Wenbo
On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.
Ma, Junhai; Ren, Wenbo; Zhan, Xueli
2017-04-01
Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.
Directory of Open Access Journals (Sweden)
Huitao Zhao
2013-01-01
Full Text Available A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998 for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.
Li, Chengxian; Liu, Haihong; Zhang, Tonghua; Yan, Fang
2017-12-01
In this paper, a gene regulatory network mediated by small noncoding RNA involving two time delays and diffusion under the Neumann boundary conditions is studied. Choosing the sum of delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the corresponding characteristic equation. It is shown that the sum of delays can induce Hopf bifurcation and the diffusion incorporated into the system can effect the amplitude of periodic solutions. Furthermore, the spatially homogeneous periodic solution always exists and the spatially inhomogeneous periodic solution will arise when the diffusion coefficients of protein and mRNA are suitably small. Particularly, the small RNA diffusion coefficient is more robust and its effect on model is much less than protein and mRNA. Finally, the explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, numerical simulations are carried out to illustrate our theoretical analysis.
Hopf Bifurcation of Compound Stochastic van der Pol System
Directory of Open Access Journals (Sweden)
Shaojuan Ma
2016-01-01
Full Text Available Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength δ and noise intensity σ on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased δ can relocate the critical value of bifurcation parameter forward while increased σ makes it backward and the influence of δ is more sensitive than σ. The results are verified by numerical simulations.
On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction.
Molnar, T G; Dombovari, Z; Insperger, T; Stepan, G
2017-11-01
The single-degree-of-freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double Hopf bifurcation point. Centre manifold reduction and normal form calculations are performed to investigate the long-term dynamics of the cutting process. The normal form of the four-dimensional centre subsystem is derived analytically, and the possible topologies in the infinite-dimensional phase space of the system are revealed. It is shown that bistable parameter regions exist where unstable periodic and, in certain cases, unstable quasi-periodic motions coexist with the equilibrium. Taking into account the non-smoothness caused by loss of contact between the tool and the workpiece, the boundary of the bistable region is also derived analytically. The results are verified by numerical continuation. The possibility of (transient) chaotic motions in the global non-smooth dynamics is shown.
Directory of Open Access Journals (Sweden)
Liming Zhao
2016-01-01
Full Text Available First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.
Two-parameters Hopf bifurcation in the Hodgkin-Huxley model
Energy Technology Data Exchange (ETDEWEB)
Wang Jiang [School of Electrical and Automation Engineering, Tianjin University, Tianjin 300072 (China)]. E-mail: jiangwang@tju.edu.cn; Geng Jianming [School of Electrical and Automation Engineering, Tianjin University, Tianjin 300072 (China); Fei Xiangyang [School of Electrical and Automation Engineering, Tianjin University, Tianjin 300072 (China)
2005-02-01
In this paper, the Hodgkin-Huxley model is studied with the leakage conductance and the sodium reversal potential selected as parameters for a two-parameter Hopf-bifurcation analysis. The influence of bifurcation on the HH model was also discussed and algebra criterion in high dimension equations was used to identify Hopf bifurcation. In addition, this paper also discuses the bifurcation approach to inherited disorders of ion channels in skeletal muscle excitable membranes.
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-01-01
Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
Views on the Hopf bifurcation with respect to voltage instabilities
Energy Technology Data Exchange (ETDEWEB)
Roa-Sepulveda, C.A. [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U.G. [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering
1994-12-31
This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.
Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System
Directory of Open Access Journals (Sweden)
Xiaojun Liu
2014-01-01
Full Text Available The Hopf bifurcation of a fractional-order Van der Pol (VDP for short system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.
Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes
Directory of Open Access Journals (Sweden)
Dawei Ding
2016-01-01
Full Text Available We focus on the Hopf bifurcation control problem of a FAST TCP model with RED gateway. The system gain parameter is chosen as the bifurcation parameter, and the stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply state feedback controller, hybrid controller, and time-delay feedback controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulations show that the hybrid controller is the most sensitive method to delay the Hopf bifurcation with identical parameter conditions. However, nonlinear state feedback control and time-delay feedback control schemes have larger control parameter range in the Internet congestion control system with FAST TCP and RED gateway. Therefore, we can choose proper control method based on practical situation including unknown conditions or parameter requirements. This paper plays an important role in setting guiding system parameters for controlling the FAST TCP and RED model.
Directory of Open Access Journals (Sweden)
Yan Zhang
2014-01-01
Full Text Available We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and nonhomogeneous periodic solutions of this particular system. In particular, we also prove that the spatial homogeneous periodic solutions bifurcating from the smallest Hopf bifurcation point of the system are always unstable. This together with the instability results of the spatially nonhomogeneous periodic solutions by Yi et al., 2009, indicates that, in this model, all the oscillatory patterns from Hopf bifurcations are unstable.
Energy Technology Data Exchange (ETDEWEB)
Jiang Xiaowu [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China); Zhou Xueyong [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China)], E-mail: xueyongzhou@126.com; Shi Xiangyun [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China); Song Xinyu [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China)], E-mail: xysong88@163.com
2008-10-15
A delay differential mathematical model that described HIV infection of CD4{sup +} T-cells is analyzed. The stability of the non-negative equilibria and the existence of Hopf bifurcation are investigated. A stability switch in the system due to variation of delay parameter has been observed, so is the phenomena of Hopf bifurcation and stable limit cycle. The estimation of the length of delay to preserve stability has been calculated. Using the normal form theory and center manifold argument, the explicit formulaes which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.
An Approach to Robust Control of the Hopf Bifurcation
Directory of Open Access Journals (Sweden)
Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
Ding, Dawei; Qian, Xin; Hu, Wei; Wang, Nian; Liang, Dong
2017-11-01
In this paper, a time-delayed feedback controller is proposed in order to control chaos and Hopf bifurcation in a fractional-order memristor-based chaotic system with time delay. The associated characteristic equation is established by regarding the time delay as a bifurcation parameter. A set of conditions which ensure the existence of the Hopf bifurcation are gained by analyzing the corresponding characteristic equation. Then, we discuss the influence of feedback gain on the critical value of fractional order and time delay in the controlled system. Theoretical analysis shows that the controller is effective in delaying the Hopf bifurcation critical value via decreasing the feedback gain. Finally, some numerical simulations are presented to prove the validity of our theoretical analysis and confirm that the time-delayed feedback controller is valid in controlling chaos and Hopf bifurcation in the fractional-order memristor-based system.
Hopf and Generalized Hopf Bifurcations in a Recurrent Autoimmune Disease Model
Zhang, Wenjing; Yu, Pei
This paper is concerned with bifurcation and stability in an autoimmune model, which was established to study an important phenomenon — blips arising from such models. This model has two equilibrium solutions, disease-free equilibrium and disease equilibrium. The positivity of the solutions of the model and the global stability of the disease-free equilibrium have been proved. In this paper, we particularly focus on Hopf bifurcation which occurs from the disease equilibrium. We present a detailed study on the use of center manifold theory and normal form theory, and derive the normal form associated with Hopf bifurcation, from which the approximate amplitude of the bifurcating limit cycles and their stability conditions are obtained. Particular attention is also paid to the bifurcation of multiple limit cycles arising from generalized Hopf bifurcation, which may yield bistable phenomenon involving equilibrium and oscillating motion. This result may explain some complex dynamical behavior in real biological systems. Numerical simulations are compared with the analytical predictions to show a very good agreement.
From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems
Khraief Haddad, Nahla; Belghith, Safya; Gritli, Hassène; Chemori, Ahmed
2017-06-01
This paper deals with the problem of obtaining stable and robust oscillations of underactuated mechanical systems. It is concerned with the Hopf bifurcation analysis of a Controlled Inertia Wheel Inverted Pendulum (C-IWIP). Firstly, the stabilization was achieved with a control law based on the Interconnection, Damping, Assignment Passive Based Control method (IDA-PBC). Interestingly, the considered closed-loop system exhibits both supercritical and subcritical Hopf bifurcation for certain gains of the control law. Secondly, we used the center manifold theorem and the normal form technique to study the stability and instability of limit cycles emerging from the Hopf bifurcation. Finally, numerical simulations were conducted to validate the analytical results in order to prove that with IDA-PBC we can control not only the unstable equilibrium but also some trajectories such as limit cycles.
An explicit example of Hopf bifurcation in fluid mechanics
Kloeden, P.; Wells, R.
1983-01-01
It is observed that a complete and explicit example of Hopf bifurcation appears not to be known in fluid mechanics. Such an example is presented for the rotating Benard problem with free boundary conditions on the upper and lower faces, and horizontally periodic solutions. Normal modes are found for the linearization, and the Veronis computation of the wave numbers is modified to take into account the imposed horizontal periodicity. An invariant subspace of the phase space is found in which the hypotheses of the Joseph-Sattinger theorem are verified, thus demonstrating the Hopf bifurcation. The criticality calculations are carried through to demonstrate rigorously, that the bifurcation is subcritical for certain cases, and to demonstrate numerically that it is subcritical for all the cases in the paper.
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Indian Academy of Sciences (India)
Weiquan Pan
2017-05-31
May 31, 2017 ... 2Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,. Yulin Normal University .... of [21], but based on the analysis of [12,22,23], for the first Lyapunov coefficient l1, .... analysis of the first Lyapunov coefficient for the Hopf bifurcation of system (2.1) ...
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Control by time delayed feedback near a Hopf bifurcation point
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Sjoerd Verduyn Lunel
2017-12-01
Full Text Available In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1 by directly studying the Floquet multipliers and 2 by use of the Hopf bifurcation theorem. We also propose an extension of the Pyragas control scheme for which the controlled system becomes a functional differential equation of neutral type. Using the observation that we are able to determine the direction of bifurcation by a relatively simple calculation of the root tendency, we find stability conditions for the periodic orbit as a solution of the neutral type equation.
DEFF Research Database (Denmark)
Corradi, Olivier; Hjorth, Poul G.; Starke, Jens
2012-01-01
an onset of oscillations of the net pedestrian flux through the doorway, described by a Hopf bifurcation. An equation-free continuation of the Hopf point in the two parameters, door width and ratio of the pedestrian velocities of the two crowds, is performed. © 2012 Society for Industrial and Applied......Using an equation-free analysis approach we identify a Hopf bifurcation point and perform a twoparameter continuation of the Hopf point for the macroscopic dynamical behavior of an interacting particle model. Due to the nature of systems with a moderate number of particles and noise, the quality...... of the available numerical information requires the use of very robust numerical algorithms for each of the building blocks of the equation-free methodology. As an example, we consider a particle model of a crowd of pedestrians where particles interact through pairwise social forces. The pedestrians move along...
Global Hopf Bifurcation for a Predator-Prey System with Three Delays
Jiang, Zhichao; Wang, Lin
2017-06-01
In this paper, a delayed predator-prey model is considered. The existence and stability of the positive equilibrium are investigated by choosing the delay τ = τ1 + τ2 as a bifurcation parameter. We see that Hopf bifurcation can occur as τ crosses some critical values. The direction of the Hopf bifurcations and the stability of the bifurcation periodic solutions are also determined by using the center manifold and normal form theory. Furthermore, based on the global Hopf bifurcation theorem for general function differential equations, which was established by J. Wu using fixed point theorem and degree theory methods, the existence of global Hopf bifurcation is investigated. Finally, numerical simulations to support the analytical conclusions are carried out.
Stability and Hopf Bifurcation for a Delayed Computer Virus Model with Antidote in Vulnerable System
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2017-01-01
Full Text Available A delayed computer virus model with antidote in vulnerable system is investigated. Local stability of the endemic equilibrium and existence of Hopf bifurcation are discussed by analyzing the associated characteristic equation. Further, direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are presented to show consistency with the obtained results.
Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC
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Μ. Μ. Alomari
2017-06-01
Full Text Available The use of a unified power flow controller (UPFC to control the bifurcations of a subsynchronous resonance (SSR in a multi-machine power system is introduced in this study. UPFC is one of the flexible AC transmission systems (FACTS where a voltage source converter (VSC is used based on gate-turn-off (GTO thyristor valve technology. Furthermore, UPFC can be used as a stabilizer by means of a power system stabilizer (PSS. The considered system is a modified version of the second system of the IEEE second benchmark model of subsynchronous resonance where the UPFC is added to its transmission line. The dynamic effects of the machine components on SSR are considered. Time domain simulations based on the complete nonlinear dynamical mathematical model are used for numerical simulations. The results in case of including UPFC are compared to the case where the transmission line is conventionally compensated (without UPFC where two Hopf bifurcations are predicted with unstable operating point at wide range of compensation levels. For UPFC systems, it is worth to mention that the operating point of the system never loses stability at all realistic compensation degrees and therefore all power system bifurcations have been eliminated.
Diekmann, O; Montijn, R
1982-01-01
We discuss a simple deterministic model for the spread, in a closed population, of an infectious disease which confers only temporary immunity. The model leads to a nonlinear Volterra integral equation of convolution type. We are interested in the bifurcation of periodic solutions from a constant solution (the endemic state) as a certain parameter (the population size) is varied. Thus we are led to study a characteristic equation. Our main result gives a fairly detailed description (in terms of Fourier coefficients of the kernel) of the traffic of roots across the imaginary axis. As a corollary we obtain the following: if the period of immunity is longer than the preceding period of incubation and infectivity, then the endemic state is unstable for large population sizes and at least one periodic solution will originate.
Hopf bifurcation in love dynamical models with nonlinear couples and time delays
Energy Technology Data Exchange (ETDEWEB)
Liao Xiaofeng [School of Computer and Information, Chongqing Jiaotong University, Chonqing 400074 (China) and Department of Computer Science and Engineering, Chongqing University, Chongqing 400030 (China)]. E-mail: xflao@cqu.edu.cn; Ran Jiouhong [Hospital of Chongqing University, Chonqing University, Chongqing 400030 (China)
2007-02-15
A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results.
Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
DEFF Research Database (Denmark)
Brøns, Morten; Desroches, Mathieu; Krupa, Martin
2015-01-01
In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized...... by a small change in one of the variables, determines the features of the mixed-mode oscillations. Period-doubling and saddle-node bifurcations lead to closed families (called isolas) of periodic solutions in a bifurcation corresponding to a singular Hopf bifurcation....
Yang, Dong-Ping; Robinson, P. A.
2017-04-01
A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.
Yang, Dong-Ping; Robinson, P A
2017-04-01
A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.
Generic Hopf-Neimark-Sacker bifurcations in feed-forward systems
Broer, Henk W.; Vegter, Gert
We show that generic Hopf-Neimark-Sacker bifurcations occur in the dynamics of a large class of feed-forward coupled cell networks. To this end we present a framework for studying such bifurcations in parametrized families of perturbed forced oscillators near weak resonance points. Our approach is
Stability and Hopf bifurcation for a delayed SLBRS computer virus model.
Zhang, Zizhen; Yang, Huizhong
2014-01-01
By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.
Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2014-01-01
Full Text Available By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.
Hopf Bifurcation in an SEIDQV Worm Propagation Model with Quarantine Strategy
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Yu Yao
2012-01-01
Full Text Available Worms exploiting zero-day vulnerabilities have drawn significant attention owing to their enormous threats to the Internet. In general, users may immunize their computers with countermeasures in exposed and infectious state, which may take a period of time. Through theoretical analysis, time delay may lead to Hopf bifurcation phenomenon so that the worm propagation system will be unstable and uncontrollable. In view of the above factors, a quarantine strategy is thus proposed in the study. In real network, unknown worms and worm variants may lead to great risks, which misuse detection system fails to detect. However, anomaly detection is of help in detecting these kinds of worm. Consequently, our proposed quarantine strategy is built on the basis of anomaly intrusion detection system. Numerical experiments show that the quarantine strategy can diminish the infectious hosts sharply. In addition, the threshold τ0 is much larger after using our quarantine strategy, which implies that people have more time to remove worms so that the system is easier to be stable and controllable without Hopf bifurcation. Finally, simulation results match numerical ones well, which fully supports our analysis.
Hopf bifurcation and chaos in a third-order phase-locked loop
Piqueira, José Roberto C.
2017-01-01
Phase-locked loops (PLLs) are devices able to recover time signals in several engineering applications. The literature regarding their dynamical behavior is vast, specifically considering that the process of synchronization between the input signal, coming from a remote source, and the PLL local oscillation is robust. For high-frequency applications it is usual to increase the PLL order by increasing the order of the internal filter, for guarantying good transient responses; however local parameter variations imply structural instability, thus provoking a Hopf bifurcation and a route to chaos for the phase error. Here, one usual architecture for a third-order PLL is studied and a range of permitted parameters is derived, providing a rule of thumb for designers. Out of this range, a Hopf bifurcation appears and, by increasing parameters, the periodic solution originated by the Hopf bifurcation degenerates into a chaotic attractor, therefore, preventing synchronization.
Schikora, S.; Wünsche, H.-J.; Henneberger, F.
2011-02-01
A subcritical Hopf bifurcation is prepared in a multisection semiconductor laser. In the free-running state, hysteresis is absent due to noise-induced escape processes. The missing branches are recovered by stabilizing them against noise through application of phase-sensitive noninvasive delayed optical feedback control. The same type of control is successfully used to stabilize the unstable pulsations born in the Hopf bifurcation. This experimental finding represents an optical counterexample to the so-called odd-number limitation of delayed feedback control. However, as a leftover of the limitation, the domains of control are extremely small.
Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources
Directory of Open Access Journals (Sweden)
Caijuan Yan
2014-01-01
Full Text Available We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratio ℛ01, we obtain sufficient conditions under which the endemic equilibrium E* of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.
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
Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia
2017-12-01
In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.
Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus
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Tao Dong
2012-01-01
Full Text Available By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.
Dynamics at infinity and a Hopf bifurcation arising in a quadratic ...
Indian Academy of Sciences (India)
Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in R 3 , the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the ...
Dynamics at infinity and a Hopf bifurcation arising in a quadratic ...
Indian Academy of Sciences (India)
Zhen Wang
2017-12-27
Dec 27, 2017 ... Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with ... quadratic autonomous system, we raise the question: does there ..... 3200. + i. 41. 3200. , N22 = −. 23. 3200. − i. 41. 3200. ,. N12 = −. 41. 800 . The dynamics on the centre manifold is then governed by the equation. ˙w = 1. 2 iw +.
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Pan, Weiquan; Li, Lijie
2017-06-01
In order to further understand a self-exciting Faraday disc dynamo (Hide et al, in Proc. R. Soc. A 452, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.
Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors
Wang, Zhen; Moroz, Irene; Wei, Zhouchao; Ren, Haipeng
2018-01-01
Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in R^3, the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the subcritical Hopf bifurcation is analysed and obtained. Numerical simulations demonstrate the correctness of the dynamical and bifurcation analyses. Moreover, by choosing appropriate parameters, this perturbed system can exhibit chaotic, quasiperiodic and periodic dynamics, as well as some coexisting attractors, such as a chaotic attractor coexisting with a periodic attractor for a>0, and a chaotic attractor coexisting with a quasiperiodic attractor for a=0. Coexisting attractors are not associated with an unstable equilibrium and thus often go undiscovered because they may occur in a small region of parameter space, with a small basin of attraction in the space of initial conditions.
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Carlos Mario Escobar Callejas
2011-12-01
Full Text Available En el presente artículo de investigación se caracteriza el tipo de bifurcación de Hopf que se presenta en el fenómeno de la bifurcación de zip para un sistema tridimensional no lineal de ecuaciones diferenciales que satisface las condiciones planteadas por Butler y Farkas, las cuales modelan la competición de dos especies predadoras por una presa singular que se regenera. Se demuestra que en todas las variedades bidimensionales invariantes del sistema considerado se desarrolla una bifurcación de Hopf supercrítica lo cual es una extensión de algunos resultados sobre el tipo de bifurcación de Hopf que se forma en el fenómeno de la bifurcación de zip en sistema con respuesta funcional del predador del tipo Holling II, [1].This research article characterizes the type of Hopf bifurcation occurring in the Zip bifurcation phenomenon for a non-linear 3D system of differential equations which meets the conditions stated by Butler and Farkas to model competition of two predators struggling for a prey. It is shown that a supercritical Hopf bifurcation is developed in all invariant two-dimensional varieties of the system considered, which is an extension of some results about the kind of Hopf bifurcation which is formed in the Zip bifurcation phenomenon in a system with functional response of the Holling-type predator.
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks
Wang, Zhen; Campbell, Sue Ann
2017-11-01
We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with ZN symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.
Stability and Hopf bifurcation on a model for HIV infection of CD4{sup +} T cells with delay
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Wang Xia [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China)], E-mail: xywangxia@163.com; Tao Youde [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China); Beijing Institute of Information Control, Beijing 100037 (China); Song Xinyu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China) and Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091 (China)], E-mail: xysong88@163.com
2009-11-15
In this paper, a delayed differential equation model that describes HIV infection of CD4{sup +} T cells is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.
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Toichiro Asada
2007-01-01
Full Text Available We explore numerically a three-dimensional discrete-time Kaldorian macrodynamic model in an open economy with fixed exchange rates, focusing on the effects of variation of the model parameters, the speed of adjustment of the goods market α, and the degree of capital mobility β on the stability of equilibrium and on the existence of business cycles. We determine the stability region in the parameter space and find that increase of α destabilizes the equilibrium more quickly than increase of β. We determine the Hopf-Neimark bifurcation curve along which business cycles are generated, and discuss briefly the occurrence of Arnold tongues. Bifurcation and Lyapunov exponent diagrams are computed providing information on the emergence, persistence, and amplitude of the cycles and illustrating the complex dynamics involved. Examples of cycles and other attractors are presented. Finally, we discuss a two-dimensional variation of the model related to a “wealth effect,” called model 2, and show that in this case, α does not destabilize the equilibrium more quickly than β, and that a Hopf-Neimark bifurcation curve does not exist in the parameter space, therefore model 2 does not produce cycles.
Zhao, Huitao; Lu, Mengxia; Zuo, Junmei
2014-01-01
A controlled model for a financial system through washout-filter-aided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system.
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.
Dai, Yunxian; Lin, Yiping; Zhao, Huitao; Khalique, Chaudry Masood
2016-06-01
In this paper, a delayed computer virus propagation model with a saturation incidence rate and a time delay describing temporary immune period is proposed and its dynamical behaviors are studied. The threshold value ℜ0 is given to determine whether the virus dies out completely. By comparison arguments and iteration technique, sufficient conditions are obtained for the global asymptotic stabilities of the virus-free equilibrium and the virus equilibrium. Taking the delay as a parameter, local Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stabilities of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, numerical simulations are carried out to illustrate the main theoretical results.
Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics
Drogoul, Audric; Veltz, Romain
2017-02-01
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.
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Daogao Wei
2015-01-01
Full Text Available Multiaxle steering is widely used in commercial vehicles. However, the mechanism of the self-excited shimmy produced by the multiaxle steering system is not clear until now. This study takes a dual-front axle heavy truck as sample vehicle and considers the influences of mid-shift transmission and dry friction to develop a 9 DOF dynamics model based on Lagrange’s equation. Based on the Hopf bifurcation theorem and center manifold theory, the study shows that dual-front axle shimmy is a self-excited vibration produced from Hopf bifurcation. The numerical method is adopted to determine how the size of dry friction torque influences the Hopf bifurcation characteristics of the system and to analyze the speed range of limit cycles and numerical characteristics of the shimmy system. The consistency of results of the qualitative and numerical methods shows that qualitative methods can predict the bifurcation characteristics of shimmy systems. The influences of the main system parameters on the shimmy system are also discussed. Improving the steering transition rod stiffness and dry friction torque and selecting a smaller pneumatic trail and caster angle can reduce the self-excited shimmy, reduce tire wear, and improve the driving stability of vehicles.
A bifurcation analysis of boiling water reactor on large domain of parametric spaces
Pandey, Vikas; Singh, Suneet
2016-09-01
The boiling water reactors (BWRs) are inherently nonlinear physical system, as any other physical system. The reactivity feedback, which is caused by both moderator density and temperature, allows several effects reflecting the nonlinear behavior of the system. Stability analyses of BWR is done with a simplified, reduced order model, which couples point reactor kinetics with thermal hydraulics of the reactor core. The linear stability analysis of the BWR for steady states shows that at a critical value of bifurcation parameter (i.e. feedback gain), Hopf bifurcation occurs. These stable and unstable domains of parametric spaces cannot be predicted by linear stability analysis because the stability of system does not include only stability of the steady states. The stability of other dynamics of the system such as limit cycles must be included in study of stability. The nonlinear stability analysis (i.e. bifurcation analysis) becomes an indispensable component of stability analysis in this scenario. Hopf bifurcation, which occur with one free parameter, is studied here and it formulates birth of limit cycles. The excitation of these limit cycles makes the system bistable in the case of subcritical bifurcation whereas stable limit cycles continues in an unstable region for supercritical bifurcation. The distinction between subcritical and supercritical Hopf is done by two parameter analysis (i.e. codimension-2 bifurcation). In this scenario, Generalized Hopf bifurcation (GH) takes place, which separates sub and supercritical Hopf bifurcation. The various types of bifurcation such as limit point bifurcation of limit cycle (LPC), period doubling bifurcation of limit cycles (PD) and Neimark-Sacker bifurcation of limit cycles (NS) have been identified with the Floquet multipliers. The LPC manifests itself as the region of bistability whereas chaotic region exist because of cascading of PD. This region of bistability and chaotic solutions are drawn on the various
Bifurcation Behavior Analysis in a Predator-Prey Model
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Nan Wang
2016-01-01
Full Text Available A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation, which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.
Stability and Hopf bifurcation in a delayed model for HIV infection of CD4{sup +}T cells
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Cai Liming [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China); Beijing Institute of Information Control, Beijing 100037 (China)], E-mail: lmcai06@yahoo.com.cn; Li Xuezhi [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China)
2009-10-15
In this paper, we consider a delayed mathematical model for the interactions of HIV infection and CD4{sup +}T cells. We first investigate the existence and stability of the Equilibria. We then study the effect of the time delay on the stability of the infected equilibrium. Criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Moreover, by applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Finally by using a delay {tau} as a bifurcation parameter, the existence of Hopf bifurcation is also investigated. Numerical simulations are presented to illustrate the analytical results.
Effects of internal noise in mesoscopic chemical systems near Hopf bifurcation
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Xiao Tiejun [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Ma Juan [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Hou Zhonghuai [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Xin Houwen [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China)
2007-11-15
The effects of internal noise in mesoscopic chemical oscillation systems have been studied analytically, in the parameter region close to the deterministic Hopf bifurcation. Starting from chemical Langevin equations, stochastic normal form equations are obtained, governing the evolution of the radius and phase of the stochastic oscillation. By stochastic averaging, the normal form equation can be solved analytically. Stationary distributions of the radius and auto-correlation functions of the phase variable are obtained. It is shown that internal noise can induce oscillation; even no deterministic oscillation exists. The radius of the noise-induced oscillation (NIO) becomes larger when the internal noise increases, but the correlation time becomes shorter. The trade-off between the strength and regularity of the NIO leads to a clear maximum in its signal-to-noise ratio when the internal noise changes, demonstrating the occurrence of internal noise coherent resonance. Since the intensity of the internal noise is inversely proportional to the system size, the phenomenon also indicates the existence of an optimal system size. These theoretical results are applied to a circadian clock system and excellent agreement with the numerical results is obtained.
Bifurcation and Hybrid Control for A Simple Hopfield Neural Networks with Delays
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Zisen Mao
2013-01-01
Full Text Available A detailed analysis on the Hopf bifurcation of a delayed Hopfield neural network is given. Moreover, a new hybrid control strategy is proposed, in which time-delayed state feedback and parameter perturbation are used to control the Hopf bifurcation of the model. Numerical simulation results confirm that the new hybrid controller using time delay is efficient in controlling Hopf bifurcation.
Discretization analysis of bifurcation based nonlinear amplifiers
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S. Feldkord
2017-09-01
Full Text Available Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov–Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov–Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge–Kutta methods transform the truncated normalform equation of the Andronov–Hopf bifurcation into the normalform equation of the Neimark–Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark–Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov–Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark–Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Discretization analysis of bifurcation based nonlinear amplifiers
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Bifurcation analysis of a Kaldor-Kalecki model of business cycle with time delay
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Liancheng Wang
2009-10-01
Full Text Available In this paper, we investigate a Kaldor-Kalecki model of business cycle with delay in both the gross product and the capital stock. Stability analysis for the equilibrium point is carried out. We show that Hopf bifurcation occurs and periodic solutions emerge as the delay crosses some critical values. By deriving the normal forms for the system, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Examples are presented to confirm our results.
DROP TAIL AND RED QUEUE MANAGEMENT WITH SMALL BUFFERS:STABILITY AND HOPF BIFURCATION
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Ganesh Patil
2011-06-01
Full Text Available There are many factors that are important in the design of queue management schemes for routers in the Internet: for example, queuing delay, link utilization, packet loss, energy consumption and the impact of router buffer size. By considering a fluid model for the congestion avoidance phase of Additive Increase Multiplicative Decrease (AIMD TCP, in a small buffer regime, we argue that stability should also be a desirable feature for network performance. The queue management schemes we study are Drop Tail and Random Early Detection (RED. For Drop Tail, the analytical arguments are based on local stability and bifurcation theory. As the buffer size acts as a bifurcation parameter, variations in it can readily lead to the emergence of limit cycles. We then present NS2 simulations to study the effect of changing buffer size on queue dynamics, utilization, window size and packet loss for three different flow scenarios. The simulations corroborate the analysis which highlights that performance is coupled with the notion of stability. Our work suggests that, in a small buffer regime, a simple Drop Tail queue management serves to enhance stability and appears preferable to the much studied RED scheme.
Stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays
Qu, Ying; Wei, Junjie; Ruan, Shigui
2010-10-01
This paper is devoted to the analysis of a maturity structured system of hematopoietic stem cell (HSC) populations in the bone marrow. The model is a system of differential equations with several time delays. We discuss the stability of equilibria and perform the analysis of Hopf bifurcation. More precisely, we first obtain a set of improved sufficient conditions ensuring the global asymptotical stability of the zero solution using the Lyapunov method and the embedding technique of asymptotically autonomous semiflows. Then we prove that there exists at least one positive periodic solution for the n-dimensional system as a time delay varies in some region. This result is established by combining Hopf bifurcation theory, the global Hopf bifurcation theorem due to Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799-4838], and a continuation theorem of coincidence degree theory. Some numerical simulations are also presented to illustrate the analytic results.
Hopf bifurcation in a dynamic IS-LM model with time delay
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Neamtu, Mihaela [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: mihaela.neamtu@fse.uvt.ro; Opris, Dumitru [Department of Applied Mathematics, Faculty of Mathematics, West University of Timisoara, Bd. V. Parvan, nr. 4, 300223 Timisoara (Romania)]. E-mail: opris@math.uvt.ro; Chilarescu, Constantin [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: cchilarescu@rectorat.uvt.ro
2007-10-15
The paper investigates the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. We show when the system is stable with respect to the delay. Some numerical examples are given to confirm the theoretical results.
Bifurcation analysis of the transition of dune shapes under a unidirectional wind.
Niiya, Hirofumi; Awazu, Akinori; Nishimori, Hiraku
2012-04-13
A bifurcation analysis of dune shape transition is made. By use of a reduced model of dune morphodynamics, the Dune Skeleton model, we elucidate the transition mechanism between different shapes of dunes under unidirectional wind. It was found that the decrease in the total amount of sand in the system and/or the lateral sand flow shifts the stable state from a straight transverse dune to a wavy transverse dune through a pitchfork bifurcation. A further decrease causes wavy transverse dunes to shift into barchans through a Hopf bifurcation. These bifurcation structures reveal the transition mechanism of dune shapes under unidirectional wind.
Numerical Bifurcation Analysis
Meijer, Hil Gaétan Ellart; Dercole, Fabio; Oldeman, Bart; Myers, R.A.
The theory of dynamical systems studies the behavior of solutions of systems, like nonlinear ordinary differential equations (ODEs), depending upon parameters. Using qualitative methods of bifurcation theory, the behavior of the system is characterized for various parameter combinations. In
Delayed Feedback Control and Bifurcation Analysis of an Autonomy System
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Zhen Wang
2013-01-01
Full Text Available An autonomy system with time-delayed feedback is studied by using the theory of functional differential equation and Hassard’s method; the conditions on which zero equilibrium exists and Hopf bifurcation occurs are given, the qualities of the Hopf bifurcation are also studied. Finally, several numerical simulations are given; which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable state or a stable periodic orbit.
Bifurcation Analysis of a Class of (n + 1)-Dimension Internet Congestion Control Systems
Xu, Wenying; Cao, Jinde; Xiao, Min
This paper investigates the stability and Hopf bifurcation induced by the time delay in a class of (n + 1)-dimension Internet congestion control systems. Although there are several previous works on simplified models of Internet congestion systems with only one or two sources and such works can reflect partly dynamical behaviors of real Internet systems, some complicated problems may inevitably be overlooked. Hence, it is meaningful to study high-dimensional models which stand closer to general realistic large-scale Internet congestion networks. By analyzing the distribution of the associated characteristic roots, we can obtain conditions for keeping systems stable. When the delay increases and exceeds a critical value, the system will undergo a Hopf bifurcation. Furthermore, the explicit formulas to determine the stability and the direction of the bifurcating periodic solution are derived by applying the normal form theory and the center manifold reduction. Finally, two numerical examples are given to verify our theoretical analysis.
Cristiano, Rony; Carvalho, Tiago; Tonon, Durval J.; Pagano, Daniel J.
2017-05-01
In this paper, Hopf and homoclinic bifurcations that occur in the sliding vector field of switching systems in R3 are studied. In particular, a dc-dc boost converter with sliding mode control and washout filter is analyzed. This device is modeled as a three-dimensional Filippov system, characterized by the existence of sliding movement and restricted to the switching manifold. The operating point of the converter is a stable pseudo-equilibrium and it undergoes a subcritical Hopf bifurcation. Such a bifurcation occurs in the sliding vector field and creates, in this field, an unstable limit cycle. The limit cycle is connected to the switching manifold and disappears when it touches the visible-invisible two-fold point, resulting in a homoclinic loop which itself closes in this two-fold point. The study of these dynamic phenomena that can be found in different power electronic circuits controlled by sliding mode control strategies are relevant from the viewpoint of the global stability and robustness of the control design.
Bifurcations analysis of turbulent energy cascade
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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.
Ferruzzo Correa, Diego Paolo; Wulff, Claudia; Piqueira, José Roberto Castilho
2015-05-01
In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence a part of the system might repeat itself, and properties of this subsystem are representative of the dynamics on the whole phase space. In this paper an analysis of the second order N-node time-delay fully connected network is presented which is based on previous work: synchronous states in time-delay coupled periodic oscillators: a stability criterion. Correa and Piqueira (2013), for a 2-node network. This study is carried out using symmetry groups. We show the existence of multiple eigenvalues forced by symmetry, as well as the existence of Hopf bifurcations. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. We determine a finite set of frequencies ω , that might correspond to Hopf bifurcations in each case for critical values of the delay. The Sn map is used to actually find Hopf bifurcations along with numerical calculations using the Lambert W function. Numerical simulations are used in order to confirm the analytical results. Although we restrict attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.
Bifurcation analysis of a spruce budworm model with diffusion and physiological structures
Xu, Xiaofeng; Wei, Junjie
2017-05-01
In this paper, the dynamics of a spruce budworm model with diffusion and physiological structures are investigated. The stability of steady state and the existence of Hopf bifurcation near positive steady state are investigated by analyzing the distribution of eigenvalues. The properties of Hopf bifurcation are determined by the normal form theory and center manifold reduction for partial functional differential equations. And global existence of periodic solutions is established by using the global Hopf bifurcation result of Wu. Finally, some numerical simulations are carried out to illustrate the analytical results.
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Pandey, Vikas; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in
2017-04-15
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
Codimension-2 bifurcations of the Kaldor model of business cycle
Energy Technology Data Exchange (ETDEWEB)
Wu, Xiaoqin P., E-mail: xpaul_wu@yahoo.co [Department of Mathematics, Computer and Information Sciences, Mississippi Valley State University, Itta Bena, MS 38941 (United States)
2011-01-15
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 in delayed feedback Jerk systems and application of chaotic control
Energy Technology Data Exchange (ETDEWEB)
Zheng Baodong [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: zbd@hit.edu.cn; Zheng Huifeng [Department of Electronics and Communication Engineering, Harbin Institute of Technology, Harbin 150001 (China)
2009-05-15
Jerk systems with delayed feedback are considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Finally, the application to chaotic control is investigated, and some numerical simulations are carried out to illustrate the obtained results.
Numerical bifurcation analysis of a class of nonlinear renewal equations
Directory of Open Access Journals (Sweden)
Dimitri Breda
2016-09-01
Full Text Available We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic- and Ricker-type population equations and exhibits transcritical, Hopf and period doubling bifurcations. The reliability is demonstrated by comparing the results to those obtained by a reduction to a Hamiltonian Kaplan-Yorke system and to those obtained by direct application of collocation methods (the latter also yield estimates for positive Lyapunov exponents in the chaotic regime. We conclude that the methodology described here works well for a class of delay equations for which currently no tailor-made tools exist (and for which it is doubtful that these will ever be constructed.
National Research Council Canada - National Science Library
Caglar Uyulan; Metin Gokasan; Seta Bogosyan
2017-01-01
The main purpose of this paper is to analyze and compare the Hopf bifurcation behavior of a two-axle railway bogie and a dual wheelset in the presence of nonlinearities, which are yaw damping forces...
Bifurcation analysis for a delayed food chain system with two functional responses
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Zizhen Zhang
2013-09-01
Full Text Available A delayed three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, using the normal form theory and center manifold theorem, the properties of Hopf bifurcation such as direction and stability are determined. Finally, numerical simulations are given to substantiate the theoretical results.
Integral Step Size Makes a Difference to Bifurcations of a Discrete-Time Hindmarsh-Rose Model
Yu, Yang; Cao, Hongjun
A three-dimensional discrete-time Hindmarsh-Rose model obtained by the forward Euler scheme is investigated in this paper. When the integral step size is chosen as a bifurcation parameter, conditions of existence for the fold bifurcation, the flip bifurcation, and the Hopf bifurcation are derived by using the center manifold theorem, bifurcation theory and a criterion of Hopf bifurcation. Numerical simulations including time series, bifurcation diagrams, Lyapunov exponents, phase portraits show the consistence with the analytical analysis. Our research results demonstrate that the integral step size makes a difference corresponding to local and global bifurcations of the three-dimensional discrete-time Hindmarsh-Rose model. These results can supply a solid analytical basis to the study of Hindmarsh-Rose model, and it is necessary to illustrate how much the integral step size is adopted in advance when numerical solutions or approximate solutions of the original continuous-time model is concerned.
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
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Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Bifurcation analysis on a delayed SIS epidemic model with stage structure
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Kejun Zhuang
2007-05-01
Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Yu, Jinchen; Peng, Mingshu
2016-10-01
In this paper, a Kaldor-Kalecki model of business cycle with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the positive equilibrium is investigated. It is found that there exist Hopf bifurcations when the discrete time delay passes a sequence of critical values. By applying the method of multiple scales, the explicit formulae which determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate our main results.
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
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Xianbin Wang
2015-01-01
Full Text Available The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.
Control of bifurcation-delay of slow passage effect by delayed self-feedback
Premraj, D.; Suresh, K.; Banerjee, Tanmoy; Thamilmaran, K.
2017-01-01
The slow passage effect in a dynamical system generally induces a delay in bifurcation that imposes an uncertainty in the prediction of the dynamical behaviors around the bifurcation point. In this paper, we investigate the influence of linear time-delayed self-feedback on the slow passage through the delayed Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator. We perform linear stability analysis to derive the Hopf bifurcation point and its stability as a function of self-feedback time delay. Interestingly, the bifurcation-delay associated with Hopf bifurcation behaves differently in two different edges. In the leading edge of the modulating signal, it decreases with increasing self-feedback delay, whereas in the trailing edge, it behaves in an opposite manner. We also show that the linear time-delayed self-feedback can reduce bifurcation-delay in pitchfork bifurcation. These results are illustrated numerically and corroborated experimentally. We also propose a mechanistic explanation of the observed behaviors. In addition, we show that our observations are robust in the presence of noise. We believe that this study of interplay of two time delays of different origins will shed light on the control of bifurcation-delay and improve our knowledge of time-delayed systems.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
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L. Borkowski
2015-01-01
Full Text Available The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.
Bifurcation and Nonlinear Oscillations.
1980-09-28
Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...the specific structure of the bifurcation near the homo- clinic orbit. Near the Hopf bifurcation, our results could also be obtained from known...on U which maps orbits of f onto orbits of g preserving the sense of time. An f E9 is structurally stable if there is a neighborhood U of f such that
Global Bifurcation of a Novel Computer Virus Propagation Model
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.
Bifurcation analysis of Rössler system with multiple delayed feedback
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Meihong Xu
2010-10-01
Full Text Available In this paper, regarding the delay as parameter, we investigate the effect of delay on the dynamics of a Rössler system with multiple delayed feedback proposed by Ghosh and Chowdhury. At first we consider the stability of equilibrium and the existence of Hopf bifurcations. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, we give a numerical simulation example which indicates that chaotic oscillation is converted into a stable steady state or a stable periodic orbit when the delay passes through certain critical values.
Turing instability and bifurcation analysis in a diffusive bimolecular system with delayed feedback
Wei, Xin; Wei, Junjie
2017-09-01
A diffusive autocatalytic bimolecular model with delayed feedback subject to Neumann boundary conditions is considered. We mainly study the stability of the unique positive equilibrium and the existence of periodic solutions. Our study shows that diffusion can give rise to Turing instability, and the time delay can affect the stability of the positive equilibrium and result in the occurrence of Hopf bifurcations. By applying the normal form theory and center manifold reduction for partial functional differential equations, we investigate the stability and direction of the bifurcations. Finally, we give some simulations to illustrate our theoretical results.
Bifurcation and Firing Patterns of the Pancreatic β-Cell
Wang, Jing; Liu, Shenquan; Liu, Xuanliang; Zeng, Yanjun
Using a model of individual isolated pancreatic β-cells, we investigated bifurcation diagrams of interspike intervals (ISIs) and largest Lyapunov exponents (LLE), which clearly demonstrated a wide range of transitions between different firing patterns. The numerical simulation results revealed the effect of different time constants and ion channels on the neuronal discharge rhythm. Furthermore, an individual cell exhibited tonic spiking, square-wave bursting, and tapered bursting. Additionally, several bifurcation phenomena can be observed in this paper, such as period-doubling, period-adding, inverse period-doubling and inverse period-adding scenarios. In addition, we researched the mechanisms underlying two kinds of bursting (tapered and square-wave bursting) by use of fast-slow dynamics analysis. Finally, we analyzed the codimension-two bifurcation of the fast subsystem and studied cusp bifurcation, generalized Hopf (or Bautin) bifurcation and Bogdanov-Takens bifurcation.
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if R01. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.
Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control
Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming
2015-05-01
With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.
Bifurcation analysis can unify ecological and evolutionary aspects of ecosystems.
Troost, T.A.; Kooi, B.W.; Kooijman, S.A.L.M.
2007-01-01
Bifurcation theory is commonly used to study the dynamical behaviour of ecosystems. It involves the analysis of points in the parameter space where the stability of the system changes qualitatively. Generally, such changes are related only to changes in environmental parameters, while the organism's
Bifurcation analysis and the travelling wave solutions of the Klein ...
Indian Academy of Sciences (India)
Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)). Keywords. Klein–Gordon–Zakharov equations; travelling wave solutions; bifurcation analysis. PACS Nos 05.45.Yv; 2.30.Jr; 04.20.Jb .... level h, it is shown that the exact periodic solutions evolute into solitary wave solution. In ref. [27], by using the ...
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. A...
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
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Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay
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Yu Yao
2014-01-01
Full Text Available Both vaccination and quarantine strategy are adopted to control the Internet worm propagation. By considering the interaction infection between computers and external removable devices, a worm propagation dynamical system with time delay under quarantine strategy is constructed based on anomaly intrusion detection system (IDS. By regarding the time delay caused by time window of anomaly IDS as the bifurcation parameter, local asymptotic stability at the positive equilibrium and local Hopf bifurcation are discussed. Through theoretical analysis, a threshold τ0 is derived. When time delay is less than τ0, the worm propagation is stable and easy to predict; otherwise, Hopf bifurcation occurs so that the system is out of control and the containment strategy does not work effectively. Numerical analysis and discrete-time simulation experiments are given to illustrate the correctness of theoretical analysis.
Bifurcation analysis of the regulation of nociceptive neuronal activity
Dik, O. E.
2017-11-01
A model of the membrane of a nociceptive neuron from a rat dorsal ganglion has been used to address the problem of analyzing the regulation of nociceptive signals by 5-hydroxy-γ-pyrone-2-carboxylic acid, which is the active pharmaceutic ingredient of the analgesic Anoceptin. The study has applied bifurcation analysis to report the relationship between the values of model parameters and the type of problem solution before and after the parameters change in response to analgesic modulation.
Iqbal, Amer
2012-01-01
We establish a relation between the refined Hopf link invariant and the S-matrix of the refined Chern-Simons theory. We show that the refined open string partition function corresponding to the Hopf link, calculated using the refined topological vertex, when expressed in the basis of Macdonald polynomials gives the S-matrix of the refined Chern-Simons theory.
Bifurcation analysis of dengue transmission model in Baguio City, Philippines
Libatique, Criselda P.; Pajimola, Aprimelle Kris J.; Addawe, Joel M.
2017-11-01
In this study, we formulate a deterministic model for the transmission dynamics of dengue fever in Baguio City, Philippines. We analyzed the existence of the equilibria of the dengue model. We computed and obtained conditions for the existence of the equilibrium states. Stability analysis for the system is carried out for disease free equilibrium. We showed that the system becomes stable under certain conditions of the parameters. A particular parameter is taken and with the use of the Theory of Centre Manifold, the proposed model demonstrates a bifurcation phenomenon. We performed numerical simulation to verify the analytical results.
Codimension-Two Bifurcation Analysis in DC Microgrids Under Droop Control
Lenz, Eduardo; Pagano, Daniel J.; Tahim, André P. N.
This paper addresses local and global bifurcations that may appear in electrical power systems, such as DC microgrids, which recently has attracted interest from the electrical engineering society. Most sources in these networks are voltage-type and operate in parallel. In such configuration, the basic technique for stabilizing the bus voltage is the so-called droop control. The main contribution of this work is a codimension-two bifurcation analysis of a small DC microgrid considering the droop control gain and the power processed by the load as bifurcation parameters. The codimension-two bifurcation set leads to practical rules for achieving a robust droop control design. Moreover, the bifurcation analysis also offers a better understanding of the dynamics involved in the problem and how to avoid possible instabilities. Simulation results are presented in order to illustrate the bifurcation analysis.
Bifurcation analysis of the fully symmetric language dynamical equation.
Mitchener, W Garrett
2003-03-01
In this paper, I study a continuous dynamical system that describes language acquisition and communication in a group of individuals. Children inherit from their parents a mechanism to learn their language. This mechanism is constrained by a universal grammar which specifies a restricted set of candidate languages. Language acquisition is not error-free. Children may or may not succeed in acquiring exactly the language of their parents. Individuals talk to each other, and successful communication contributes to biological (or cultural) fitness. I provide a full bifurcation analysis of the case where the parameters are chosen to yield a highly symmetric dynamical system. Populations approach either an incoherent steady state, where many different candidate languages are represented in the population, or a coherent steady state, where the majority of the population speaks a single language. The main result of the paper is a description of how learning reliability affects the stability of these two kinds of equilibria. I rigorously find all fixed points, determine their stabilities, and prove that all populations tend to some fixed point. I also demonstrate that the fixed point representing an incoherent steady state becomes unstable in an S (n)-symmetric transcritical bifurcation as learning becomes more reliable.
Asset Price Dynamics in a Chartist-Fundamentalist Model with Time Delays: A Bifurcation Analysis
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Loretti I. Dobrescu
2016-01-01
Full Text Available This paper studies the dynamic behavior of asset prices using a chartist-fundamentalist model with two speculative markets. To this effect, we employ a differential system with delays à la Dibeh (2007 to describe the price dynamics and we assume that the two markets are coupled via diffusive coupling terms. We study two different time delay cases, namely, when both markets experience the same time delay and when the time delay is different across markets. First, we theoretically determine that the equilibrium exists and investigate its stability. Second, we establish the general conditions for the existence of local Hopf bifurcations and analyze their direction and stability. The common conclusion from both the delay scenarios we consider is that coupled speculative markets with heterogeneous agents in each, but with different price dynamics, can be synchronized through diffusive coupling. Finally, we provide some numerical illustrations to confirm our theoretical findings.
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P
2011-01-01
Background— Controversy persists regarding the correct strategy for bifurcation lesions. Therefore, we combined the patient-level data from 2 large trials with similar methodology: the NORDIC Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study (BBC ONE). Methods and Results— B...
Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem
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Yi Wang
2015-01-01
Full Text Available A wetland ecosystem is studied theoretically and numerically to reveal the rules of dynamics which can be quite accurate to better describe the observed spatial regularity of tussock vegetation. Mathematical theoretical works mainly investigate the stability of constant steady states, the existence of nonconstant steady states, and bifurcation, which can deduce a standard parameter control relation and in return can provide a theoretical basis for the numerical simulation. Numerical analysis indicates that the theoretical works are correct and the wetland ecosystem can show rich dynamical behaviors not only regular spatial patterns. Our results further deepen and expand the study of dynamics in the wetland ecosystem. In addition, it is successful to display tussock formation in the wetland ecosystem may have important consequences for aquatic community structure, especially for species interactions and biodiversity. All these results are expected to be useful in the study of the dynamic complexity of wetland ecosystems.
Bifurcation analysis of vertical transmission model with preventive strategy
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Gosalamang Ricardo Kelatlhegile
2016-07-01
Full Text Available We formulate and analyze a deterministic mathematical model for the prevention of a disease transmitted horizontally and vertically in a population of varying size. The model incorporates prevention of disease on individuals at birth and adulthood and allows for natural recovery from infection. The main aim of the study is to investigate the impact of a preventive strategy applied at birth and at adulthood in reducing the disease burden. Bifurcation analysis is explored to determine existence conditions for establishment of the epidemic states. The results of the study showed that in addition to the disease-free equilibrium there exist multiple endemic equilibria for the model reproduction number below unity. These results may have serious implications on the design of intervention programs and public health policies. Numerical simulations were carried out to illustrate analytical results.
Underwood, Robert G
2015-01-01
This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras, and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course. Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields, and linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforw...
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
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Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Stability and bifurcation for an SEIS epidemic model with the impact of media
Huo, Hai-Feng; Yang, Peng; Xiang, Hong
2018-01-01
A novel SEIS epidemic model with the impact of media is introduced. By analyzing the characteristic equation of equilibrium, the basic reproduction number is obtained and the stability of the steady states is proved. The occurrence of a forward, backward and Hopf bifurcation is derived. Numerical simulations and sensitivity analysis are performed. Our results manifest that media can regard as a good indicator in controlling the emergence and spread of the epidemic disease.
Baird, Bill
1986-08-01
A neural network model describing pattern recognition in the rabbit olfactory bulb is analysed to explain the changes in neural activity observed experimentally during classical Pavlovian conditioning. EEG activity recorded from an 8×8 arry of 64 electrodes directly on the surface on the bulb shows distinct spatial patterns of oscillation that correspond to the animal's recognition of different conditioned odors and change with conditioning to new odors. The model may be considered a variant of Hopfield's model of continuous analog neural dynamics. Excitatory and inhibitory cell types in the bulb and the anatomical architecture of their connection requires a nonsymmetric coupling matrix. As the mean input level rises during each breath of the animal, the system bifurcates from homogenous equilibrium to a spatially patterned oscillation. The theory of multiple Hopf bifurcations is employed to find coupled equations for the amplitudes of these unstable oscillatory modes independent of frequency. This allows a view of stored periodic attractors as fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory.
Bifurcation Tools for Flight Dynamics Analysis and Control System Design Project
National Aeronautics and Space Administration — Modern bifurcation analysis methods have been proposed for investigating flight dynamics and control system design in highly nonlinear regimes and also for the...
Bifurcation Tools for Flight Dynamics Analysis and Control System Design Project
National Aeronautics and Space Administration — The purpose of the project is the development of a computational package for bifurcation analysis and advanced flight control of aircraft. The development of...
Bifurcation analysis of nephron pressure and flow regulation
DEFF Research Database (Denmark)
Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, N.-H.
1996-01-01
One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between...
Bifurcation analysis and the travelling wave solutions of the Klein ...
Indian Academy of Sciences (India)
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by ...
A bifurcation analysis for the Lugiato-Lefever equation
Godey, Cyril
2017-05-01
The Lugiato-Lefever equation is a cubic nonlinear Schrödinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
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...
An alternative bifurcation analysis of the Rose-Hindmarsh model
Energy Technology Data Exchange (ETDEWEB)
Nikolov, Svetoslav [Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia (Bulgaria)]. E-mail: s.nikolov@imbm.bas.bg
2005-03-01
The paper presents an alternative study of the bifurcation behavior of the Rose-Hindmarsh model using Lyapunov-Andronov's theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov's value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose-Hindmarsh system take place under hard stability loss.
Ishibashi, Yuki; Grundeken, Maik J; Nakatani, Shimpei; Iqbal, Javaid; Morel, Marie-Angele; Généreux, Philippe; Girasis, Chrysafios; Wentzel, Jolanda J; Garcia-Garcia, Hector M; Onuma, Yoshinobu; Serruys, Patrick W
2015-03-01
The accuracy and precision of quantitative coronary angiography (QCA) software dedicated for bifurcation lesions compared with conventional single-vessel analysis remains unknown. Furthermore, comparison of different bifurcation analysis algorithms has not been performed. Six plexiglas phantoms with 18 bifurcations were manufactured with a tolerance Analysis System (CAAS; Version 5.10, Pie Medical Imaging, Maastricht, The Netherlands) and QAngio XA (Version 7.3, Medis Medical Imaging System BV, Leiden, The Netherlands) software packages. Conventional single-vessel analysis underestimated the reference vessel diameter and percent diameter stenosis in the proximal main vessel while it overestimated these parameters in the distal main vessel and side branch. CAAS software showed better overall accuracy and precision than QAngio XA (with automatic Y- or T-shape bifurcation algorithm selection) for various phantom diameters including minimum lumen diameter (0.012 ± 0.103 mm vs. 0.041 ± 0.322 mm, P = 0.003), reference vessel diameter (-0.050 ± 0.043 mm vs. 0.116 ± 0.610 mm, P = 0.026), and % diameter stenosis (-0.94 ± 4.07 % vs. 1.74 ± 7.49 %, P = 0.041). QAngio XA demonstrated higher minimal lumen diameter, reference vessel diameter, and % diameter stenosis when compared to the actual phantom diameters; however, the accuracy of these parameters improved to a similar level as CAAS when the sole T-shape algorithm in the QAnxio XA was used. The use of the single-vessel QCA method is inaccurate in bifurcation lesions. Both CAAS and QAngio XA (when the T shape is systematically used) bifurcation software packages are suitable for quantitative assessment of bifurcations. © 2014 Wiley Periodicals, Inc.
Dynamics and geometry near resonant bifurcations
Broer, Hendrik; Holtman, Sijbo J.; Vegter, Gert; Vitolo, Renato
This paper provides an overview of the universal study of families of dynamical systems undergoing a Hopf-NeAmarck-Sacker bifurcation as developed in [1-4]. The focus is on the local resonance set, i.e., regions in parameter space for which periodic dynamics occurs. A classification of the
Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System
Directory of Open Access Journals (Sweden)
Qianiqian Zheng
2017-01-01
Full Text Available Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS, Stochastic Reaction-Diffusion System (SRDS is more complex and it is very difficult to deal with the noise function. In this paper, we have presented a method to solve it and obtained the conditions of how the Turing bifurcation and Hopf bifurcation arise through linear stability analysis of local equilibrium. In addition, we have developed the amplitude equation with a pair of wave vector by using Taylor series expansion, multiscaling, and further expansion in powers of small parameter. Our analysis facilitates finding regions of bifurcations and understanding the pattern formation mechanism of SRDS. Finally, the simulation shows that the analytical results agree with numerical simulation.
Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate
Ren, Jingli; Yuan, Qigang
2017-08-01
A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.
Yi, Guo-Sheng; Wang, Jiang; Han, Chun-Xiao; Deng, Bin; Wei, Xi-Le; Jin, Qi-Tao
2014-05-01
Noninvasive direct current (DC) electric stimulation of central nervous system is today a promising therapeutic option to alleviate the symptoms of a number of neurological disorders. Despite widespread use of this noninvasive brain modulation technique, a generalizable explanation of its biophysical basis has not been described which seriously restricts its application and development. This paper investigated the dynamical behaviors of Hodgkin's three classes of neurons exposed to DC electric field based on a conductance-based neuron model. With phase plane and bifurcation analysis, the different responses of each class of neuron to the same stimulation are shown to derive from distinct spike initiating dynamics. Under the effects of negative DC electric field, class 1 neuron generates repetitive spike through a saddle-node on invariant circle (SNIC) bifurcation, while it ceases this repetitive behavior through a Hopf bifurcation; Class 2 neuron generates repetitive spike through a Hopf bifurcation, meanwhile it ceases this repetitive behavior also by a Hopf bifurcation; Class 3 neuron can generate single spike through a quasi-separatrix-crossing (QSC) at first, then it generates repetitive spike through a Hopf bifurcation, while it ceases this repetitive behavior through a SNIC bifurcation. Furthermore, three classes of neurons' spiking frequency f-electric field E (f-E) curves all have parabolic shape. Our results highlight the effects of external DC electric field on neuronal activity from the biophysical modeling point of view. It can contribute to the application and development of noninvasive DC brain modulation technique.
Wacławczyk, Marta; Oberlack, Martin
2016-03-01
We address the criticism of Frewer et al. concerning the paper "Application of the extended Lie group analysis to the Hopf functional formulation of the Burgers equation" [J. Math. Phys. 54, 072901 (2013)]. Most importantly, we stress that we never claimed that any new statistical symmetries were found in this paper. The aim of this paper was to apply the Lie group analysis to an equation with functional derivatives and derive invariant solutions for this equation. These results still stand as they are, most important, mathematically correct. We address also other critical statements of Frewer et al. and show that there is a connection between the translational invariance of statistics and transformations of the functional Φ. To sum up, key ideas and fundamental result in the work of Wacławczyk and Oberlack are still unaffected.
A tailored solver for bifurcation analysis of ocean-climate models
de Niet, A.C.; Wubs, F.W.; Terwisscha van Scheltinga, A.D.; Dijkstra, H.A.
2007-01-01
In this paper, we present a new linear system solver for use in a fully-implicit ocean model. The new solver allows to perform bifurcation analysis of relatively high-resolution primitive-equation ocean-climate models. It is based on a block-ILU approach and takes special advantage of the
Numerical Bifurcation Methods and their Application to Fluid Dynamics : Analysis beyond Simulation
Dijkstra, Henk A.; Wubs, Fred W.; Cliffe, Andrew K.; Doedel, Eusebius; Dragomirescu, Ioana F.; Eckhardt, Bruno; Gelfgat, Alexander Yu.; Hazel, Andrew L.; Lucarini, Valerio; Salinger, Andy G.; Phipps, Erik T.; Sanchez-Umbria, Juan; Schuttelaars, Henk; Tuckerman, Laurette S.; Thiele, Uwe
We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical
Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation
Dijkstra, H.A.|info:eu-repo/dai/nl/073504467; Wubs, F.W.; et al, [No Value; Thiele, U.
2014-01-01
We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical
Experimental bifurcation analysis of an impact oscillator - Tuning a non-invasive control scheme
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Santos, Ilmar
2013-01-01
We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype for electromag...
Miura, Yasunari; Sugiyama, Yuki
2017-12-01
We present a general method for analyzing macroscopic collective phenomena observed in many-body systems. For this purpose, we employ diffusion maps, which are one of the dimensionality-reduction techniques, and systematically define a few relevant coarse-grained variables for describing macroscopic phenomena. The time evolution of macroscopic behavior is described as a trajectory in the low-dimensional space constructed by these coarse variables. We apply this method to the analysis of the traffic model, called the optimal velocity model, and reveal a bifurcation structure, which features a transition to the emergence of a moving cluster as a traffic jam.
Energy Technology Data Exchange (ETDEWEB)
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2016-10-15
A new class of bifurcations is defined in discrete dynamical systems, and methods for their diagnostics and the analysis of their properties are presented. The TQ-bifurcations considered are implemented in discrete mappings and are related to the qualitative rearrangement of the shape of trajectories in an extended space of states. Within the demonstration of the main capabilities of the toolkit, an analysis is carried out of a logistic mapping in a domain to the right of the period-doubling limit point. Five critical values of the parameter are found for which the geometric structure of the trajectories of the mapping experiences a qualitative rearrangement. In addition, an analysis is carried out of the so-called “trace map,” which arises in the problems of quantum-mechanical description of various properties of discrete crystalline and quasicrystalline lattices.
Makarenko, A. V.
2016-10-01
A new class of bifurcations is defined in discrete dynamical systems, and methods for their diagnostics and the analysis of their properties are presented. The TQ-bifurcations considered are implemented in discrete mappings and are related to the qualitative rearrangement of the shape of trajectories in an extended space of states. Within the demonstration of the main capabilities of the toolkit, an analysis is carried out of a logistic mapping in a domain to the right of the period-doubling limit point. Five critical values of the parameter are found for which the geometric structure of the trajectories of the mapping experiences a qualitative rearrangement. In addition, an analysis is carried out of the so-called "trace map," which arises in the problems of quantum-mechanical description of various properties of discrete crystalline and quasicrystalline lattices.
The formal theory of Hopf algebras part II: the case of Hopf algebras ...
African Journals Online (AJOL)
The category HopfR of Hopf algebras over a commutative unital ring R is analyzed with respect to its categorical properties. The main results are: (1) For every ring R the category HopfR is locally presentable, it is coreflective in the category of bialgebras over R, over every R-algebra there exists a cofree Hopf algebra. (2) If ...
Bifurcation without parameters
Liebscher, Stefan
2015-01-01
Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
On period doubling bifurcations of cycles and the harmonic balance method
Energy Technology Data Exchange (ETDEWEB)
Itovich, Griselda R. [Departamento de Matematica, FAEA, Universidad Nacional del Comahue, Neuquen Q8300BCX (Argentina)] e-mail: gitovich@arnet.com.ar; Moiola, Jorge L. [Departamento de Ingenieria Electrica y de Computadoras Universidad Nacional del Sur, Bahia Blanca B8000CPB (Argentina)] e-mail: jmoiola@criba.edu.ar
2006-02-01
This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method.
Regularizations of two-fold bifurcations in planar piecewise smooth systems using blowup
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
type of limit cycle that does not appear to be present in the original PWS system. For both types of limit cycle, we show that the criticality of the Hopf bifurcation that gives rise to periodic orbits is strongly dependent on the precise form of the regularization. Finally, we analyse the limit cycles...... as locally unique families of periodic orbits of the regularization and connect them, when possible, to limit cycles of the PWS system. We illustrate our analysis with numerical simulations and show how the regularized system can undergo a canard explosion phenomenon...
Coxeter groups and Hopf algebras
Aguiar, Marcelo
2011-01-01
An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary backgrou
A Dynamic Analysis for an Anaerobic Digester: Stability and Bifurcation Branches
Directory of Open Access Journals (Sweden)
Alejandro Rincón
2014-01-01
Full Text Available This work presents a dynamic analysis for an anaerobic digester, supported on the analytical application of the indirect Lyapunov method. The mass-balance model considered is based on two biological reaction pathways and involves both Monod and Haldane representations of the specific biomass growth rates. The dilution rate, the influent concentration of chemical oxygen demand (COD, and the influent concentration of volatile fatty acids (VFA are considered as stability parameters. Several characteristics are determined analytically for the normal operation equilibrium point: (i equilibrium coordinates, (ii parameter conditions that lead to positive values of the equilibrium state variables, (iii parameter conditions for locally stable nature of the equilibrium, (iv coordinates for the local bifurcation points—fold and transcritical—, and (v coordinates of the crossing between bifurcation points. These factors are computed analytically and explicitly as expressions of the dilution rate and the influent concentrations of COD and VFA.
Bifurcation Analysis of a DC-DC Bidirectional Power Converter Operating with Constant Power Loads
Cristiano, Rony; Pagano, Daniel J.; Benadero, Luis; Ponce, Enrique
Direct current (DC) microgrids (MGs) are an emergent option to satisfy new demands for power quality and integration of renewable resources in electrical distribution systems. This work addresses the large-signal stability analysis of a DC-DC bidirectional converter (DBC) connected to a storage device in an islanding MG. This converter is responsible for controlling the balance of power (load demand and generation) under constant power loads (CPLs). In order to control the DC bus voltage through a DBC, we propose a robust sliding mode control (SMC) based on a washout filter. Dynamical systems techniques are exploited to assess the quality of this switching control strategy. In this sense, a bifurcation analysis is performed to study the nonlinear stability of a reduced model of this system. The appearance of different bifurcations when load parameters and control gains are changed is studied in detail. In the specific case of Teixeira Singularity (TS) bifurcation, some experimental results are provided, confirming the mathematical predictions. Both a deeper insight in the dynamic behavior of the controlled system and valuable design criteria are obtained.
Hopf algebras and congruence subgroups
Sommerhauser, Yorck
2007-01-01
We prove that the kernel of the natural action of the modular group on the center of the Drinfel'd double of a semisimple Hopf algebra is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.
Directory of Open Access Journals (Sweden)
He Lin
2016-01-01
Full Text Available This study considers the bifurcation evolutions for a combining spiral gear transmission through parameter domain structure analysis. The system nonlinear vibration equations are created with piecewise backlash and general errors. Gill’s numerical integration algorithm is implemented in calculating the vibration equation sets. Based on cell-mapping method (CMM, two-dimensional dynamic domain planes have been developed and primarily focused on the parameters of backlash, transmission error, mesh frequency and damping ratio, and so forth. Solution demonstrates that Period-doubling bifurcation happens as the mesh frequency increases; moreover nonlinear discontinuous jump breaks the periodic orbit and also turns the periodic state into chaos suddenly. In transmission error planes, three cell groups which are Period-1, Period-4, and Chaos have been observed, and the boundary cells are the sensitive areas to dynamic response. Considering the parameter planes which consist of damping ratio associated with backlash, transmission error, mesh stiffness, and external load, the solution domain structure reveals that the system step into chaos undergoes Period-doubling cascade with Period-2m (m: integer periodic regions. Direct simulations to obtain the bifurcation diagram and largest Lyapunov exponent (LE match satisfactorily with the parameter domain solutions.
Hopf Bifurcation in a Cobweb Model with Discrete Time Delays
Directory of Open Access Journals (Sweden)
Luca Gori
2014-01-01
Full Text Available We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1 if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2 if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle is high enough.
Amplified Hopf bifurcations in feed-forward networks
Rink, B.W.; Sanders, J.A.
2013-01-01
In [B. Rink and J. Sanders, Trans. Amer. Math. Soc., to appear] the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with 2-dimensional cells. Our
Bifurcation analysis of parametrically excited bipolar disorder model
Nana, Laurent
2009-02-01
Bipolar II disorder is characterized by alternating hypomanic and major depressive episode. We model the periodic mood variations of a bipolar II patient with a negatively damped harmonic oscillator. The medications administrated to the patient are modeled via a forcing function that is capable of stabilizing the mood variations and of varying their amplitude. We analyze analytically, using perturbation method, the amplitude and stability of limit cycles and check this analysis with numerical simulations.
Energy Technology Data Exchange (ETDEWEB)
Peters, John W.; Miller, Anne-Frances; Jones, Anne K.; King, Paul W.; Adams, Michael W. W.
2016-04-01
Electron bifurcation is the recently recognized third mechanism of biological energy conservation. It simultaneously couples exergonic and endergonic oxidation-reduction reactions to circumvent thermodynamic barriers and minimize free energy loss. Little is known about the details of how electron bifurcating enzymes function, but specifics are beginning to emerge for several bifurcating enzymes. To date, those characterized contain a collection of redox cofactors including flavins and iron-sulfur clusters. Here we discuss the current understanding of bifurcating enzymes and the mechanistic features required to reversibly partition multiple electrons from a single redox site into exergonic and endergonic electron transfer paths.
Chanda, Sandip; De, Abhinandan
2016-12-01
A social welfare optimization technique has been proposed in this paper with a developed state space based model and bifurcation analysis to offer substantial stability margin even in most inadvertent states of power system networks. The restoration of the power market dynamic price equilibrium has been negotiated in this paper, by forming Jacobian of the sensitivity matrix to regulate the state variables for the standardization of the quality of solution in worst possible contingencies of the network and even with co-option of intermittent renewable energy sources. The model has been tested in IEEE 30 bus system and illustrious particle swarm optimization has assisted the fusion of the proposed model and methodology.
The Wiener-Hopf method in electromagnetics
Zich, Rodolfo; Daniele, Vito
2014-01-01
A function-theoretic method, The Wiener-Hopf technique has found applications in a variety of fields, most notably in analytical studies of diffraction and scattering of waves. The Wiener‐Hopf Method in Electromagnetics is an advanced academic book which provides a rare comprehensive treatment of the Wiener-Hopf method. Using a high level mathematical approach to complex electromagnetics problems and applications, this new book illustrates the wide range of the latest applications, including ...
Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers
Li, Nianqiang; Susanto, H.; Cemlyn, B. R.; Henning, I. D.; Adams, M. J.
2017-07-01
A detailed stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers (VCSELs) is presented. We consider both steady-state and dynamical regimes. In the case of steady-state operation, we carry out a small-signal (asymptotic) stability analysis of the steady-state solutions for a representative set of spin-VCSEL parameters. Compared with full numerical simulation, we show this produces surprisingly accurate results over the whole range of pump ellipticity, and spin-VCSEL bias up to 1.5 times the threshold. We then combine direct numerical integration of the extended spin-flip model and standard continuation technique to examine the underlying dynamics. We find that the spin VCSEL undergoes a period-doubling or quasiperiodic route to chaos as either the pump magnitude or polarization ellipticity is varied. Moreover, we find that different dynamical states can coexist in a finite interval of pump intensity, and observe a hysteresis loop whose width is tunable via the pump polarization. Finally we report a comparison of stability maps in the plane of the pump polarization against pump magnitude produced by categorizing the dynamic output of a spin VCSEL from time-domain simulations, against supercritical bifurcation curves obtained by the standard continuation package auto. This helps us better understand the underlying dynamics of the spin VCSELs.
Automaticity in acute ischemia: Bifurcation analysis of a human ventricular model
Bouchard, Sylvain; Jacquemet, Vincent; Vinet, Alain
2011-01-01
Acute ischemia (restriction in blood supply to part of the heart as a result of myocardial infarction) induces major changes in the electrophysiological properties of the ventricular tissue. Extracellular potassium concentration ([Ko+]) increases in the ischemic zone, leading to an elevation of the resting membrane potential that creates an “injury current” (IS) between the infarcted and the healthy zone. In addition, the lack of oxygen impairs the metabolic activity of the myocytes and decreases ATP production, thereby affecting ATP-sensitive potassium channels (IKatp). Frequent complications of myocardial infarction are tachycardia, fibrillation, and sudden cardiac death, but the mechanisms underlying their initiation are still debated. One hypothesis is that these arrhythmias may be triggered by abnormal automaticity. We investigated the effect of ischemia on myocyte automaticity by performing a comprehensive bifurcation analysis (fixed points, cycles, and their stability) of a human ventricular myocyte model [K. H. W. J. ten Tusscher and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol.AJPHAP0363-613510.1152/ajpheart.00109.2006 291, H1088 (2006)] as a function of three ischemia-relevant parameters [Ko+], IS, and IKatp. In this single-cell model, we found that automatic activity was possible only in the presence of an injury current. Changes in [Ko+] and IKatp significantly altered the bifurcation structure of IS, including the occurrence of early-after depolarization. The results provide a sound basis for studying higher-dimensional tissue structures representing an ischemic heart.
Sase, Takumi; Katori, Yuichi; Komuro, Motomasa; Aihara, Kazuyuki
2017-01-01
We investigate a discrete-time network model composed of excitatory and inhibitory neurons and dynamic synapses with the aim at revealing dynamical properties behind oscillatory phenomena possibly related to brain functions. We use a stochastic neural network model to derive the corresponding macroscopic mean field dynamics, and subsequently analyze the dynamical properties of the network. In addition to slow and fast oscillations arising from excitatory and inhibitory networks, respectively, we show that the interaction between these two networks generates phase-amplitude cross-frequency coupling (CFC), in which multiple different frequency components coexist and the amplitude of the fast oscillation is modulated by the phase of the slow oscillation. Furthermore, we clarify the detailed properties of the oscillatory phenomena by applying the bifurcation analysis to the mean field model, and accordingly show that the intermittent and the continuous CFCs can be characterized by an aperiodic orbit on a closed curve and one on a torus, respectively. These two CFC modes switch depending on the coupling strength from the excitatory to inhibitory networks, via the saddle-node cycle bifurcation of a one-dimensional torus in map (MT1SNC), and may be associated with the function of multi-item representation. We believe that the present model might have potential for studying possible functional roles of phase-amplitude CFC in the cerebral cortex. PMID:28424606
Observer-Pattern Modeling and Slow-Scale Bifurcation Analysis of Two-Stage Boost Inverters
Zhang, Hao; Wan, Xiaojin; Li, Weijie; Ding, Honghui; Yi, Chuanzhi
2017-06-01
This paper deals with modeling and bifurcation analysis of two-stage Boost inverters. Since the effect of the nonlinear interactions between source-stage converter and load-stage inverter causes the “hidden” second-harmonic current at the input of the downstream H-bridge inverter, an observer-pattern modeling method is proposed by removing time variance originating from both fundamental frequency and hidden second harmonics in the derived averaged equations. Based on the proposed observer-pattern model, the underlying mechanism of slow-scale instability behavior is uncovered with the help of eigenvalue analysis method. Then eigenvalue sensitivity analysis is used to select some key system parameters of two-stage Boost inverter, and some behavior boundaries are given to provide some design-oriented information for optimizing the circuit. Finally, these theoretical results are verified by numerical simulations and circuit experiment.
Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz's Growth Functions
Rocha, J. Leonel; Taha, Abdel-Kaddous; Fournier-Prunaret, D.
In this paper, we study the dynamics and bifurcation properties of a three-parameter family of 1D Gompertz's growth functions, which are defined by the population size functions of the Gompertz logistic growth equation. The dynamical behavior is complex leading to a diversified bifurcation structure, leading to the big bang bifurcations of the so-called “box-within-a-box” fractal type. We provide and discuss sufficient conditions for the existence of these bifurcation cascades for 1D Gompertz's growth functions. Moreover, this work concerns the description of some bifurcation properties of a Hénon's map type embedding: a “continuous” embedding of 1D Gompertz's growth functions into a 2D diffeomorphism. More particularly, properties that characterize the big bang bifurcations are considered in relation with this coupling of two population size functions, varying the embedding parameter. The existence of communication areas of crossroad area type or swallowtails are identified for this 2D diffeomorphism.
Imura, Jun-ichi; Ueta, Tetsushi
2015-01-01
This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.
Chung, K. W.; Chan, C. L.; Lee, B. H. K.
2007-01-01
A perturbation-incremental (PI) method is presented for the computation, continuation and bifurcation analysis of limit cycle oscillations (LCO) of a two-degree-of-freedom aeroelastic system containing a freeplay structural nonlinearity. Both stable and unstable LCOs can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Thus, the present method is capable of detecting complex aeroelastic responses such as periodic motion with harmonics, period-doubling (PD), saddle-node bifurcation, Neimark-Sacker bifurcation and the coexistence of limit cycles. Emanating branch from a PD bifurcation can be constructed. This method can also be applied to any piecewise linear systems.
Pseudo-chaotic oscillations in CRISPR-virus coevolution predicted by bifurcation analysis.
Berezovskaya, Faina S; Wolf, Yuri I; Koonin, Eugene V; Karev, Georgy P
2014-07-02
The CRISPR-Cas systems of adaptive antivirus immunity are present in most archaea and many bacteria, and provide resistance to specific viruses or plasmids by inserting fragments of foreign DNA into the host genome and then utilizing transcripts of these spacers to inactivate the cognate foreign genome. The recent development of powerful genome engineering tools on the basis of CRISPR-Cas has sharply increased the interest in the diversity and evolution of these systems. Comparative genomic data indicate that during evolution of prokaryotes CRISPR-Cas loci are lost and acquired via horizontal gene transfer at high rates. Mathematical modeling and initial experimental studies of CRISPR-carrying microbes and viruses reveal complex coevolutionary dynamics. We performed a bifurcation analysis of models of coevolution of viruses and microbial host that possess CRISPR-Cas hereditary adaptive immunity systems. The analyzed Malthusian and logistic models display complex, and in particular, quasi-chaotic oscillation regimes that have not been previously observed experimentally or in agent-based models of the CRISPR-mediated immunity. The key factors for the appearance of the quasi-chaotic oscillations are the non-linear dependence of the host immunity on the virus load and the partitioning of the hosts into the immune and susceptible populations, so that the system consists of three components. Bifurcation analysis of CRISPR-host coevolution model predicts complex regimes including quasi-chaotic oscillations. The quasi-chaotic regimes of virus-host coevolution are likely to be biologically relevant given the evolutionary instability of the CRISPR-Cas loci revealed by comparative genomics. The results of this analysis might have implications beyond the CRISPR-Cas systems, i.e. could describe the behavior of any adaptive immunity system with a heritable component, be it genetic or epigenetic. These predictions are experimentally testable. This manuscript was reviewed by
Application of bifurcation analysis for determining the mechanism of coding of nociceptive signals
Dik, O. E.; Shelykh, T. N.; Plakhova, V. B.; Nozdrachev, A. D.; Podzorova, S. A.; Krylov, B. V.
2015-10-01
The patch clamp method is used for studying the characteristics of slow sodium channels responsible for coding of nociceptive signals. Quantitative estimates of rate constants of transitions of "normal" and pharmacologically modified activation gating mechanisms of these channels are obtained. A mathematical model of the type of Hogdkin-Huxley nociceptive neuron membrane is constructed. Cometic acid, which is a drug substance of a new nonopioid analgesic, is used as a pharmacological agent. The application of bifurcation analysis makes it possible to outline the boundaries of the region in which a periodic impulse activity is generated. This boundary separates the set of values of the model parameter for which periodic pulsation is observed from the values for which such pulsations are absent or damped. The results show that the finest effect of modulation of physical characteristic of a part of a protein molecule and its effective charge suppresses the excitability of the nociceptive neuron membrane and, hence, leads to rapid reduction of pain.
Multi-layer holographic bifurcative neural network system for real-time adaptive EOS data analysis
Liu, Hua-Kuang; Huang, K. S.; Diep, J.
1993-01-01
Optical data processing techniques have the inherent advantage of high data throughout, low weight and low power requirements. These features are particularly desirable for onboard spacecraft in-situ real-time data analysis and data compression applications. the proposed multi-layer optical holographic neural net pattern recognition technique will utilize the nonlinear photorefractive devices for real-time adaptive learning to classify input data content and recognize unexpected features. Information can be stored either in analog or digital form in a nonlinear photofractive device. The recording can be accomplished in time scales ranging from milliseconds to microseconds. When a system consisting of these devices is organized in a multi-layer structure, a feedforward neural net with bifurcating data classification capability is formed. The interdisciplinary research will involve the collaboration with top digital computer architecture experts at the University of Southern California.
Analysis of Blood Flow in a Partially Blocked Bifurcated Blood Vessel
Abdul-Razzak, Hayder; Elkassabgi, Yousri; Punati, Pavan K.; Nasser, Naseer
2009-09-01
Coronary artery disease is a major cause of death in the United States. It is the narrowing of the lumens of the coronary blood vessel by a gradual build-up of fatty material, atheroma, which leads to the heart muscle not receiving enough blood. This my ocardial ischemia can cause angina, a heart attack, heart failure as well as sudden cardiac death [9]. In this project a solid model of bifurcated blood vessel with an asymmetric stenosis is developed using GAMBIT and imported into FLUENT for analysis. In FLUENT, pressure and velocity distributions in the blood vessel are studied under different conditions, where the size and position of the blockage in the blood vessel are varied. The location and size of the blockage in the blood vessel are correlated with the pressures and velocities distributions. Results show that such correlation may be used to predict the size and location of the blockage.
Bifurcation analysis to the Lugiato-Lefever equation in one space dimension
Miyaji, T.; Ohnishi, I.; Tsutsumi, Y.
2010-11-01
We study the stability and bifurcation of steady states for a certain kind of damped driven nonlinear Schrödinger equation with cubic nonlinearity and a detuning term in one space dimension, mathematically in a rigorous sense. It is known by numerical simulations that the system shows lots of coexisting spatially localized structures as a result of subcritical bifurcation. Since the equation does not have a variational structure, unlike the conservative case, we cannot apply a variational method for capturing the ground state. Hence, we analyze the equation from a viewpoint of bifurcation theory. In the case of a finite interval, we prove the fold bifurcation of nontrivial stationary solutions around the codimension two bifurcation point of the trivial equilibrium by exact computation of a fifth-order expansion on a center manifold reduction. In addition, we analyze the steady-state mode interaction and prove the bifurcation of mixed-mode solutions, which will be a germ of localized structures on a finite interval. Finally, we study the corresponding problem on the entire real line by use of spatial dynamics. We obtain a small dissipative soliton bifurcated adequately from the trivial equilibrium.
Bifurcation analysis of a diffusive predator–prey model in spatially heterogeneous environment
Directory of Open Access Journals (Sweden)
Biao Wang
2017-05-01
Full Text Available We investigate positive steady states of a diffusive predator–prey model in spatially heterogeneous environment. In comparison with the spatially homogeneous environment, the dynamics of the predator–prey model of spatial heterogeneity is more complicated. Our studies show that if dispersal rate of the prey is treated as a bifurcation parameter, for some certain ranges of death rate and dispersal rate of the predator, there exist multiply positive steady state solutions bifurcating from semi-trivial steady state of the model in spatially heterogeneous environment, whereas there exists only one positive steady state solution which bifurcates from semi-trivial steady state of the model in homogeneous environment.
Dynamical Analysis of the Hindmarsh-Rose Neuron With Time Delays.
Lakshmanan, S; Lim, C P; Nahavandi, S; Prakash, M; Balasubramaniam, P
2017-08-01
This brief is mainly concerned with a series of dynamical analyses of the Hindmarsh-Rose (HR) neuron with state-dependent time delays. The dynamical analyses focus on stability, Hopf bifurcation, as well as chaos and chaos control. Through the stability and bifurcation analysis, we determine that increasing the external current causes the excitable HR neuron to exhibit periodic or chaotic bursting/spiking behaviors and emit subcritical Hopf bifurcation. Furthermore, by choosing a fixed external current and varying the time delay, the stability of the HR neuron is affected. We analyze the chaotic behaviors of the HR neuron under a fixed external current through time series, bifurcation diagram, Lyapunov exponents, and Lyapunov dimension. We also analyze the synchronization of the chaotic time-delayed HR neuron through nonlinear control. Based on an appropriate Lyapunov-Krasovskii functional with triple integral terms, a nonlinear feedback control scheme is designed to achieve synchronization between the uncontrolled and controlled models. The proposed synchronization criteria are derived in terms of linear matrix inequalities to achieve the global asymptotical stability of the considered error model under the designed control scheme. Finally, numerical simulations pertaining to stability, Hopf bifurcation, periodic, chaotic, and synchronized models are provided to demonstrate the effectiveness of the derived theoretical results.
Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion
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Shaban Aly
2016-01-01
Full Text Available The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008. The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.
Critical points bifurcation analysis of high-ℓ bending dynamics in acetylene
Tyng, Vivian; Kellman, Michael E.
2009-12-01
The bending dynamics of acetylene with pure vibrational angular momentum excitation and quantum number ℓ ≠0 are analyzed through the method of critical points analysis, used previously [V. Tyng and M. E. Kellman, J. Phys. Chem. B 110, 18859 (2006)] for ℓ =0 to find new anharmonic modes born in bifurcations of the low-energy normal modes. Critical points in the reduced phase space are computed for continuously varied bend polyad number Nb=n4+n5 as ℓ =ℓ4+ℓ5 is varied between 0 and 20. It is found that the local L, orthogonal O, precessional P, and counter-rotator CR families persist for all ℓ. In addition, for ℓ ≥8, there is a fifth family of critical points which, unlike the previous families, has no fixed relative phase ("off great circle" OGC). The concept of the minimum energy path in the polyad space is developed. With restriction to ℓ =0 this is the local mode family L. This has an intuitive relation to the minimum energy path or reaction mode for acetylene-vinylidene isomerization. With ℓ ≥0 included as a polyad number, the ℓ =0 minimum energy path forms a troughlike channel in the minimum energy surface in the polyad space, which consists of a complex mosaic of L, O, and OGC critical points. There is a division of the complete set of critical points into layers, the minimum energy surface forming the lowest.
Pereira, R F; de S Pinto, S E; Viana, R L; Lopes, S R; Grebogi, C
2007-06-01
Many chaotic dynamical systems of physical interest present a strong form of nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant set contains periodic orbits possessing different numbers of unstable eigendirections. The onset of UDV is usually related to the loss of transversal stability of an unstable fixed point embedded in the chaotic set. In this paper, we present a new mechanism for the onset of UDV, whereby the period of the unstable orbits losing transversal stability tends to infinity as we approach the onset of UDV. This mechanism is unveiled by means of a periodic orbit analysis of the invariant chaotic attractor for two model dynamical systems with phase spaces of low dimensionality, and seems to depend heavily on the chaotic dynamics in the invariant set. We also described, for these systems, the blowout bifurcation (for which the chaotic set as a whole loses transversal stability) and its relation with the situation where the effects of UDV are the most intense. For the latter point, we found that chaotic trajectories off, but very close to, the invariant set exhibit the same scaling characteristic of the so-called on-off intermittency.
A generic Hopf algebra for quantum statistical mechanics
Energy Technology Data Exchange (ETDEWEB)
Solomon, A I [Physics and Astronomy Department, The Open University, Milton Keynes MK7 6AA (United Kingdom); Duchamp, G H E [Institut Galilee, LIPN, CNRS UMR 7030 99 Av. J-B Clement, F-93430 Villetaneuse (France); Blasiak, P; Horzela, A [H Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Division of Theoretical Physics, ul. Eliasza-Radzikowskiego 152, PL 31-342 Krakow (Poland); Penson, K A, E-mail: a.i.solomon@open.ac.u, E-mail: gduchamp2@free.f, E-mail: pawel.blasiak@ifj.edu.p, E-mail: andrzej.horzela@ifj.edu.p, E-mail: penson@lptl.jussieu.f [Lab. de Phys. Theor. de la Matiere Condensee, University of Paris VI (France)
2010-09-15
In this paper, we present a Hopf algebra description of a bosonic quantum model, using the elementary combinatorial elements of Bell and Stirling numbers. Our objective in doing this is as follows. Recent studies have revealed that perturbative quantum field theory (pQFT) displays an astonishing interplay between analysis (Riemann zeta functions), topology (Knot theory), combinatorial graph theory (Feynman diagrams) and algebra (Hopf structure). Since pQFT is an inherently complicated study, so far not exactly solvable and replete with divergences, the essential simplicity of the relationships between these areas can be somewhat obscured. The intention here is to display some of the above-mentioned structures in the context of a simple bosonic quantum theory, i.e. a quantum theory of non-commuting operators that do not depend on space-time. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs, analogous to the Feynman diagrams of pQFT, which we show possess a Hopf algebra structure. Our approach is based on the quantum canonical partition function for a boson gas.
Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
Directory of Open Access Journals (Sweden)
Reit Marco
2016-06-01
Full Text Available Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.
Directory of Open Access Journals (Sweden)
Vitaly A Selivanov
Full Text Available The mitochondrial electron transport chain transforms energy satisfying cellular demand and generates reactive oxygen species (ROS that act as metabolic signals or destructive factors. Therefore, knowledge of the possible modes and bifurcations of electron transport that affect ROS signaling provides insight into the interrelationship of mitochondrial respiration with cellular metabolism. Here, a bifurcation analysis of a sequence of the electron transport chain models of increasing complexity was used to analyze the contribution of individual components to the modes of respiratory chain behavior. Our algorithm constructed models as large systems of ordinary differential equations describing the time evolution of the distribution of redox states of the respiratory complexes. The most complete model of the respiratory chain and linked metabolic reactions predicted that condensed mitochondria produce more ROS at low succinate concentration and less ROS at high succinate levels than swelled mitochondria. This prediction was validated by measuring ROS production under various swelling conditions. A numerical bifurcation analysis revealed qualitatively different types of multistationary behavior and sustained oscillations in the parameter space near a region that was previously found to describe the behavior of isolated mitochondria. The oscillations in transmembrane potential and ROS generation, observed in living cells were reproduced in the model that includes interaction of respiratory complexes with the reactions of TCA cycle. Whereas multistationarity is an internal characteristic of the respiratory chain, the functional link of respiration with central metabolism creates oscillations, which can be understood as a means of auto-regulation of cell metabolism.
Energy Technology Data Exchange (ETDEWEB)
Erjaee, G H [Mathematics and Physics Department, Qatar University, Doha (Qatar)], E-mail: erjaee@qu.edu.qa
2008-02-15
In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system.
Erjaee, G. H.
2008-02-01
In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system.
Chen, Xiaodong; Zielinski, Rachel; Ghadiali, Samir N
2014-10-01
Although mechanical ventilation is a life-saving therapy for patients with severe lung disorders, the microbubble flows generated during ventilation generate hydrodynamic stresses, including pressure and shear stress gradients, which damage the pulmonary epithelium. In this study, we used computational fluid dynamics to investigate how gravity, inertia, and surface tension influence both microbubble flow patterns in bifurcating airways and the magnitude/distribution of hydrodynamic stresses on the airway wall. Direct interface tracking and finite element techniques were used to simulate bubble propagation in a two-dimensional (2D) liquid-filled bifurcating airway. Computational solutions of the full incompressible Navier-Stokes equation were used to investigate how inertia, gravity, and surface tension forces as characterized by the Reynolds (Re), Bond (Bo), and Capillary (Ca) numbers influence pressure and shear stress gradients at the airway wall. Gravity had a significant impact on flow patterns and hydrodynamic stress magnitudes where Bo > 1 led to dramatic changes in bubble shape and increased pressure and shear stress gradients in the upper daughter airway. Interestingly, increased pressure gradients near the bifurcation point (i.e., carina) were only elevated during asymmetric bubble splitting. Although changes in pressure gradient magnitudes were generally more sensitive to Ca, under large Re conditions, both Re and Ca significantly altered the pressure gradient magnitude. We conclude that inertia, gravity, and surface tension can all have a significant impact on microbubble flow patterns and hydrodynamic stresses in bifurcating airways.
Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model
Thies, Jonas; Wubs, Fred; Dijkstra, Henk 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 (O(10(5))) degrees of freedom such as multi-layer
New features of the software MatCont for bifurcation analysis of dynamical systems.
Dhooge, A.; Govaerts, W.; Kouznetsov, Iouri Aleksandrovitsj; Meijer, Hil Gaétan Ellart; Sautois, B.
2008-01-01
Bifurcation software is an essential tool in the study of dynamical systems. From the beginning (the first packages were written in the 1970's) it was also used in the modelling process, in particular to determine the values of critical parameters. More recently, it is used in a systematic way in
A generalization of Connes-Kreimer Hopf algebra
Byun, Jungyoon
2005-07-01
"Bonsai" Hopf algebras, introduced here, are generalizations of Connes-Kreimer Hopf algebras, which are motivated by Feynman diagrams and renormalization. We show that we can find operad structure on the set of bonsais. We introduce a new differential on these bonsai Hopf algebras, which is inspired by the tree differential. The cohomologies of these are computed here, and the relationship of this differential with the appending operation * of Connes-Kreimer Hopf algebras is investigated.
Homfly Polynomials of Generalized Hopf Links
Morton, Hugh R.; Hadji, Richard J.
2001-01-01
Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish that two natural skein maps have distinct eigenvalues, answering a question raised by Chan, and use this result to calculate the Homfly polynomial of some more general reverse stri...
Coset for Hopf fibration and squashing
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Machiko; Tomizawa, Shinya, E-mail: mhatsuda@post.kek.j, E-mail: tomizawa@post.kek.j [Theory Division, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801 (Japan)
2009-11-21
We provide a simple derivation of metrics for fundamental geometrical deformations such as Hopf fibration, squashing and the Z{sub k} quotient which play essential roles in recent studies on the AdS{sub 4}/CFT{sub 3}. A general metric formula of Hopf fibrations for complex and quaternion cosets is presented. Squashing is given by a similarity transformation which changes the metric preserving the isometric symmetry of the projective space. On the other hand, the Z{sub k} quotient is given as a lens space which changes the topology preserving the 'local' metric.
Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities
Directory of Open Access Journals (Sweden)
Haitao Liao
2013-01-01
Full Text Available In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.
Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential
Goodman, Roy H.
2017-11-01
The nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. The problem is reduced to a finite-dimensional Hamiltonian system by a Galerkin truncation. Families of oscillatory orbits are sought in the neighborhoods of the system's nine branches of standing wave solutions. Normal forms are computed in the neighborhood of these branches' various Hamiltonian Hopf and saddle-node bifurcations, showing how the oscillatory orbits change as a parameter is increased. Numerical experiments show agreement between normal form theory and numerical solutions to the reduced system and NLS/GP near the Hamiltonian Hopf bifurcations and some subtle disagreements near the saddle-node bifurcations due to exponentially small terms in the asymptotics.
Feynman graphs and related Hopf algebras
Energy Technology Data Exchange (ETDEWEB)
Duchamp, G H E [Institut Galilee, LIPN, CNRS UMR 7030 99 Av. J.-B. Clement, F-93430 Villetaneuse (France); Blasiak, P [H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences ul. Eliasza-Radzikowskiego 152, PL 31342 Cracow (Poland); Horzela, A [H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences ul. Eliasza-Radzikowskiego 152, PL 31342 Cracow (Poland); Penson, K A [Laboratoire de Physique Theorique de la Matiere Condensee Universite Pierre et Marie Curie, CNRS UMR 7600 Tour 24 - 2ieme et., 4 pl. Jussieu, F 75252 Paris Cedex 05 (France); Solomon, A I [Laboratoire de Physique Theorique de la Matiere Condensee Universite Pierre et Marie Curie, CNRS UMR 7600 Tour 24 - 2ieme et., 4 pl. Jussieu, F 75252 Paris Cedex 05 (France); Open University, Physics and Astronomy Department Milton Keynes MK7 6AA (United Kingdom)
2006-02-28
In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there is a Hopf Algebra structure associated with this problem which is, in a certain sense, unique.
Zhang, Hao; Ding, Honghui; Yi, Chuanzhi
2017-06-01
This paper deals with the design-oriented analysis of slow-scale bifurcations in single phase DC-AC inverters. Since DC-AC inverter belongs to a class of nonautonomous piecewise systems with periodic equilibrium orbits, the original averaged model has to be translated into an equivalent autonomous one via a virtual rotating coordinate transformation in order to simplify the theoretical analysis. Based on the virtual equivalent model, eigenvalue sensitivity is used to estimate the effect of the important parameters on the system stability. Furthermore, theoretical analysis is performed to identify slow-scale bifurcation behaviors by judging in what way the eigenvalue loci of the Jacobian matrix move under the variation of some important parameters. In particular, the underlying mechanism of the slow-scale unstable phenomenon is uncovered and discussed thoroughly. In addition, some behavior boundaries are given in the parameter space, which are suitable for optimizing the circuit design. Finally, physical experiments are performed to verify the above theoretical results.
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
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Wen-Qing Zhang
2013-01-01
Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.
Oscillatory Stability and Eigenvalue Sensitivity Analysis of A DFIG Wind Turbine System
DEFF Research Database (Denmark)
Yang, Lihui; Xu, Zhao; Østergaard, Jacob
2011-01-01
This paper focuses on modeling and oscillatory stability analysis of a wind turbine with doubly fed induction generator (DFIG). A detailed mathematical model of DFIG wind turbine with vector-control loops is developed, based on which the loci of the system Jacobian's eigenvalues have been analyzed......, showing that, without appropriate controller tuning a Hopf bifurcation can occur in such a system due to various factors, such as wind speed. Subsequently, eigenvalue sensitivity with respect to machine and control parameters is performed to assess their impacts on system stability. Moreover, the Hopf...... bifurcation boundaries of the key parameters are also given. They can be used to guide the tuning of those DFIG parameters to ensure stable operation in practice. The computer simulations are conducted to validate the developed model and to verify the theoretical analysis....
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek
2009-01-01
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.
The geometric Hopf invariant and surgery theory
Crabb, Michael
2017-01-01
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
Bifurcations in the regularized Ericksen bar model
Grinfeld, M.; Lord, G. J. (Gabriel J.)
2007-01-01
We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of M\\"uller's conjecture \\cite{Muller} concerning the symmetry of local minimizers of the associated energy functional and describe in detail the stru...
Design and analysis of a MEMS-based bifurcate-shape piezoelectric energy harvester
Energy Technology Data Exchange (ETDEWEB)
Luo, Yuan; Gan, Ruyi, E-mail: 2471390146@qq.com; Wan, Shalang; Xu, Ruilin; Zhou, Hanxing [Chongqing Municipal Level Key Laboratory of Photoelectronic Information Sensing and Transmitting Technology, Chongqing University of Posts and Telecommunications, 400065, Chongqing, Chongqing Municipality (China)
2016-04-15
This paper presents a novel piezoelectric energy harvester, which is a MEMS-based device. This piezoelectric energy harvester uses a bifurcate-shape. The derivation of the mathematical modeling is based on the Euler-Bernoulli beam theory, and the main mechanical and electrical parameters of this energy harvester are analyzed and simulated. The experiment result shows that the maximum output voltage can achieve 3.3 V under an acceleration of 1 g at 292.11 Hz of frequency, and the output power can be up to 0.155 mW under the load of 0.4 MΩ. The power density is calculated as 496.79 μWmm{sup −3}. Besides that, it is demonstrated efficiently at output power and voltage and adaptively in practical vibration circumstance. This energy harvester could be used for low-power electronic devices.
An Extended Continuation Problem for Bifurcation Analysis in the Presence of Constraints
DEFF Research Database (Denmark)
Dankowicz, Harry; Schilder, Frank
2010-01-01
of the corresponding higher-co-dimension solution manifolds. In particular, the formalism is demonstrated to clearly separate between the essential functionality required of core routines in application-oriented continuation packages, on the one hand; and the functionality provided by auxiliary toolboxes that encode...... classes of continuation problems and user-definitions that narrowly focus on a particular problem implementation, on the other hand. Several examples are chosen to illustrate the formalism and its implementation in the recently developed continuation core package COCO and auxiliary toolboxes, including...... continuation of families of periodic orbits in a hybrid dynamical system with impacts and friction as well as detection and constrained continuation of selected degeneracies characteristic of such systems, such as grazing and switching-sliding bifurcations....
DEFF Research Database (Denmark)
Ramzan, Naveed; Faheem, Muhammad; Gani, Rafiqul
2010-01-01
A packed reactive distillation column producing ethyl tert-butyl ether from tert-butyl alcohol and ethanol was simulated for detection of multiple steady states using Aspen Plus®. A rate-based approach was used to make the simulation model more realistic. A base-case was first developed and fine......-tuned to fit experimental data. Sensitivity analyses were then performed for reboiler duty and distillate molar flow as continuation parameters to trace the respective bifurcation curves in the region of multiplicity. The results show output multiplicity at three distinct steady states at high reboiler duties....... Input multiplicities were detected at high reflux ratios. Temperature and composition profiles of the solution branches were analyzed to identify the stable and desirable steady state. The optimum operating point was determined to be at a reboiler duty of 0.38 kW and a reflux ratio of 5–7. These results...
Bifurcation analysis of a model of the budding yeast cell cycle
Battogtokh, Dorjsuren; Tyson, John J.
2004-09-01
We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable steady states of high or low kinase activity). The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity (two stable oscillatory states), we explore possible effects of extrinsic fluctuations on cell cycle progression.
Bifurcation analysis and phase diagram of a spin-string model with buckled states
Ruiz-Garcia, M.; Bonilla, L. L.; Prados, A.
2017-12-01
We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.
Bifurcation and Nonlinear Dynamic Analysis of Externally Pressurized Double Air Films Bearing System
Directory of Open Access Journals (Sweden)
Cheng-Chi Wang
2014-01-01
Full Text Available This paper studies the chaotic and nonlinear dynamic behaviors of a rigid rotor supported by externally pressurized double air films (EPDAF bearing system. A hybrid numerical method combining the differential transformation method and the finite difference method is used to calculate pressure distribution of EPDAF bearing system and bifurcation phenomenon of rotor center orbits. The results obtained for the orbits of the rotor center are in good agreement with those obtained using the traditional finite difference approach. The results presented summarize the changes which take place in the dynamic behavior of the EPDAF bearing system as the rotor mass and bearing number are increased and therefore provide a useful guideline for the bearing system.
Dynamics of motion of a clot through an arterial bifurcation: a finite element analysis
Abolfazli, Ehsan; Fatouraee, Nasser; Vahidi, Bahman
2014-10-01
Although arterial embolism is important as a major cause of brain infarction, little information is available about the hemodynamic factors which govern the path emboli tend to follow. A method which predicts the trajectory of emboli in carotid arteries would be of a great value in understanding ischemic attack mechanisms and eventually devising hemodynamically optimal techniques for prevention of strokes. In this paper, computational models are presented to investigate the motion of a blood clot in a human carotid artery bifurcation. The governing equations for blood flow are the Navier-Stokes formulations. To achieve large structural movements, the arbitrary Lagrangian-Eulerian formulation (ALE) with an adaptive mesh method was employed for the fluid domain. The problem was solved by simultaneous solution of the fluid and the structure equations. In this paper, the phenomenon was simulated under laminar and Newtonian flow conditions. The measured stress-strain curve obtained from ultrasound elasticity imaging of the thrombus was set to a Sussman-Bathe material model representing embolus material properties. Shear stress magnitudes in the inner wall of the internal carotid artery (ICA) were measured. High magnitudes of wall shear stress (WSS) occurred in the areas in which the embolus and arterial are in contact with each other. Stress distribution in the embolus was also calculated and areas prone to rapture were identified. Effects of embolus size and embolus density on its motion velocity were investigated and it was observed that an increase in either embolus size or density led to a reduction in movement velocity of the embolus. Embolus trajectory and shear stress from a simulation of embolus movement in a three-dimensional model with patient-specific carotid artery bifurcation geometry are also presented.
Hopf-algebra description of noncommutative-spacetime symmetries
Agostini, A; D'Andrea, F; Andrea, Francesco D'
2003-01-01
In the study of certain noncommutative versions of Minkowski spacetime there is still a large ambiguity concerning the characterization of their symmetries. Adopting as our case study the kappaMinkowski noncommutative space-time, on which a large literature is already available, we propose a line of analysis of noncommutative-spacetime symmetries that relies on the introduction of a Weyl map (connecting a given function in the noncommutative Minkowski with a corresponding function in commutative Minkowski) and of a compatible notion of integration in the noncommutative spacetime. We confirm (and we establish more robustly) previous suggestions that the commutative-spacetime notion of Lie-algebra symmetries must be replaced, in the noncommutative-spacetime context, by the one of Hopf-algebra symmetries. We prove that in kappaMinkowski it is possible to construct an action which is invariant under a Poincare-like Hopf algebra of symmetries with 10 generators, in which the noncommutativity length scale has the r...
Rota-Baxter algebras and the Hopf algebra of renormalization
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi-Fard, K.
2006-06-15
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)
Differential geometry on Hopf algebras and quantum groups
Energy Technology Data Exchange (ETDEWEB)
Watts, Paul [Univ. of California, Berkeley, CA (United States)
1994-12-15
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined.
Analysis of a quadratic system obtained from a scalar third order differential equation
Directory of Open Access Journals (Sweden)
Fabio Scalco Dias
2010-11-01
Full Text Available In this article, we study the nonlinear dynamics of a quadratic system in the three dimensional space which can be obtained from a scalar third order differential equation. More precisely, we study the stability and bifurcations which occur in a parameter dependent quadratic system in the three dimensional space. We present an analytical study of codimension one, two and three Hopf bifurcations, generic Bogdanov-Takens and fold-Hopf bifurcations.
Bifurcation analysis for ion acoustic waves in a strongly coupled plasma including trapped electrons
El-Labany, S. K.; El-Taibany, W. F.; Atteya, A.
2018-02-01
The nonlinear ion acoustic wave propagation in a strongly coupled plasma composed of ions and trapped electrons has been investigated. The reductive perturbation method is employed to derive a modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation. To solve this equation in case of dissipative system, the tangent hyperbolic method is used, and a shock wave solution is obtained. Numerical investigations show that, the ion acoustic waves are significantly modified by the effect of polarization force, the trapped electrons and the viscosity coefficients. Applying the bifurcation theory to the dynamical system of the derived mKdV-Burgers equation, the phase portraits of the traveling wave solutions of both of dissipative and non-dissipative systems are analyzed. The present results could be helpful for a better understanding of the waves nonlinear propagation in a strongly coupled plasma, which can be produced by photoionizing laser-cooled and trapped electrons [1], and also in neutron stars or white dwarfs interior.
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...
Dangerous Bifurcations Revisited
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Saha, Arindam; Banerjee, Soumitro; Sushko, Irina; Gardini, Laura
2016-12-01
A dangerous border collision bifurcation has been defined as the dynamical instability that occurs when the basins of attraction of stable fixed points shrink to a set of zero measure as the parameter approaches the bifurcation value from either side. This results in almost all trajectories diverging off to infinity at the bifurcation point, despite the eigenvalues of the fixed points before and after the bifurcation being within the unit circle. In this paper, we show that similar bifurcation phenomena also occur when the stable orbit in question is of a higher periodicity or is chaotic. Accordingly, we propose a generalized definition of dangerous bifurcation suitable for any kind of attracting sets. We report two types of dangerous border collision bifurcations and show that, in addition to the originally reported mechanism typically involving singleton saddle cycles, there exists one more situation where the basin boundary is formed by a repelling closed invariant curve.
Generalized Cole–Hopf transformations for generalized Burgers ...
Indian Academy of Sciences (India)
2015-10-15
Oct 15, 2015 ... A detailed review of the invention of Cole–Hopf transformations for the Burgers equation and all the subsequent works which include generalizations of the Burgers equation and the corresponding developments in Cole–Hopf transformations are documented.
The Leibniz-Hopf algebra and Lyndon words
M. Hazewinkel (Michiel)
1996-01-01
textabstractLet ${cal Z$ denote the free associative algebra ${ol Z langle Z_1 , Z_2 , ldots rangle$ over the integers. This algebra carries a Hopf algebra structure for which the comultiplication is $Z_n mapsto Sigma_{i+j=n Z_i otimes Z_j$. This the noncommutative Leibniz-Hopf algebra. It carries a
Generalized Poincare algebras, Hopf algebras and {kappa}-Minkowski spacetime
Energy Technology Data Exchange (ETDEWEB)
Kovacevic, D., E-mail: domagoj.kovacevic@fer.hr [Faculty of Electrical Engineering and Computing, Unska 3, HR-10000 Zagreb (Croatia); Meljanac, S., E-mail: meljanac@irb.hr [Rudjer Boskovic Institute, Bijenicka c. 54, HR-10002 Zagreb (Croatia); Pachol, A., E-mail: pachol@raunvis.hi.is [Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik (Iceland); Strajn, R., E-mail: rina.strajn@gmail.com [Rudjer Boskovic Institute, Bijenicka c. 54, HR-10002 Zagreb (Croatia)
2012-05-01
We propose a generalized description for the {kappa}-Poincare-Hopf algebra as a symmetry quantum group of underlying {kappa}-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of {kappa}-Minkowski algebra realization. For the given realization of {kappa}-Minkowski spacetime there is a unique {kappa}-Poincare-Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with {kappa}-Poincare algebras which are related to {kappa}-Poincare-Hopf algebra with undeformed Lorentz algebra. Known bases of {kappa}-Poincare-Hopf algebra are obtained as special cases. Also deformation of igl(4) Hopf algebra compatible with the {kappa}-Minkowski spacetime is presented. Some physical applications are briefly discussed.
Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay
Yao, Yu; Zhang, Zhao; Xiang, Wenlong; Yang, Wei; Gao, Fuxiang
2014-01-01
Both vaccination and quarantine strategy are adopted to control the Internet worm propagation. By considering the interaction infection between computers and external removable devices, a worm propagation dynamical system with time delay under quarantine strategy is constructed based on anomaly intrusion detection system (IDS). By regarding the time delay caused by time window of anomaly IDS as the bifurcation parameter, local asymptotic stability at the positive equilibrium and local Hopf bi...
Secondary bifurcation for a nonlocal Allen-Cahn equation
Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji
2017-09-01
This paper studies the Neumann problem of a nonlocal Allen-Cahn equation in an interval. A main result finds a symmetry breaking (secondary) bifurcation point on the bifurcation curve of solutions with odd-symmetry. Our proof is based on a level set analysis for the associated integral map. A method using the complete elliptic integrals proves the uniqueness of secondary bifurcation point. We also show some numerical simulations concerning the global bifurcation structure.
Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed
DEFF Research Database (Denmark)
Matsushita, Hiroshi; Miyata, T.; Christiansen, Lasse Engbo
2002-01-01
The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests...... conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear...
Asymmetric bifurcated halogen bonds.
Novák, Martin; Foroutan-Nejad, Cina; Marek, Radek
2015-03-07
Halogen bonding (XB) is being extensively explored for its potential use in advanced materials and drug design. Despite significant progress in describing this interaction by theoretical and experimental methods, the chemical nature remains somewhat elusive, and it seems to vary with the selected system. In this work we present a detailed DFT analysis of three-center asymmetric halogen bond (XB) formed between dihalogen molecules and variously 4-substituted 1,2-dimethoxybenzene. The energy decomposition, orbital, and electron density analyses suggest that the contribution of electrostatic stabilization is comparable with that of non-electrostatic factors. Both terms increase parallel with increasing negative charge of the electron donor molecule in our model systems. Depending on the orientation of the dihalogen molecules, this bifurcated interaction may be classified as 'σ-hole - lone pair' or 'σ-hole - π' halogen bonds. Arrangement of the XB investigated here deviates significantly from a recent IUPAC definition of XB and, in analogy to the hydrogen bonding, the term bifurcated halogen bond (BXB) seems to be appropriate for this type of interaction.
Nielsen, Kenneth H M; Pociot, Flemming M; Ottesen, Johnny T
2014-09-01
Type 1 diabetes is a disease with serious personal and socioeconomic consequences that has attracted the attention of modellers recently. But as models of this disease tend to be complicated, there has been only limited mathematical analysis to date. Here we address this problem by providing a bifurcation analysis of a previously published mathematical model for the early stages of type 1 diabetes in diabetes-prone NOD mice, which is based on the data available in the literature. We also show positivity and the existence of a family of attracting trapping regions in the positive 5D cone, converging towards a smaller trapping region, which is the intersection over the family. All these trapping regions are compact sets, and thus, practical weak persistence is guaranteed. We conclude our analysis by proposing 4 novel treatment strategies: increasing the phagocytic ability of resting macrophages or activated macrophages, increasing the phagocytic ability of resting and activated macrophages simultaneously and lastly, adding additional macrophages to the site of inflammation. The latter seems counter-intuitive at first glance, but nevertheless it appears to be the most promising, as evidenced by recent results. © The Authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Ray, Rajendra K.; Kumar, Atendra
2017-08-01
In this paper, an incompressible two-dimensional shear flow past a square cylinder problem is investigated numerically using a higher order compact finite difference scheme. Simulations are presented for three sets of Reynolds numbers, 100, 200, and 500, with various shear parameter (K) values ranging from 0.0 to 0.4. The purpose of the present study is to elaborate the influence of shear rate on the vortex shedding phenomenon behind the square cylinder. The results presented here show that the vortex shedding phenomenon strongly depends on Re as well as K. The strength and size of vortices shed behind the cylinder vary as a function of Re and K. When K is larger than a critical value, the vortex shedding phenomenon has completely disappeared depending on the Reynolds number. Apart from the numerical study, a thorough theoretical investigation has been done by using a topology based structural bifurcation analysis for unsteady flow separations from the walls of the cylinder. Through this analysis, we study the exact locations of the bifurcation points associated with secondary and tertiary vortices with appropriate non-dimensional time of occurrence. To the best of our knowledge, this is the first time, a topological aspect based structural bifurcation analysis has been done to understand the vortex shedding phenomenon and flow separation for this problem.
Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation
Directory of Open Access Journals (Sweden)
Chao Liu
2014-01-01
Full Text Available A hybrid SIR vector disease model with incubation is established, where susceptible host population satisfies the logistic equation and the recovered host individuals are commercially harvested. It is utilized to discuss the transmission mechanism of infectious disease and dynamical effect of commercial harvest on population dynamics. Positivity and permanence of solutions are analytically investigated. By choosing economic interest of commercial harvesting as a parameter, dynamical behavior and local stability of model system without time delay are studied. It reveals that there is a phenomenon of singularity induced bifurcation as well as local stability switch around interior equilibrium when economic interest increases through zero. State feedback controllers are designed to stabilize model system around the desired interior equilibria in the case of zero economic interest and positive economic interest, respectively. By analyzing corresponding characteristic equation of model system with time delay, local stability analysis around interior equilibrium is discussed due to variation of time delay. Hopf bifurcation occurs at the critical value of time delay and corresponding limit cycle is also observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied. Numerical simulations are carried out to show consistency with theoretical analysis.
Energy Technology Data Exchange (ETDEWEB)
Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)
2017-04-15
Highlights: • A simplified model with nonlinear void reactivity feedback is studied. • Method of multiple scales for nonlinear analysis and oscillation characteristics. • Second order void reactivity dominates in determining system dynamics. • Opposing signs of linear and quadratic void reactivity enhances global safety. - Abstract: In the present work, the effect of nonlinear void reactivity on the dynamics of a simplified lumped-parameter model for a boiling water reactor (BWR) is investigated. A mathematical model of five differential equations comprising of neutronics and thermal-hydraulics encompassing the nonlinearities associated with both the reactivity feedbacks and the heat transfer process has been used. To this end, we have considered parameters relevant to RBMK for which the void reactivity is known to be nonlinear. A nonlinear analysis of the model exploiting the method of multiple time scales (MMTS) predicts the occurrence of the two types of Hopf bifurcation, namely subcritical and supercritical, leading to the evolution of limit cycles for a range of parameters. Numerical simulations have been performed to verify the analytical results obtained by MMTS. The study shows that the nonlinear reactivity has a significant influence on the system dynamics. A parametric study with varying nominal reactor power and operating conditions in coolant channel has also been performed which shows the effect of change in concerned parameter on the boundary between regions of sub- and super-critical Hopf bifurcations in the space constituted by the two coefficients of reactivities viz. the void and the Doppler coefficient of reactivities. In particular, we find that introduction of a negative quadratic term in the void reactivity feedback significantly increases the supercritical region and dominates in determining the system dynamics.
A versatile class of prototype dynamical systems for complex bifurcation cascades of limit cycles
Sándor, Bulcsú; Gros, Claudius
2015-07-01
A general class of prototype dynamical systems is introduced, which allows to study the generation of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling and homoclinic bifurcations, and transitions to chaos induced by sequences of limit cycle bifurcations. The prototype systems are adaptive, with friction forces f(V(x)) being functionally dependent exclusively on the mechanical potential V(x), characterized in turn by a finite number of local minima. We discuss several low-dimensional systems, with friction forces f(V) which are linear, quadratic or cubic polynomials in the potential V. We point out that the zeros of f(V) regulate both the relative importance of energy uptake and dissipation respectively, serving at the same time as bifurcation parameters, hence allowing for an intuitive interpretation of the overall dynamical behavior. Starting from simple Hopf- and homoclinic bifurcations, complex sequences of limit cycle bifurcations are observed when the energy uptake gains progressively in importance.
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...
Hopf Bifurcation and Delay-Induced Turing Instability in a Diffusive lac Operon Model
Cao, Xin; Song, Yongli; Zhang, Tonghua
In this paper, we investigate the dynamics of a lac operon model with delayed feedback and diffusion effect. If the system is without delay or the delay is small, the positive equilibrium is stable so that there are no spatial patterns formed; while the time delay is large enough the equilibrium becomes unstable so that rich spatiotemporal dynamics may occur. We have found that time delay can not only incur temporal oscillations but also induce imbalance in space. With different initial values, the system may have different spatial patterns, for instance, spirals with one head, four heads, nine heads, and even microspirals.
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Indian Academy of Sciences (India)
School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China; Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, People's Republic of China ...
Effect of pollution on the total factor productivity and the Hopf bifurcation
David Desmarchelier
2013-01-01
In a recent contribution, Empora and Mamuneas (2011) find a positive relation between pollution emissions and the total factor productivity (TFP). In the present paper, we show that this positive effect reduces the effect of pollution on the marginal utility of consumption for which a limit cycle occurs.
El Aroudi, Abdelali
2014-05-01
Recently, nonlinearities have been shown to play an important role in increasing the extracted energy of vibration-based energy harvesting systems. In this paper, we study the dynamical behavior of a piecewise linear (PWL) spring-mass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. Different configurations of the PWL model and their corresponding state-space regions are derived. Then, from this PWL model, extensive numerical simulations are carried out by computing time-domain waveforms, state-space trajectories and frequency responses under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Filippov method, Poincaré map modeling and finite difference method (FDM). The Floquet multipliers are calculated using these three approaches and a good concordance is obtained among them. The performance of the system in terms of the harvested energy is studied by considering both purely harmonic excitation and a noisy vibrational source. A frequency-domain analysis shows that the harvested energy could be larger at low frequencies as compared to an equivalent linear system, in particular, for relatively low excitation intensities. This could be an advantage for potential use of this system in low frequency ambient vibrational-based energy harvesting applications. © 2014 World Scientific Publishing Company.
Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman
2017-12-01
In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.
Ideal relaxation of the Hopf fibration
Smiet, Christopher Berg; Candelaresi, Simon; Bouwmeester, Dirk
2017-07-01
Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.
Bifurcation and instability problems in vortex wakes
DEFF Research Database (Denmark)
Aref, Hassan; Brøns, Morten; Stremler, Mark A.
2007-01-01
A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...... in a periodic strip is considered. The classical results of von Kármán concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued...
Zhioua, M.; El Aroudi, A.; Belghith, S.; Bosque-Moncusí, J. M.; Giral, R.; Al Hosani, K.; Al-Numay, M.
A study of a DC-DC boost converter fed by a photovoltaic (PV) generator and supplying a constant voltage load is presented. The input port of the converter is controlled using fixed frequency pulse width modulation (PWM) based on the loss-free resistor (LFR) concept whose parameter is selected with the aim to force the PV generator to work at its maximum power point. Under this control strategy, it is shown that the system can exhibit complex nonlinear behaviors for certain ranges of parameter values. First, using the nonlinear models of the converter and the PV source, the dynamics of the system are explored in terms of some of its parameters such as the proportional gain of the controller and the output DC bus voltage. To present a comprehensive approach to the overall system behavior under parameter changes, a series of bifurcation diagrams are computed from the circuit-level switched model and from a simplified model both implemented in PSIM© software showing a remarkable agreement. These diagrams show that the first instability that takes place in the system period-1 orbit when a primary parameter is varied is a smooth period-doubling bifurcation and that the nonlinearity of the PV generator is irrelevant for predicting this phenomenon. Different bifurcation scenarios can take place for the resulting period-2 subharmonic regime depending on a secondary bifurcation parameter. The boundary between the desired period-1 orbit and subharmonic oscillation resulting from period-doubling in the parameter space is obtained by calculating the eigenvalues of the monodromy matrix of the simplified model. The results from this model have been validated with time-domain numerical simulation using the circuit-level switched model and also experimentally from a laboratory prototype. This study can help in selecting the parameter values of the circuit in order to delimit the region of period-1 operation of the converter which is of practical interest in PV systems.
Mahdi, Abtahi Seyed; Hossein, Sadati Seyed
2013-09-01
The different methodologies for the study of nonlinear asymmetric Kelvin-type gyrostat satellite consisting of the heteroclinic bifurcation and chaos are investigated in this work. The dynamical model of the gyrostat satellite involves the attitude orientation along with the translational motion in the circular orbit. The mathematical model of the Kelvin-type gyrostat satellite is first derived using the Hamiltonian approach in the Roto-Translatory motion under the gravity gradient perturbations. Since the model of the system is too complex, the coupled equations of motion are reduced using the modified Deprit canonical transformation by the Serret-Andoyer variables in the spin-orbit dynamics. The simulation results demonstrate the heteroclinic bifurcation route to chaos in the Roto-Translatory motion of the gyrostat satellite due to the effects of the orbital motion and the gravity gradient perturbation on the attitude dynamics. According to the numerical solutions, the intersection of the stable and unstable manifolds in the heteroclinic orbits around the saddle point lead to the occurrence of the heteroclinic bifurcation and chaotic responses in the perturbed system. Chaos behaviour in the system is also analyzed using the phase portrait trajectories, Poincare' section, and the time history responses. Moreover, the Lyapunov exponent criterion verifies numerically the existence of chaos in the Roto-Translatory motion of the system.
Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points
Jia, Bing; Gu, Huaguang
2017-06-01
Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Köpf, Michael H
2014-10-07
© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.
Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in R4
Directory of Open Access Journals (Sweden)
Tiansi Zhang
2015-01-01
Full Text Available We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field in R4. We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of homoclinic-doubling bifurcation in the case 1+α>β>ν. Meanwhile, after reparametrizing the parameter, a periodic-doubling bifurcation appears and may be close to a saddle-node bifurcation, if the parameter is varied. These scenarios correspond to the occurrence of chaos. Based on our analysis, bifurcation diagrams of these bifurcations are depicted.
Quantum walks, deformed relativity and Hopf algebra symmetries.
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-28
We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. © 2016 The Author(s).
Izhikevich, Eugene M.
1998-04-01
The cusp bifurcation provides one of the simplest routes leading to bistability and hysteresis in neuron dynamics. We show that weakly connected networks of neurons near cusp bifurcations that satisfy a certain adaptation condition have quite interesting and complicated dynamics. First, we prove that any such network can be transformed into a canonical model by an appropriate continuous change of variables. Then we show that the canonical model can operate as a multiple attractor neural network or as a globally asymptotically stable neural network depending on the choice of parameters.
Bifurcations in two coupled Rössler systems
DEFF Research Database (Denmark)
Rasmussen, J; Mosekilde, Erik; Reick, C.
1996-01-01
The paper presents a detailed bifurcation analysis of two symmetrically coupled Rössler systems. The symmetry in the coupling does not allow any one direction to become preferred, and the coupled system is therefore an example of a dissipative system that cannot be considered as effectively one......-dimensional. The results are presented in terms of one- and two-parmeter bifurcation diagrams. A particularly interesting finding is the replacement of some of the period-doubling bifurcations by torus bifurcations. By virtue of this replacement, instead of a Feigenbaum transition to chaos a transition via torus...
Huang, Dongmei; Xu, Wei
2017-11-01
In this paper, the combination of the cubic nonlinearity and time delay is proposed to improve the performance of a piecewise-smooth (PWS) system with negative stiffness. Dynamical properties, feedback control performance and symmetry-breaking bifurcation are mainly considered for a PWS system with negative stiffness under nonlinear position and velocity feedback control. For the free vibration system, the homoclinic-like orbits are firstly derived. Then, the amplitude-frequency response of the controlled system is obtained analytically in aspect of the Lindstedt-Poincaré method and the method of multiple scales, which is also verified through the numerical results. In this regard, a softening-type behavior, which directly leads to the multi-valued responses, is illustrated over the negative position feedback. Especially, the five-valued responses in which three branches of them are stable are found. And complex multi-valued characteristics are also observed in the force-amplitude responses. Furthermore, for explaining the effectiveness of feedback control, the equivalent damping and stiffness are also introduced. Sensitivity of the system response to the feedback gain and time delay is comprehensively considered and interesting dynamical properties are found. Relatively, from the perspective of suppressing the maximum amplitude and controlling the resonance stability, the selection of the feedback parameters is discussed. Finally, the symmetry-breaking bifurcation and chaotic motion are considered.
Oya, T.; Yanagimoto, J.; Ito, K.; Uemura, G.; Mori, N.
2017-09-01
In metal forming, progress in material models is required to construct a general and reliable fracture prediction framework because of the increased use of advanced materials and growing demand for higher prediction accuracy. In this study, a fracture prediction framework based on bifurcation theory is constructed. A novel material model based on the stress-rate dependence related to a non-associated flow rule is presented. This model is based on a non-associated flow rule with an arbitrary higher-order yield function and a plastic potential function for any anisotropic material. This formulation is combined with the stress-rate-dependent plastic constitutive equation, which is known as the Ito-Goya rule, to construct a generalized plastic constitutive model in which non-normality and non-associativity are reasonably included. Then, by adopting three-dimensional bifurcation theory, which is referred to the 3D theory, a new theoretical framework for fracture prediction based on the initiation of a shear band is constructed. Using virtual material data, a numerical simulation is carried out to produce a fracture limit diagram, which is used to investigate the characteristics of the proposed methodology.
Yi, Guo-Sheng; Wang, Jiang; Wei, Xi-Le; Tsang, Kai-Ming; Chan, Wai-Lok; Deng, Bin; Han, Chun-Xiao
2014-06-01
To investigate how extracellular electric field modulates neuron activity, a reduced two-compartment neuron model in the presence of electric field is introduced in this study. Depending on neuronal geometric and internal coupling parameters, the behaviors of the model have been studied extensively. The neuron model can exist in quiescent state or repetitive spiking state in response to electric field stimulus. Negative electric field mainly acts as inhibitory stimulus to the neuron, positive weak electric field could modulate spiking frequency and spike timing when the neuron is already active, and positive electric fields with sufficient intensity could directly trigger neuronal spiking in the absence of other stimulations. By bifurcation analysis, it is observed that there is saddle-node on invariant circle bifurcation, supercritical Hopf bifurcation and subcritical Hopf bifurcation appearing in the obtained two parameter bifurcation diagrams. The bifurcation structures and electric field thresholds for triggering neuron firing are determined by neuronal geometric and coupling parameters. The model predicts that the neurons with a nonsymmetric morphology between soma and dendrite, are more sensitive to electric field stimulus than those with the spherical structure. These findings suggest that neuronal geometric features play a crucial role in electric field effects on the polarization of neuronal compartments. Moreover, by determining the electric field threshold of our biophysical model, we could accurately distinguish between suprathreshold and subthreshold electric fields. Our study highlights the effects of extracellular electric field on neuronal activity from the biophysical modeling point of view. These insights into the dynamical mechanism of electric field may contribute to the investigation and development of electromagnetic therapies, and the model in our study could be further extended to a neuronal network in which the effects of electric fields on
Bifurcation of Hyperbolic Planforms
Chossat, Pascal; Faye, Grégory; Faugeras, Olivier
2011-02-01
Motivated by a model for the perception of textures by the visual cortex in primates, we analyze the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperbolic plane {D} (Poincaré disc). We make use of the concept of a periodic lattice in {D} to further reduce the problem to one on a compact Riemann surface {D}/\\varGamma, where Γ is a cocompact, torsion-free Fuchsian group. The knowledge of the symmetry group of this surface allows us to use the machinery of equivariant bifurcation theory. Solutions which generically bifurcate are called "H-planforms", by analogy with the "planforms" introduced for pattern formation in Euclidean space. This concept is applied to the case of an octagonal periodic pattern, where we are able to classify all possible H-planforms satisfying the hypotheses of the Equivariant Branching Lemma. These patterns are, however, not straightforward to compute, even numerically, and in the last section we describe a method for computation illustrated with a selection of images of octagonal H-planforms.
Analysis of a Mathematical Model of Emerging Infectious Disease Leading to Amphibian Decline
Directory of Open Access Journals (Sweden)
Muhammad Dur-e-Ahmad
2014-01-01
Full Text Available We formulate a three-dimensional deterministic model of amphibian larvae population to investigate the cause of extinction due to the infectious disease. The larvae population of the model is subdivided into two classes, exposed and unexposed, depending on their vulnerability to disease. Reproduction ratio ℛ0 has been calculated and we have shown that if ℛ01, we discussed different scenarios under which an infected population can survive or be eliminated using stability and persistence analysis. Finally, we also used Hopf bifurcation analysis to study the stability of periodic solutions.
Universal Baxterization for Z-graded Hopf algebras
Energy Technology Data Exchange (ETDEWEB)
Dancer, K A; Finch, P E; Isaac, P S [Centre for Mathematical Physics, School of Physical Sciences, University of Queensland, Brisbane 4072 (Australia)
2007-12-14
We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with Z-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group U{sub q}[sl(2)]. (fast track communication)
Probe Knots and Hopf Insulators with Ultracold Atoms
Deng, Dong-Ling; Wang, Sheng-Tao; Sun, Kai; Duan, L.-M.
2018-01-01
Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing. D.L.D., S.T.W. and L.M.D. are supported by the ARL, the IARPA LogiQ program, and the AFOSR MURI program, and supported by Tsinghua University for their visits. K.S. acknowledges the support from NSF under Grant No. PHY1402971. D.L.D. is also supported by JQI-NSF-PFC and LPS-MPO-CMTC at the final stage of this paper.
Euler potentials for the MHD Kamchatnov-Hopf soliton solution
Semenov, VS; Korovinski, DB; Biernat, HK
2002-01-01
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf
Generalized Cole–Hopf transformations for generalized Burgers ...
Indian Academy of Sciences (India)
2015-10-15
Oct 15, 2015 ... Generalized Cole–Hopf transformations for generalized. Burgers equations. B MAYIL VAGANAN∗ and E EMILY PRIYA. Department of Applied Mathematics and Statistics, School of Mathematics,. Madurai Kamaraj University, Madurai 625 021, India. ∗Corresponding author. E-mail: vkbmv66@gmail.com.
The planar algebra of a semisimple and cosemisimple Hopf algebra
Indian Academy of Sciences (India)
To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with non-zero modulus and of depth two. This association is shown to yield a bijection ...
Bifurcation of learning and structure formation in neuronal maps
DEFF Research Database (Denmark)
Marschler, Christian; Faust-Ellsässer, Carmen; Starke, Jens
2014-01-01
to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable...
Marković, V. M.; Čupić, Ž.; Ivanović, A.; Kolar-Anić, Lj.
2011-12-01
Stoichiometric network analysis (SNA) represents a powerful mathematical tool for stability analysis of complex stoichiometric networks. Recently, the important improvement of the method has been made, according to which instability relations can be entirely expressed via reaction rates, instead of thus far used, in general case undefined, current rates. Such an improved SNA methodology was applied to the determination of exact instability conditions of the extended model of the hypothalamic-pituitary-adrenal (HPA) axis, a neuroendocrinological system, whose hormone concentrations exert complex oscillatory evolution. For emergence of oscillations, the Hopf bifurcation condition was utilized. Instability relations predicted by SNA showed good correlation with numerical simulation data of the HPA axis model.
Response and bifurcation of rotor with squeeze film damper on elastic support
Energy Technology Data Exchange (ETDEWEB)
Qin Weiyang; Zhang Jinfu; Ren Xingmin [Department of Engineering Mechanics, Northwestern Polytechnical University, Xi' an 710072 (China)
2009-01-15
This paper investigates the nonlinear response and bifurcation of rotor with Squeezed Film Damper (SFD) supported on elastic foundation. The motion equations are derived. To analyze the bifurcation of nonlinear response of SFD rotor, the Floquet Multipliers is obtained by solving the perturbation equations with numerical method. For computing Floquet Multipliers, a novel method is presented in this paper, which can begin integration at the stable solution. Simulation results are given in two figures. One figure, which consists of eight subfigures, gives the effect of rotating speed on the response of SFD damper supported on elastic foundation: with increasing rotating speed, the nonlinear response evolves from quasi-period to period, then jumps between different periods, and finally returns to quasi-period; the corresponding bifurcations are saddle-node bifurcation and secondary Hopf bifurcation. The second figure, which consists of six subfigures, shows that: the support stiffness has large influence on the response of bearings and film force in SFD; large support stiffness can lead to oil whirl in SFD.
Critical bifurcation surfaces of 3D discrete dynamics
Directory of Open Access Journals (Sweden)
Michael Sonis
2000-01-01
Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators
Farkhooi, Farzad
2015-01-01
We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of inter-event density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework, can readily be extended to the analysis of systems with more state variables. To exhibit this, we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate stability of this system and we show it undergoes a super-critical Hopf bifurcation to collective synchronization.
Computation of focal values and stability analysis of 4-dimensional systems
Directory of Open Access Journals (Sweden)
Bo Sang
2015-08-01
Full Text Available This article presents a recursive formula for computing the n-th singular point values of a class of 4-dimensional autonomous systems, and establishes the algebraic equivalence between focal values and singular point values. The formula is linear and then avoids complicated integrating operations, therefore the calculation can be carried out by computer algebra system such as Maple. As an application of the formula, bifurcation analysis is made for a quadratic system with a Hopf equilibrium, which can have three small limit cycles around an equilibrium point. The theory and methodology developed in this paper can be used for higher-dimensional systems.
Control of Fold Bifurcation Application on Chemostat around Critical Dilution Rate
DEFF Research Database (Denmark)
Pedersen, Kurt; Jørgensen, Sten Bay
1999-01-01
Based on a bifurcation analysis of a process it is possible to point out where there might be operational problems due to change of stability of the process. One such change is investigated, Fold bifurcations. This type of bifurcation is associated with hysteresis/multiple steady states, which co...
Doi, Hiroshi; Maehara, Akiko; Mintz, Gary S; Dani, Lokesh; Leon, Martin B; Grube, Eberhard
2009-11-01
We used intravascular ultrasound (IVUS) to assess the efficacy of the Cappella Sideguard stent system for treating coronary bifurcation lesions. Treatment of bifurcation lesions is associated with restenosis at the side branch (SB) ostium, presumably due to inadequate coverage or stent-vessel wall malapposition. To address these limitations, the Sideguard stent was developed. It includes a balloon-deployed, self-expanding, thin-strut, low-stress, nitinol bare metal stent with anatomic funnel-shaped flaring at the SB ostium. Of 25 patients enrolled in the Sideguard I First-In-Man study, complete serial (after intervention and 6-month follow-up) IVUS images were available in 11 patients. All patients were treated with (1) predilation of the SB, (2) Sideguard stenting in the SB, (3) Cypher stenting in the main vessel, and (4) kissing balloon inflations. The Sideguard stent area at the SB carina increased from 3.9 +/- 1.2 to 4.6 +/- 1.1 mm(2) (p = 0.04), resulting in no change in lumen area (3.9 +/- 1.3 vs 4.0 +/- 1.3 mm(2), p = 0.77) despite an intimal hyperplasia (IH) area of 0.6 +/- 0.7 mm(2). Six patients had minimal IH; the increase in stent area translated into an increase in lumen area of 0.4 +/- 0.6 mm(2); 5 patients had relatively more IH (1.3 +/- 0.4 mm(2)), but the increase in stent area of 1.3 +/- 0.3 mm(2) compensated for the IH, resulting in no lumen decrease. In contrast, the main vessel stent area at the carina did not change (5.9 +/- 1.1 vs 6.0 +/- 1.2 mm(2), p = 0.35). In conclusion, serial IVUS analyses of the self-expanding bare metal Sideguard stent indicate preserved SB ostial lumen dimensions at follow-up due to additional increases in stent area that more than compensated for IH.
Bifurcations and chaos of time delay Lorenz system with dimension 2n+1
Mahmoud, Gamal M.; Arafa, Ayman A.; Mahmoud, Emad E.
2017-11-01
The aim of this paper is to introduce a generalized form of the Lorenz system with time delay. Instead of considering each state variable of the Lorenz system belonging to R, the paper considers two of them belonging to Rn. Hence the Lorenz system has (2 n+1) dimension. This system appears in several applied sciences such as engineering, physics and networks. The stability of the trivial and nontrivial fixed points and the existence of Hopf bifurcations are studied analytically. Using the normal form theory and center manifold argument, the direction and the stability of the bifurcating periodic solutions are determined. Finally, numerical simulations are calculated to confirm our theoretical results. The paper concludes that the dynamics of this system are rich. Additionally, the values of the delay parameter at which chaotic and hyperchaotic solutions exist for different values of n using Lyapunov exponents and Kolmogorov-Sinai entropy are calculated numerically.
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
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Kazuki Hasebe
2010-09-01
Full Text Available This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and their mutual relations. The Hopf maps of division algebras provide a prototype relation between monopoles and fuzzy spheres. Generalization of complex numbers to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an interesting hierarchical structure made of ''compounds'' of lower dimensional spheres. We give a physical interpretation for such particular structure of fuzzy spheres by utilizing Landau models in generic even dimensions. With Grassmann algebra, we also introduce a graded version of the Hopf map, and discuss its relation to fuzzy supersphere in context of supersymmetric Landau model.
Zhang, Wei-Ya; Li, Yong-Li; Chang, Xiao-Yong; Wang, Nan
2013-09-01
In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system (FESS) with a permanent magnet (PM) brushless direct-current (DC) motor (BLDCM) is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments.
Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics
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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.
On the bifurcations of a rigid rotor response in squeeze-film dampers
Inayat-Hussain, J. I.; Kanki, H.; Mureithi, N. W.
2003-03-01
The effectiveness of squeeze-film dampers in controlling vibrations in rotating machinery may be limited by the nonlinear interactions between large rotor imbalance forces with fluid-film forces induced by dampers operating in cavitated conditions. From a practical point of view, the occurrence of nonsynchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the rotor, which in turn may rapidly induce fatigue failure. The bifurcations in the response of a rigid rotor supported by cavitated squeeze-film dampers resulting from such interactions are presented in this paper. The effects of design and operating parameters, namely the bearing parameter (/B), gravity parameter (/W), spring parameter (/S) and unbalance parameter (/U), on the bifurcations of the rotor response are investigated. Spring parameter (/S) values between 0 and 1 are considered. A spring parameter value of /S=0 represents the special case of dampers without centering springs. With the exception of the case /S=1, jump phenomena appeared to be a common bifurcation that occurred at certain combinations of /B, /W and /U irrespective of the value of /S. Period-doubling and secondary Hopf bifurcations which occurred for low values of /S (=0.5. For very low stiffness values (/Sfilm forces in cavitated dampers, occurring in industrial rotating machinery, cannot be de-emphasized.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
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Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators.
Farkhooi, Farzad; van Vreeswijk, Carl
2015-07-17
We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of the interevent density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework can readily be extended to the analysis of systems with more state variables and provides a population density treatment to evolve them in their thermodynamical limits. To demonstrate this we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate its stability and numerically study the nonequilibrium behavior of the system after the bifurcation. We show that this system undergoes a supercritical Hopf bifurcation to collective synchronization.
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...
International Workshop "Groups, Rings, Lie and Hopf Algebras"
2003-01-01
The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.
Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra
van den Hijligenberg, N.W.; van den Hijligenberg, N.; Martini, Ruud
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebrastructure of U(g).
Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra
van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of
Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra
N.W. van den Hijligenberg; R. Martini
1995-01-01
textabstractWe discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra
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 in two-dimensional reversible maps
Post, T.; Capel, H.W.; Quispel, G.R.W.; van der Weele, J.P.
1990-01-01
We give a treatment of the non-resonant bifurcations involving asymmetric fixed points with Jacobian J≠1 in reversible mappings of the plane. These bifurcations include the saddle-node bifurcation not in the neighbourhood of a fixed point with J≠1, as well as the so-called transcritical bifurcations
Numerical Analysis of General Trends in Single-Phase Natural Circulation in a 2D-Annular Loop
Directory of Open Access Journals (Sweden)
Gilles Desrayaud
2008-01-01
Full Text Available The aim of this paper is to address fluid flow behavior of natural circulation in a 2D-annular loop filled with water. A two-dimensional, numerical analysis of natural convection in a 2D-annular closed-loop thermosyphon has been performed for various radius ratios from 1.2 to 2.0, the loop being heated at a constant flux over the bottom half and cooled at a constant temperature over the top half. It has been numerically shown that natural convection in a 2D-annular closed-loop thermosyphon is capable of showing pseudoconductive regime at pitchfork bifurcation, stationary convective regimes without and with recirculating regions occurring at the entrance of the exchangers, oscillatory convection at Hopf bifurcation and Lorenz-like chaotic flow. The complexity of the dynamic properties experimentally encountered in toroidal or rectangular loops is thus also found here.
Bifurcations at the dawn of Modern Science
Coullet, Pierre
2012-11-01
In this article we review two classical bifurcation problems: the instability of an axisymmetric floating body studied by Archimedes, 2300 years ago and the multiplicity of images observed in curved mirrors, a problem which has been solved by Alhazen in the 11th century. We will first introduce these problems in trying to keep some of the flavor of the original analysis and then, we will show how they can be reduced to a question of extremal distances studied by Apollonius.
Subcritical, nontypical and period-doubling bifurcations of a delta wing in a low speed wind tunnel
Korbahti, Banu; Kagambage, Emile; Andrianne, Thomas; Abdul Razak, Norizham; Dimitriadis, Grigorios
2011-04-01
Limit Cycle Oscillations (LCOs) involving Delta wings are an important area of research in modern aeroelasticity. Such phenomena can be the result of geometric or aerodynamic nonlinearity. In this paper, a flexible half-span Delta wing is tested in a low speed wind tunnel in order to investigate its dynamic response. The wing is designed to be more flexible than the models used in previous research on the subject in order to expand the airspeed range in which LCOs occur. The experiments reveal that this wing features a very rich bifurcation behavior. Three types of bifurcation are observed for the first time for such an aeroelastic system: subcritical bifurcations, period-doubling/period-halving and nontypical bifurcations. They give rise to a great variety of LCOs, even at very low angles of attack. The LCOs resulting from the nontypical bifurcation display Hopf-type behavior, i.e. having fundamental frequencies equal to one of the linear modal frequencies. All of the other LCOs have fundamental frequencies that are unrelated to the underlying linear system modes.
Bifurcation Adds Flavor to Basketball
Min, Byeong June
2016-01-01
We report an emergence of bifurcation in basketball, a single-particle system governed by Newtonian mechanics. When shooting the basketball, the obvious control parameters are the launch speed and the launch angle. We propose to use the three-dimensional velocity phase-space volume associated with the given launch parameters to quantify the difficulty of the shooting. The optimal launch angle that maximizes the associated phase-space volume undergoes a bifurcation as the launch speed is increased, if the shooter is farther than a critical distance away from the hoop. Thus, the bifurcation makes it very important to control the launch speed accurately. If the air resistance is removed, the bifurcation disappears and the phase-space volume distribution becomes dispersionless and shrinks in magnitude.
Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael; Grundeken, Maik; Généreux, Philippe; Popma, Jeffrey; Costa, Ricardo; Stankovic, Goran; Tu, Shengxian; Reiber, Johan H. C.; Aben, Jean-Paul; Lassen, Jens Flensted; Louvard, Yves; Lansky, Alexandra; Serruys, Patrick W.
2017-01-01
Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary
DEFF Research Database (Denmark)
Nielsen, Kenneth Hagde Mandrup; Ottesen, Johnny T.; Pociot, Flemming
2014-01-01
Type 1 diabetes is a disease with serious personal and socioeconomic consequences that has attracted the attention of modellers recently. But as models of this disease tend to be complicated, there has been only limited mathematical analysis to date. Here we address this problem by providing a bi...
Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family.
Garcia Costas, Amaya M; Poudel, Saroj; Miller, Anne-Frances; Schut, Gerrit J; Ledbetter, Rhesa N; Fixen, Kathryn R; Seefeldt, Lance C; Adams, Michael W W; Harwood, Caroline S; Boyd, Eric S; Peters, John W
2017-11-01
energy conservation. Bifurcating enzymes couple thermodynamically unfavorable reactions with thermodynamically favorable reactions in an overall spontaneous process. Here we show that the electron-transferring flavoprotein (Etf) enzyme family exhibits far greater diversity than previously recognized, and we provide a phylogenetic analysis that clearly delineates bifurcating versus nonbifurcating members of this family. Structural modeling of proteins within these groups reveals key differences between the bifurcating and nonbifurcating Etfs. Copyright © 2017 American Society for Microbiology.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
Energy Technology Data Exchange (ETDEWEB)
Vasilevskaya, Tatiana M., E-mail: t_vasilevs@mail.ru [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation); Sementsov, Dmitriy I.; Shutyi, Anatoliy M. [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation)
2012-09-15
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: Black-Right-Pointing-Pointer An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. Black-Right-Pointing-Pointer Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. Black-Right-Pointing-Pointer Both regular and chaotic precession modes are realized within bifurcation resonance range. Black-Right-Pointing-Pointer Appearance of dynamic bistability is typical for bifurcation resonance.
Bifurcation of Lane Change and Control on Highway for Tractor-Semitrailer under Rainy Weather
Directory of Open Access Journals (Sweden)
Tao Peng
2017-01-01
Full Text Available A new method is proposed for analyzing the nonlinear dynamics and stability in lane changes on highways for tractor-semitrailer under rainy weather. Unlike most of the literature associated with a simulated linear dynamic model for tractor-semitrailers steady steering on dry road, a verified 5DOF mechanical model with nonlinear tire based on vehicle test was used in the lane change simulation on low adhesion coefficient road. According to Jacobian matrix eigenvalues of the vehicle model, bifurcations of steady steering and sinusoidal steering on highways under rainy weather were investigated using a numerical method. Furthermore, based on feedback linearization theory, taking the tractor yaw rate and joint angle as control objects, a feedback linearization controller combined with AFS and DYC was established. The numerical simulation results reveal that Hopf bifurcations are identified in steady and sinusoidal steering conditions, which translate into an oscillatory behavior leading to instability. And simulations of urgent step and single-lane change in high velocity show that the designed controller has good effects on eliminating bifurcations and improving lateral stability of tractor-semitrailer, during lane changing on highway under rainy weather. It is a valuable reference for safety design of tractor-semitrailers to improve the traffic safety with driver-vehicle-road closed-loop system.
Inverse Problem In Optical Tomography Using Diffusion Approximation and Its Hopf-Cole Transformation
Directory of Open Access Journals (Sweden)
Taufiquar R. Khan
2003-12-01
Full Text Available In this paper, we derive the Hopf-Cole transformation to the diffusion approximation. We find the analytic solution to the one dimensional diffusion approximation and its Hopf-Cole transformation for a homogenous constant background medium. We demonstrate that for a homogenous constant background medium in one dimension, the Hopf-Cole transformation improves the stability of the inverse problem. We also derive a Green's function scaling of the higher dimensional diffusion approximation for an inhomogeneous background medium and discuss a two step reconstruction algorithm.
Quantitative angiography methods for bifurcation lesions
DEFF Research Database (Denmark)
Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael
2017-01-01
Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary...... angiography (QCA) methods for the evaluation of bifurcation lesions have been subject to extensive research. Single-vessel QCA has been shown to be inaccurate for the assessment of bifurcation lesion dimensions. For this reason, dedicated bifurcation software has been developed and validated. These software...
From Quantum Mechanics to Quantum Field Theory: The Hopf route
Energy Technology Data Exchange (ETDEWEB)
Solomon, A I [Physics and Astronomy Department, Open University, Milton Keynes MK7 6AA (United Kingdom); Duchamp, G H E [Institut Galilee, LIPN, CNRS UMR 7030 99 Av. J.-B. Clement, F-93430 Villetaneuse (France); Blasiak, P; Horzela, A [H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Division of Theoretical Physics, ul. Eliasza-Radzikowskiego 152, PL 31-342 Krakow (Poland); Penson, K A, E-mail: a.i.solomon@open.ac.uk, E-mail: gduchamp2@free.fr, E-mail: pawel.blasiak@ifj.edu.pl, E-mail: andrzej.horzela@ifj.edu.pl, E-mail: penson@lptl.jussieu.fr [Lab.de Phys.Theor. de la Matiere Condensee, University of Paris VI (France)
2011-03-01
We show that the combinatorial numbers known as Bell numbers are generic in quantum physics. This is because they arise in the procedure known as Normal ordering of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, inter alia. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the exponential generating function of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.
Fredholm theory for Wiener-Hopf plus Hankel operators
Bogveradze, Giorgi
2008-01-01
Na presente tese consideramos combinações algébricas de operadores de Wiener-Hopf e de Hankel com diferentes classes de símbolos de Fourier. Nomeadamente, foram considerados símbolos matriciais na classe de elementos quase periódicos, semi-quase periódicos, quase periódicos por troços e certas funções matriciais sectoriais. Adicionalmente, foi dedicada atenção também aos operadores de Toeplitz mais Hankel com símbolos quase periódicos por troços e com símbolos escalares poss...
Quasi-Hopf twistors for elliptic quantum groups
Jimbo, M; Odake, S; Shiraishi, J
1997-01-01
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al., Felder). Fronsdal made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebra U_q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universal R matrix of U_q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Fronsdal's findings. This construction entails that, for generic values of the deformation parameters, representation theory for U_q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebra A_{q,p}(^sl_2).
Two-Tone Suppression and Combination Tone Generation as Computations Performed by the Hopf Cochlea
Stoop, R.; Kern, A.
2004-12-01
Recent evidence suggests that the compressive nonlinearity responsible for the extreme dynamic range of the mammalian cochlea is implemented in the form of Hopf amplifiers. Whereas Helmholtz's original concept of the cochlea was that of a frequency analyzer, Hopf amplifiers can be stimulated not only by one, but also by neighboring frequencies. To reduce the resulting computational overhead, the mammalian cochlea is aided by two-tone suppression. We show that the laws governing two-tone suppression and the generation of combination tones naturally emerge from the Hopf-cochlea concept. Thus the Hopf concept of the cochlea reproduces not only local properties like the correct frequency response, but additionally accounts for more complex hearing phenomena that may be related to auditory signal computation.
Critical Points and Bifurcations of the Three-Dimensional Onsager Model for Liquid Crystals
Vollmer, Michaela A. C.
2017-11-01
We study the bifurcation diagram of the Onsager free-energy functional for liquid crystals with orientation parameter on the sphere. In particular, we concentrate on the bifurcations from the isotropic solution for a general class of two-body interaction potentials including the Onsager kernel. Reformulating the problem as a non-linear eigenvalue problem for the kernel operator, we prove that spherical harmonics are the corresponding eigenfunctions and we present a direct relationship between the coefficients of the Taylor expansion of this class of interaction potentials and their eigenvalues. We find explicit expressions for all bifurcation points corresponding to bifurcations from the isotropic state of the Onsager free-energy functional equipped with the Onsager interaction potential. A substantial amount of our analysis is based on the use of spherical harmonics and a special algorithm for computing expansions of products of spherical harmonics in terms of spherical harmonics is presented. Using a Lyapunov-Schmidt reduction, we derive a bifurcation equation depending on five state variables. The dimension of this state space is further reduced to two dimensions by using the rotational symmetry of the problem and the invariant theory of groups. On the basis of these results, we show that the first bifurcation from the isotropic state of the Onsager interaction potential is a transcritical bifurcation and that the corresponding solution is uniaxial. In addition, we prove some global properties of the bifurcation diagram such as the fact that the trivial solution is the unique local minimiser if the bifurcation parameter is high, that it is not a local minimiser if the bifurcation parameter is small, the boundedness of all equilibria of the functional and that the bifurcation branches are either unbounded or that they meet another bifurcation branch.
Global Bifurcation of a Novel Computer Virus Propagation Model
Ren, Jianguo; Xu, Yonghong; Liu, Jiming
2014-01-01
In a recent paper by J. Ren et al. (2012), a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bif...
Advance elements of optoisolation circuits nonlinearity applications in engineering
Aluf, Ofer
2017-01-01
This book on advanced optoisolation circuits for nonlinearity applications in engineering addresses two separate engineering and scientific areas, and presents advanced analysis methods for optoisolation circuits that cover a broad range of engineering applications. The book analyzes optoisolation circuits as linear and nonlinear dynamical systems and their limit cycles, bifurcation, and limit cycle stability by using Floquet theory. Further, it discusses a broad range of bifurcations related to optoisolation systems: cusp-catastrophe, Bautin bifurcation, Andronov-Hopf bifurcation, Bogdanov-Takens (BT) bifurcation, fold Hopf bifurcation, Hopf-Hopf bifurcation, Torus bifurcation (Neimark-Sacker bifurcation), and Saddle-loop or Homoclinic bifurcation. Floquet theory helps as to analyze advance optoisolation systems. Floquet theory is the study of the stability of linear periodic systems in continuous time. Another way to describe Floquet theory, it is the study of linear systems of differential equations with p...
A codimension two bifurcation in a railway bogie system
DEFF Research Database (Denmark)
Zhang, Tingting; True, Hans; Dai, Huanyun
2017-01-01
In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness (Formula pr...
High-resolution mapping of bifurcations in nonlinear biochemical circuits
Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.
2016-08-01
Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.
Bifurcation-free design method of pulse energy converter controllers
Energy Technology Data Exchange (ETDEWEB)
Kolokolov, Yury [Institute of Applied Mathematics, Informatics and Control, Yugra State University, 16 Chekhova str., Khanty-Mansiysk 628012 (Russian Federation); Ustinov, Pavel [Department of Design and Technology of Electronic and Computer Systems, Orel State Technical University, 29 Naugorskoye Shosse, Orel 302020 (Russian Federation); CReSTIC, Universite de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, Reims Cedex 2, 51687 (France)], E-mail: pavel-ustinov@yandex.ru; Essounbouli, Najib; Hamzaoui, Abdelaziz [CReSTIC, Universite de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, Reims Cedex 2, 51687 (France)
2009-12-15
In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current-direct current (DC-DC) buck converter with an input electromagnetic interference filter.
Global bifurcations in a piecewise-smooth Cournot duopoly game
Energy Technology Data Exchange (ETDEWEB)
Tramontana, Fabio, E-mail: f.tramontana@univpm.i [Universita degli Studi di Urbino, Department of Economics and Quantitative Methods, Via Saffi 42, 61029 Urbino (Italy); Gardini, Laura, E-mail: laura.gardini@uniurb.i [Universita degli Studi di Urbino, Department of Economics and Quantitative Methods, Via Saffi 42, 61029 Urbino (Italy); Puu, Toenu [CERUM, Umea University, SE-90187 Umea (Sweden)
2010-12-15
The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu . The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Sacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.
[Intracranial carotid artery bifurcation aneurysms].
Vega-Basulto, S D; Montejo-Montejo, J
Intracranial carotid artery bifurcation aneurysms are infrequent but its clinical behavior, high risk of bleeding and complex anatomic relationships of the sac permit to consider these lesions as a challenge cases. 497 patients harboring intracranial aneurysms were operated on at Manuel Ascunce Domenech Hospital, Camagüey, Cuba between January 1982 to august 2001. We utilized microsurgical procedures, optical magnification, specialized neuroanesthesia and Intensive Care Unit postoperatory following. All patients were evaluated clinically with World Federation Neurological Surgeon Scale and Glasgow Outcome Scale. There were 16 patients with intracranial carotid artery bifurcation aneurysms (3.2 %). 12 patients were under 40 years and 50% were between 16 and 30 years old. All patients present intracranial bleeding. There was 87.5% of total or partial recuperation. There was one death only. Postoperative deficit were observed at 44% but 31% disappeared three month later. Intracranial carotid artery bifurcation aneurysms are complex anatomoclinical lesions. Clinically, we observed high tendency to bleed and multiplicity. Anatomically, these sacs have complex arterial relationship that difficult dissection and clipping. They have frequent postoperative morbidity. Multiple or bilateral aneurysmal sacs will be clipped by one surgical procedure.
Xu, Yunan; Chen, Xinguang; Yu, Bin; Joseph, Verlin; Stanton, Bonita
2017-09-22
This study tested the complex relationship among the perceived benefit from and cost of condom use, self-efficacy and condom use among adolescents as a nonlinear dynamic process. Participants were 12th graders in public Bahamian high schools who reported having had sex and frequency of condom use. Results revealed that the perceived benefit and perceived cost as asymmetry variables were significantly associated with condom use (p < 0.001) after controlling for covariates. The association was bifurcated by the variable self-efficacy (p < 0.001). Furthermore, the cusp model was better than linear and logistic regression models in predicting the dynamic changes in condom use behavior, judged by the AIC and BIC, and R(2) criteria. These results suggest that adolescent condom use may follow a nonlinear rather than linear dynamic process. Emphasizing bifurcation variables such as self-efficacy that promote sudden change could be essential to strengthen current evidence-based intervention programs in encouraging condom use. Copyright © 2017. Published by Elsevier Ltd.
A simple SIS epidemic model with a backward bifurcation.
van den Driessche, P; Watmough, J
2000-06-01
It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria.
Bifurcation characteristics and safe basin of MSMA microgripper subjected to stochastic excitation
Directory of Open Access Journals (Sweden)
Z. W. Zhu
2015-02-01
Full Text Available A kind of magnetic shape memory alloy (MSMA microgripper is proposed in this paper, and its nonlinear dynamic characteristics are studied when the stochastic perturbation is considered. Nonlinear differential items are introduced to explain the hysteretic phenomena of MSMA, and the constructive relationships among strain, stress, and magnetic field intensity are obtained by the partial least-square regression method. The nonlinear dynamic model of a MSMA microgripper subjected to in-plane stochastic excitation is developed. The stationary probability density function of the system’s response is obtained, the transition sets of the system are determined, and the conditions of stochastic bifurcation are obtained. The homoclinic and heteroclinic orbits of the system are given, and the boundary of the system’s safe basin is obtained by stochastic Melnikov integral method. The numerical and experimental results show that the system’s motion depends on its parameters, and stochastic Hopf bifurcation appears in the variation of the parameters; the area of the safe basin decreases with the increase of the stochastic excitation, and the boundary of the safe basin becomes fractal. The results of this paper are helpful for the application of MSMA microgripper in engineering fields.
Bifurcations and chaos in convection taking non-Fourier heat-flux
Layek, G. C.; Pati, N. C.
2017-11-01
In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.
La factorización de una transformada de Fourier en el método de Wiener-Hopf
Directory of Open Access Journals (Sweden)
José Rosales-Ortega
2009-02-01
Full Text Available Using the Wiener-Hopf method, we factorize the Fourier Transform of the kernel of a singular integral equation as the product of two functions: one holomorphic in the upper semiplan and the other holomophic in the lower semiplan. Keywords: function product, Fourier transform, Wiener-Hopf method.
Wiener-Hopf Design of the Two-Degree-of-Freedom Controller for the Standard Model
Energy Technology Data Exchange (ETDEWEB)
Cho, Yong Seok [Konyang University (Korea); Choi, Goon Ho [Han Mi Technique research institute (Korea); Park, Ki Heon [Sungkyunkwan University (Korea)
2000-03-01
In this paper, Wiener-Hopf design of the two-degree-of-freedom(2DOF) controller configuration is treated for the standard plant model. It is shown that the 2DOF structure makes it possible to treat the design of feedback properties and reference tracking problem separately. Wiener-Hopf factorization technique is used to obtain the optimal controller which minimizes a given quadratic cost index. The class of all stabilizing controllers that yield finite cost index is also characterized An illustrative example is given for the step reference tracking problem which can not be treated by the conventional H{sub 2} controller formula. (author). 10 refs., 3 figs.
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow
Energy Technology Data Exchange (ETDEWEB)
Smith, L. D., E-mail: lachlan.smith@monash.edu [Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800 (Australia); CSIRO Mineral Resources, Clayton, Victoria 3800 (Australia); Rudman, M. [Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800 (Australia); Lester, D. R. [School of Civil, Environmental and Chemical Engineering, RMIT University, Melbourne, Victoria 3000 (Australia); Metcalfe, G. [CSIRO Manufacturing, Highett, Victoria 3190 (Australia); Department of Mechanical and Product Design Engineering, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia); School of Mathematical Sciences, Monash University, Clayton, Victoria 3800 (Australia)
2016-05-15
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.
Bifurcations in dissipative fermionic dynamics
Napolitani, Paolo; Colonna, Maria; Di Prima, Mariangela
2014-05-01
The Boltzmann-Langevin One-Body model (BLOB), is a novel one-body transport approach, based on the solution of the Boltzmann-Langevin equation in three dimensions; it is used to handle large-amplitude phase-space fluctuations and has a broad applicability for dissipative fermionic dynamics. We study the occurrence of bifurcations in the dynamical trajectories describing heavy-ion collisions at Fermi energies. The model, applied to dilute systems formed in such collisions, reveals to be closer to the observation than previous attempts to include a Langevin term in Boltzmann theories. The onset of bifurcations and bimodal behaviour in dynamical trajectories, determines the fragment-formation mechanism. In particular, in the proximity of a threshold, fluctuations between two energetically favourable mechanisms stand out, so that when evolving from the same entrance channel, a variety of exit channels is accessible. This description gives quantitative indications about two threshold situations which characterise heavy-ion collisions at Fermi energies. First, the fusion-to-multifragmentation threshold in central collisions, where the system either reverts to a compact shape, or splits into several pieces of similar sizes. Second, the transition from binary mechanisms to neck fragmentation (in general, ternary channels), in peripheral collisions.
Kolokolov, Yury; Monovskaya, Anna
The paper completes the cycle of the research devoted to the development of the experimental bifurcation analysis (not computer simulations) in order to answer the following questions: whether qualitative changes occur in the dynamics of local climate systems in a centennial timescale?; how to analyze such qualitative changes with daily resolution for local and regional space-scales?; how to establish one-to-one daily correspondence between the dynamics evolution and economic consequences for productions? To answer the questions, the unconventional conceptual model to describe the local climate dynamics was proposed and verified in the previous parts. That model (HDS-model) originates from the hysteresis regulator with double synchronization and has a variable structure due to competition between the amplitude quantization and the time quantization. The main advantage of the HDS-model is connected with the possibility to describe “internally” (on the basis of the self-regulation) the specific causal effects observed in the dynamics of local climate systems instead of “external” description of three states of the hysteresis behavior of climate systems (upper, lower and transient states). As a result, the evolution of the local climate dynamics is based on the bifurcation diagrams built by processing the data of meteorological observations, where the strange effects of the essential interannual daily variability of annual temperature variation are taken into account and explained. It opens the novel possibilities to analyze the local climate dynamics taking into account the observed resultant of all internal and external influences on each local climate system. In particular, the paper presents the viewpoint on how to estimate economic damages caused by climate-related hazards through the bifurcation analysis. That viewpoint includes the following ideas: practically each local climate system is characterized by its own time pattern of the natural qualitative
Race-ethnic variation in carotid bifurcation geometry.
Koch, Sebastian; Nelson, Donoffa; Rundek, Tatjana; Mandrekar, Jay; Rabinstein, Alejandro
2009-01-01
Disturbances in local blood flow influenced by arterial geometry contribute to atherogenesis. Carotid bifurcation hemodynamics depend on the relative sizes of the common carotid artery (CCA), internal carotid artery (ICA), and external carotid artery (ECA), which vary considerably among individuals. The prevalence of carotid bifurcation atherosclerosis differs among race-ethnic groups and is generally lower in African Americans despite a more adverse vascular risk factor profile. We here examine whether there are race-ethnic differences in carotid bifurcation anatomy. The diameters of the CCA, carotid bulb, ICA, and ECA were measured from consecutive cerebral angiograms of African American, white, and Caribbean Hispanic patients. The bulb/CCA, ICA/CCA, ECA/CCA, ECA/ICA, and total cross-sectional outflow/inflow ratio ([ICA(2) + ECA(2)]/CCA(2)) were calculated. The final analysis included 272 bifurcations of which 103 were among white, 87 Hispanic, and 82 African American patients. The mean age of the population was 59.8 +/- 15.8 years and 148 (54.4%) were men. African Americans had a lower ICA/CCA ratio (P ECA ratio (P ECA/CCA ratio (P groups. We found significant differences in the relative sizes of the ICA, ECA, and CCA among race-ethnic groups. African Americans had a proportionally smaller ICA and larger ECA in comparison with whites and Caribbean Hispanics.
Crisis bifurcations in plane Poiseuille flow.
Zammert, Stefan; Eckhardt, Bruno
2015-04-01
Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.
Voltage stability, bifurcation parameters and continuation methods
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F.L. [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction.
Wang, Haixia; Wang, Qingyun; Lu, Qishao; Zheng, Yanhong
2013-04-01
The properties of equilibria and phase synchronization involving burst synchronization and spike synchronization of two electrically coupled HR neurons are studied in this paper. The findings reveal that in the non-delayed system the existence of equilibria can be turned into intersection of two odd functions, and two types of equilibria with symmetry and non-symmetry can be found. With the stability and bifurcation analysis, the bifurcations of equilibria are investigated. For the delayed system, the equilibria remain unchanged. However, the Hopf bifurcation point is drastically affected by time delay. For the phase synchronization, we focus on the synchronization transition from burst synchronization to spike synchronization in the non-delayed system and the effect of coupling strength and time delay on spike synchronization in delayed system. In addition, corresponding firing rhythms and spike synchronized regions are obtained in the two parameters plane. The results allow us to better understand the properties of equilibria, multi-time-scale properties of synchronization and temporal encoding scheme in neuronal systems.
Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity
Directory of Open Access Journals (Sweden)
Antonio Olivas Martinez
2009-01-01
Full Text Available We consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition.
Deformations of constant mean curvature surfaces preserving symmetries and the Hopf differential
DEFF Research Database (Denmark)
Brander, David; Dorfmeister, Josef
2015-01-01
We define certain deformations between minimal and non-minimal constant mean curvature (CMC) surfaces in Euclidean space E3 which preserve the Hopf differential. We prove that, given a CMC H surface f, either minimal or not, and a fixed basepoint z0 on this surface, there is a naturally defined...
The Hopf algebra of (q)multiple polylogarithms with non-positive arguments
Ebrahimi-Fard, Kurusch; Manchon, Dominique; Singer, Johannes
2015-01-01
We consider multiple polylogarithms in a single variable at non-positive integers. Defining a connected graded Hopf algebra, we apply Connes' and Kreimer's algebraic Birkhoff decomposition to renormalize multiple polylogarithms at non-positive integer arguments, which satisfy the shuffle relation. The q-analogue of this result is as well presented, and compared to the classical case.
WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS
Directory of Open Access Journals (Sweden)
Mr. Vladimir A. Smagin
2016-12-01
Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.
Semiclassical catastrophe theory of simple bifurcations
Magner, A. G.; Arita, K.
2017-10-01
The Fedoriuk-Maslov catastrophe theory of caustics and turning points is extended to solve the bifurcation problems by the improved stationary phase method (ISPM). The trace formulas for the radial power-law (RPL) potentials are presented by the ISPM based on the second- and third-order expansion of the classical action near the stationary point. A considerable enhancement of contributions of the two orbits (pair consisting of the parent and newborn orbits) at their bifurcation is shown. The ISPM trace formula is proposed for a simple bifurcation scenario of Hamiltonian systems with continuous symmetries, where the contributions of the bifurcating parent orbits vanish upon approaching the bifurcation point due to the reduction of the end-point manifold. This occurs since the contribution of the parent orbits is included in the term corresponding to the family of the newborn daughter orbits. Taking this feature into account, the ISPM level densities calculated for the RPL potential model are shown to be in good agreement with the quantum results at the bifurcations and asymptotically far from the bifurcation points.
Attractivity and bifurcation for nonautonomous dynamical systems
Rasmussen, Martin
2007-01-01
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
Bifurcation study of blood flow control in the kidney
Ford Versypt, Ashlee N.; Makrides, Elizabeth; Arciero, Julia C.; Ellwein, Laura; Layton, Anita T.
2016-01-01
Renal blood flow is maintained within a narrow window by a set of intrinsic autoregulatory mechanisms. Here, a mathematical model of renal hemodynamics control in the rat kidney is used to understand the interactions between two major renal autoregulatory mechanisms: the myogenic response and tubuloglomerular feedback. A bifurcation analysis of the model equations is performed to assess the effects of the delay and sensitivity of the feedback system and the time constants governing the response of vessel diameter and smooth muscle tone. The results of the bifurcation analysis are verified using numerical simulations of the full nonlinear model. Both the analytical and numerical results predict the generation of limit cycle oscillations under certain physiologically relevant conditions, as observed in vivo. PMID:25747903
Bifurcation for non linear ordinary differential equations with singular perturbation
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Safia Acher Spitalier
2016-10-01
Full Text Available We study a family of singularly perturbed ODEs with one parameter and compare their solutions to the ones of the corresponding reduced equations. The interesting characteristic here is that the reduced equations have more than one solution for a given set of initial conditions. Then we consider how those solutions are organized for different values of the parameter. The bifurcation associated to this situation is studied using a minimal set of tools from non standard analysis.
Bifurcating optical pattern recognition in photorefractive crystals
Liu, Hua-Kuang
1993-01-01
A concept of bifurcating optical pattern rocognizer (BIOPAR) is described and demonstrated experimentally, using barium titanate crystal. When an input is applied to BIOPAR, the output may be directed to two ports.
Bifurcations of mixed-mode oscillations in a stellate cell model
Wechselberger, Martin; Weckesser, Warren
2009-08-01
Experimental recordings of the membrane potential of stellate cells within the entorhinal cortex show a transition from subthreshold oscillations (STOs) via mixed-mode oscillations (MMOs) to relaxation oscillations under increased injection of depolarizing current. Acker et al. introduced a 7D conductance based model which reproduces many features of the oscillatory patterns observed in these experiments. For the first time, we present a comprehensive bifurcation analysis of this model by using the software package AUTO. In particular, we calculate the stable MMO branches within the bifurcation diagram of this model, as well as other MMO patterns which are unstable. We then use geometric singular perturbation theory to demonstrate how the bifurcations are governed by a 3D reduced model introduced by Rotstein et al. We extend their analysis to explain all observed MMO patterns within the bifurcation diagram. A key role in this bifurcation analysis is played by a novel homoclinic bifurcation structure connecting to a saddle equilibrium on the unstable branch of the corresponding critical manifold. This type of homoclinic connection is possible due to canards of folded node (folded saddle-node) type.
Uniform semiclassical approximations for umbilic bifurcation catastrophes
Main, J
1998-01-01
Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from the standard representations of the elementary catastrophes and to directly relate the uniform solutions to classical periodic orbit parameters. The method is simple even for ungeneric bifurcations with corank 2 such as the umbilic catastrophes. We demonstrate the technique on a hyperbolic umbilic in the diamagnetic Kepler problem.
Experimental bifurcations and chaos in a modified self-sustained macro electromechanical system
Kitio Kwuimy, C. A.; Nana, B.; Woafo, P.
2010-07-01
A class of self-sustained Macro ElectroMechanical (MaEMS) Systems is made up of a Rayleigh-Duffing oscillator actuating a mechanical arm through a magnetic coupling. In this paper, to avoid experimental constraints, an audio amplifier is added to the device. Quenching phenomenon, bifurcation and chaos are predicted and shown to occur in a device of this class of MaEMS. Especially by using linear stability analysis, the condition for the quenching phenomenon is derived. Chaos and bifurcation are predicted using Lyapunov exponent and bifurcation diagram. A prototype of device is designed and fabricated. Experimental results for this device that are consistent with results from theoretical investigations are presented and convincingly show quenching phenomenon, bifurcation and chaos.
Optimal response to non-equilibrium disturbances under truncated Burgers-Hopf dynamics
Thalabard, Simon; Turkington, Bruce
2017-04-01
We model and compute the average response of truncated Burgers-Hopf dynamics to finite perturbations away from the Gibbs equipartition energy spectrum using a dynamical optimization framework recently conceptualized in a series of papers. Non-equilibrium averages are there approximated in terms of geodesic paths in probability space that ‘best-fit’ the Liouvillean dynamics over a family of quasi-equilibrium trial densities. By recasting the geodesic principle as an optimal control problem, we solve numerically for the non-equilibrium responses using an augmented Lagrangian, non-linear conjugate gradient descent method. For moderate perturbations, we find an excellent agreement between the optimal predictions and the direct numerical simulations of the truncated Burgers-Hopf dynamics. In this near-equilibrium regime, we argue that the optimal response theory provides an approximate yet predictive counterpart to fluctuation-dissipation identities.
A note on sub-Riemannian structures associated with complex Hopf fibrations
Li, Chengbo; Zhan, Huaying
2013-03-01
Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf fibration naturally appear in quantum mechanics. We study the curvature maps for such a sub-Riemannian structure and express them using the Riemannian curvature tensor of the Fubini-Study metric of the complex projective space and the curvature form of the Hopf fibration. We also estimate the number of conjugate points of a sub-Riemannian extremal in terms of the bounds of the sectional curvature and the curvature form. It presents a typical example for the study of curvature maps and comparison theorems for a general corank 1 sub-Riemannian structure with symmetries done by C. Li and I. Zelenko (2011) in [2].
Re-Entrant Hexagons and Locked Turing-Hopf Fronts in the CIMA Reaction
DEFF Research Database (Denmark)
Mosekilde, Erik; Larsen, F.; Dewel, G.
1998-01-01
Aspects of the mode-interaction and pattern-selection processes in far-from-equilibrium chemical reaction-diffusion systems are studied through numerical simulation of the Lengyel-Epstein Model. The competition between Hopf oscillations and Turing stripes is investigated by following the propagat...... the propagation of a front connecting the two modes. In certain parameter regimes, mode-locking is found to occur....
A nonlinear deformed su(2) algebra with a two-colour quasitriangular Hopf structure
Bonatsos, Dennis; Kolokotronis, P; Ludu, A; Quesne, C
1996-01-01
Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J_0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as ${\\cal A}^+_q(1)$. This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su_q(2) and ${\\cal A}^+_q(1)$, is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su_q(2) is car...
Bifurcation kinetics of drug uptake by Gram-negative bacteria.
Westfall, David A; Krishnamoorthy, Ganesh; Wolloscheck, David; Sarkar, Rupa; Zgurskaya, Helen I; Rybenkov, Valentin V
2017-01-01
Cell envelopes of many bacteria consist of two membranes studded with efflux transporters. Such organization protects bacteria from the environment and gives rise to multidrug resistance. We report a kinetic model that accurately describes the permeation properties of this system. The model predicts complex non-linear patterns of drug uptake complete with a bifurcation, which recapitulate the known experimental anomalies. We introduce two kinetic parameters, the efflux and barrier constants, which replace those of Michaelis and Menten for trans-envelope transport. Both compound permeation and efflux display transitions, which delineate regimes of efficient and inefficient efflux. The first transition is related to saturation of the transporter by the compound and the second one behaves as a bifurcation and involves saturation of the outer membrane barrier. The bifurcation was experimentally observed in live bacteria. We further found that active efflux of a drug can be orders of magnitude faster than its diffusion into a cell and that the efficacy of a drug depends both on its transport properties and therapeutic potency. This analysis reveals novel physical principles in the behavior of the cellular envelope, creates a framework for quantification of small molecule permeation into bacteria, and should invigorate structure-activity studies of novel antibiotics.
Estimating the stochastic bifurcation structure of cellular networks.
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Carl Song
2010-03-01
Full Text Available High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. Since cellular networks are inherently noisy, we generalize the traditional bifurcation diagram of deterministic systems theory to stochastic dynamical systems. We demonstrate how statistical methods for density estimation, in particular, mixture density and conditional mixture density estimators, can be employed to establish empirical bifurcation diagrams describing the bistable genetic switch network controlling galactose utilization in yeast Saccharomyces cerevisiae. These approaches allow us to make novel qualitative and quantitative observations about the switching behavior of the galactose network, and provide a framework that might be useful to extract information needed for the development of quantitative network models.
Patient-specific computer modelling of coronary bifurcation stenting: the John Doe programme.
Mortier, Peter; Wentzel, Jolanda J; De Santis, Gianluca; Chiastra, Claudio; Migliavacca, Francesco; De Beule, Matthieu; Louvard, Yves; Dubini, Gabriele
2015-01-01
John Doe, an 81-year-old patient with a significant distal left main (LM) stenosis, was treated using a provisional stenting approach. As part of an European Bifurcation Club (EBC) project, the complete stenting procedure was repeated using computational modelling. First, a tailored three-dimensional (3D) reconstruction of the bifurcation anatomy was created by fusion of multislice computed tomography (CT) imaging and intravascular ultrasound. Second, finite element analysis was employed to deploy and post-dilate the stent virtually within the generated patient-specific anatomical bifurcation model. Finally, blood flow was modelled using computational fluid dynamics. This proof-of-concept study demonstrated the feasibility of such patient-specific simulations for bifurcation stenting and has provided unique insights into the bifurcation anatomy, the technical aspects of LM bifurcation stenting, and the positive impact of adequate post-dilatation on blood flow patterns. Potential clinical applications such as virtual trials and preoperative planning seem feasible but require a thorough clinical validation of the predictive power of these computer simulations.
Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect
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Wenjie Hu
2018-01-01
Full Text Available The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear.
The dynamo bifurcation in rotating spherical shells
Morin, Vincent; 10.1142/S021797920906378X
2010-01-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transit......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...
Symmetric/asymmetric bifurcation behaviours of a bogie system
DEFF Research Database (Denmark)
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue
2013-01-01
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel–rail contact relation are investigated in detail by the ‘resultant bifurcation diagram’ method with slo...
Codimension 2 Bifurcations of Iterated Maps
Meijer, H.G.E.
2006-01-01
This thesis investigates some properties of discrete-time dynamical systems, generated by iterated maps. In particular we study local bifurcations where two parameters are essential to describe the dynamical properties of the system near a fixed point or a cycle. There are 11 such cases. Knowledge
Percutaneous coronary intervention for coronary bifurcation disease
DEFF Research Database (Denmark)
Lassen, Jens Flensted; Holm, Niels Ramsing; Banning, Adrian
2016-01-01
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...
Bifurcation of self-folded polygonal bilayers
Abdullah, Arif M.; Braun, Paul V.; Hsia, K. Jimmy
2017-09-01
Motivated by the self-assembly of natural systems, researchers have investigated the stimulus-responsive curving of thin-shell structures, which is also known as self-folding. Self-folding strategies not only offer possibilities to realize complicated shapes but also promise actuation at small length scales. Biaxial mismatch strain driven self-folding bilayers demonstrate bifurcation of equilibrium shapes (from quasi-axisymmetric doubly curved to approximately singly curved) during their stimulus-responsive morphing behavior. Being a structurally instable, bifurcation could be used to tune the self-folding behavior, and hence, a detailed understanding of this phenomenon is appealing from both fundamental and practical perspectives. In this work, we investigated the bifurcation behavior of self-folding bilayer polygons. For the mechanistic understanding, we developed finite element models of planar bilayers (consisting of a stimulus-responsive and a passive layer of material) that transform into 3D curved configurations. Our experiments with cross-linked Polydimethylsiloxane samples that change shapes in organic solvents confirmed our model predictions. Finally, we explored a design scheme to generate gripper-like architectures by avoiding the bifurcation of stimulus-responsive bilayers. Our research contributes to the broad field of self-assembly as the findings could motivate functional devices across multiple disciplines such as robotics, artificial muscles, therapeutic cargos, and reconfigurable biomedical devices.
Climate bifurcation during the last deglaciation?
Lenton, T.M.; Livina, V.N.; Dakos, V.; Scheffer, M.
2012-01-01
There were two abrupt warming events during the last deglaciation, at the start of the Bolling-Allerod 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
Solvability of an Integral Equation of Volterra-Wiener-Hopf Type
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Nurgali K. Ashirbayev
2014-01-01
Full Text Available The paper presents results concerning the solvability of a nonlinear integral equation of Volterra-Stieltjes type. We show that under some assumptions that equation has a continuous and bounded solution defined on the interval 0,∞ and having a finite limit at infinity. As a special case of the mentioned integral equation we obtain an integral equation of Volterra-Wiener-Hopf type. That fact enables us to formulate convenient and handy conditions ensuring the solvability of the equation in question in the class of functions defined and continuous on the interval 0,∞ and having finite limits at infinity.
Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity
Baldomá Barraca, Inmaculada; Castejón i Company, Oriol; Martínez-Seara Alonso, M. Teresa
2013-01-01
In this paper we prove the breakdown of a heteroclinic connection in the analytic versal unfoldings of the generic Hopf-zero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order if one performs the normal form around the origin, therefore it is a phenomenon “beyond all orders”. In this paper we provide a formula for the distance between the corresponding stable and unstable one-dimensional manifolds which is given by an exponentially s...
Red'kov, V. M.
2011-01-01
In the work some relations between three techniques, Hopf's bundle, Kustaanheimo-Stiefel's bundle, 3-space with spinor structure have been examined. The spinor space is viewed as a real space that is minimally (twice as much) extended in comparison with an ordinary vector 3-space: at this instead of 2\\pi-rotation now only 4\\pi-rotation is taken to be the identity transformation in the geometrical space. With respect to a given P-orientation of an initial unextended manyfold, vector or pseudov...
Cole-Hopf-like transformation for Schroedinger equations containing complex nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Kaniadakis, G.; Scarfone, A.M. [Dipartimento di Fisica, Politecnico di Torino, Torino (Italy) and Istituto Nazionale di Fisica della Materia, Unita del Politecnico di Torino, Torino (Italy)]. E-mails: kaniadakis@polito.it; scarfone@polito.it
2002-03-01
We consider systems which conserve the particle number and are described by Schroedinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf-like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. (author)
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
Climate bifurcation during the last deglaciation
Lenton, T. M.; Livina, V. N.; Dakos, V.; Scheffer, M.
2012-01-01
The last deglaciation was characterised by two abrupt warming events, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying causes 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. However, the abrupt Dansgaard-Oeschger (DO) events during the last ice age were probably triggered by stochastic fluctuations without bifurcation or early warning, and whether the onset of the Bølling-Allerød (DO event 1) was preceded by slowing down or not is debated. Here we show that the interval from the Last Glacial Maximum to the end of the Younger Dryas, as recorded in three Greenland ice cores with two different climate proxies, was accompanied by a robust slowing down in climate dynamics and an increase in climate variability, consistent with approaching bifurcation. 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 Bølling warming marked a distinct destabilisation of the climate system, which excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. There is some evidence for slowing down in the transition to and during the Younger Dryas. We infer that a bifurcation point was finally 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. The lack of a large triggering perturbation at the end of the Younger Dryas, and the fact that subsequent meltwater perturbations did not cause sustained cooling, support the
Optimal Revascularization Strategy on Medina 0,1,0 Left Main Bifurcation Lesions in Type 2 Diabetes.
Zheng, Xuwei; Peng, Hongyu; Zhao, Donghui; Ma, Qin; Fu, Kun; Chen, Guo; Fan, Qian; Liu, Jinghua
2016-01-01
Aim. Diabetes mellitus (DM) is a major risk factor for cardiovascular disease. The implications of a diagnosis of DM are as severe as the diagnosis of coronary artery disease. For many patients with complex coronary artery disease, optimal revascularization strategy selection and optimal medical therapy are equally important. In this study, we compared the hemodynamic results of different stenting techniques for Medina 0,1,0 left main bifurcation lesions. Methods. We use idealized left main bifurcation models and computational fluid dynamics analysis to evaluate hemodynamic parameters which are known to affect the risk of restenosis and thrombosis at stented bifurcation. The surface integrals of time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) at bifurcation site were quantified. Results. Crossover stenting without final kissing balloon angioplasty provided the most favorable hemodynamic results (integrated values of TAWSS = 2.96 × 10(-4) N, OSI = 4.75 × 10(-6) m(2)) with bifurcation area subjected to OSI values >0.25, >0.35, and >0.45 calculated as 0.39 mm(2), 0.06 mm(2), and 0 mm(2), respectively. Conclusion. Crossover stenting only offers hemodynamic advantages over other stenting techniques for Medina 0,1,0 left main bifurcation lesions and large bifurcation angle is associated with unfavorable flow profiles.
Optimal Revascularization Strategy on Medina 0,1,0 Left Main Bifurcation Lesions in Type 2 Diabetes
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Xuwei Zheng
2016-01-01
Full Text Available Aim. Diabetes mellitus (DM is a major risk factor for cardiovascular disease. The implications of a diagnosis of DM are as severe as the diagnosis of coronary artery disease. For many patients with complex coronary artery disease, optimal revascularization strategy selection and optimal medical therapy are equally important. In this study, we compared the hemodynamic results of different stenting techniques for Medina 0,1,0 left main bifurcation lesions. Methods. We use idealized left main bifurcation models and computational fluid dynamics analysis to evaluate hemodynamic parameters which are known to affect the risk of restenosis and thrombosis at stented bifurcation. The surface integrals of time-averaged wall shear stress (TAWSS and oscillatory shear index (OSI at bifurcation site were quantified. Results. Crossover stenting without final kissing balloon angioplasty provided the most favorable hemodynamic results (integrated values of TAWSS = 2.96 × 10−4 N, OSI = 4.75 × 10−6 m2 with bifurcation area subjected to OSI values >0.25, >0.35, and >0.45 calculated as 0.39 mm2, 0.06 mm2, and 0 mm2, respectively. Conclusion. Crossover stenting only offers hemodynamic advantages over other stenting techniques for Medina 0,1,0 left main bifurcation lesions and large bifurcation angle is associated with unfavorable flow profiles.
Models and Stability Analysis of Boiling Water Reactors
Energy Technology Data Exchange (ETDEWEB)
John Dorning
2002-04-15
We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model that includes: space-time modal neutron kinetics based on spatial w-modes; single- and two-phase flow in parallel boiling channels; fuel rod heat conduction dynamics; and a simple model of the recirculation loop. The BR model is represented by a set of time-dependent nonlinear ordinary differential equations, and is studied as a dynamical system using the modern bifurcation theory and nonlinear dynamical systems analysis. We first determine the stability boundary (SB) - or Hopf bifurcation set- in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value; then we transform the SB to the practical power-flow map used by BWR operating engineers and regulatory agencies. Using this SB, we show that the normal operating point at 100% power is very stable, that stability of points on the 100% rod line decreases as the flow rate is reduced, and that operating points in the low-flow/high-power region are least stable. We also determine the SB that results when the modal kinetics is replaced by simple point reactor kinetics, and we thereby show that the first harmonic mode does not have a significant effect on the SB. However, we later show that it nevertheless has a significant effect on stability because it affects the basin of attraction of stable operating points. Using numerical simulations we show that, in the important low-flow/high-power region, the Hopf bifurcation that occurs as the SB is crossed is subcritical; hence, growing oscillations can result following small finite perturbations of stable steady-states on the 100% rod line at points in the low-flow/high-power region. Numerical simulations are also performed to calculate the decay ratios (DRs) and frequencies of oscillations for various points on the 100% rod line. It is
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
Impact of leakage delay on bifurcation in high-order fractional BAM neural networks.
Huang, Chengdai; Cao, Jinde
2018-02-01
The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.
Topological Hopf and Chain Link Semimetal States and Their Application to Co2 Mn Ga
Chang, Guoqing; Xu, Su-Yang; Zhou, Xiaoting; Huang, Shin-Ming; Singh, Bahadur; Wang, Baokai; Belopolski, Ilya; Yin, Jiaxin; Zhang, Songtian; Bansil, Arun; Lin, Hsin; Hasan, M. Zahid
2017-10-01
Topological semimetals can be classified by the connectivity and dimensionality of the band crossings in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2 MnGa as a candidate. Both Hopf link and chainlike bulk band crossings and unconventional topological surface states are identified.
Hybrid control of bifurcation and chaos in stroboscopic model of Internet congestion control system
Ding, Da-Wei; Zhu, Jie; Luo, Xiao-Shu
2008-01-01
Interaction between transmission control protocol (TCP) and random early detection (RED) gateway in the Internet congestion control system has been modelled as a discrete-time dynamic system which exhibits complex bifurcating and chaotic behaviours. In this paper, a hybrid control strategy using both state feedback and parameter perturbation is employed to control the bifurcation and stabilize the chaotic orbits embedded in this discrete-time dynamic system of TCP/RED. Theoretical analysis and numerical simulations show that the bifurcation is delayed and the chaotic orbits are stabilized to a fixed point, which reliably achieves a stable average queue size in an extended range of parameters and even completely eliminates the chaotic behaviour in a particular range of parameters. Therefore it is possible to decrease the sensitivity of RED to parameters. By using the hybrid strategy, we may improve the stability and performance of TCP/RED congestion control system significantly.
Nemeth, Michael P.
2010-01-01
A comprehensive development of nondimensional parameters and equations for nonlinear and bifurcations analyses of quasi-shallow shells, based on the Donnell-Mushtari-Vlasov theory for thin anisotropic shells, is presented. A complete set of field equations for geometrically imperfect shells is presented in terms general of lines-of-curvature coordinates. A systematic nondimensionalization of these equations is developed, several new nondimensional parameters are defined, and a comprehensive stress-function formulation is presented that includes variational principles for equilibrium and compatibility. Bifurcation analysis is applied to the nondimensional nonlinear field equations and a comprehensive set of bifurcation equations are presented. An extensive collection of tables and figures are presented that show the effects of lamina material properties and stacking sequence on the nondimensional parameters.
Experimental Study of Flow in a Bifurcation
Fresconi, Frank; Prasad, Ajay
2003-11-01
An instability known as the Dean vortex occurs in curved pipes with a longitudinal pressure gradient. A similar effect is manifest in the flow in a converging or diverging bifurcation, such as those found in the human respiratory airways. The goal of this study is to characterize secondary flows in a bifurcation. Particle image velocimetry (PIV) and laser-induced fluorescence (LIF) experiments were performed in a clear, plastic model. Results show the strength and migration of secondary vortices. Primary velocity features are also presented along with dispersion patterns from dye visualization. Unsteadiness, associated with a hairpin vortex, was also found at higher Re. This work can be used to assess the dispersion of particles in the lung. Medical delivery systems and pollution effect studies would profit from such an understanding.
Modal bifurcation in a high-Tc superconducting levitation system
Taguchi, D.; Fujiwara, S.; Sugiura, T.
2011-05-01
This paper deals with modal bifurcation of a multi-degree-of-freedom high-Tc superconducting levitation system. As modeling of large-scale high-Tc superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-Tc superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-Tc superconducting levitation systems.
Bifurcation and Chaos in a Pulse Width modulation controlled Buck Converter
DEFF Research Database (Denmark)
Kocewiak, Lukasz; Bak, Claus Leth; Munk-Nielsen, Stig
2007-01-01
by a system of piecewise-smooth nonautonomous differential equations. The research are focused on chaotic oscillations analysis and analytical search for bifurcations dependent on parameter. The most frequent route to chaos by the period doubling is observed in the second order DC-DC buck converter. Other...... bifurcations as a complex behaviour in power electronic system evidence are also described. In order to verify theoretical study the experimental DC-DC buck converter was build. The results obtained from three sources were presented and compared. A very good agreement between theory and experiment was observed....
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T....... The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Stenting of bifurcation lesions: a rational approach.
Lefèvre, T; Louvard, Y; Morice, M C; Loubeyre, C; Piéchaud, J F; Dumas, P
2001-12-01
The occurrence of stenosis in or next to coronary bifurcations is relatively frequent and generally underestimated. In our experience, such lesions account for 15%-18% of all percutaneous coronary intervention > (PCI). The main reasons for this are (1) the coronary arteries are like the branches of a tree with many ramifications and (2) because of axial plaque redistribution, especially after stent implantation, PCI of lesions located next to a coronary bifurcation almost inevitably cause plaque shifting in the side branches. PCI treatment of coronary bifurcation lesions remains challenging. Balloon dilatation treatment used to be associated with less than satisfactory immediate results, a high complication rate, and an unacceptable restenosis rate. The kissing balloon technique resulted in improved, though suboptimal, outcomes. Several approaches were then suggested, like rotative or directional atherectomy, but these techniques did not translate into significantly enhanced results. With the advent of second generation stents, in 1996, the authors decided to set up an observational study on coronary bifurcation stenting combined with a bench test of the various stents available. Over the last 5 years, techniques, strategies, and stent design have improved. As a result, the authors have been able to define a rational approach to coronary bifurcation stenting. This bench study analyzed the behavior of stents and allowed stents to be discarded that are not compatible with the treatment of coronary bifurcations. Most importantly, this study revealed that stent deformation due to the opening of a strut is a constant phenomenon that must be corrected by kissing balloon inflation. Moreover, it was observed that the opening of a stent strut into a side branch could permit the stenting, at least partly, of the side branch ostium. This resulted in the provocative concept of "stenting both branches with a single stent." Therefore, a simple approach is currently implemented
Consequences of entropy bifurcation in non-Maxwellian astrophysical environments
Leubner, M. P.
2008-07-01
Non-extensive systems, accounting for long-range interactions and correlations, are fundamentally related to non-Maxwellian distributions where a duality of equilibria appears in two families, the non-extensive thermodynamic equilibria and the kinetic equilibria. Both states emerge out of particular entropy generalization leading to a class of probability distributions, where bifurcation into two stationary states is naturally introduced by finite positive or negative values of the involved entropic index kappa. The limiting Boltzmann-Gibbs-Shannon state (BGS), neglecting any kind of interactions within the system, is subject to infinite entropic index and thus characterized by self-duality. Fundamental consequences of non-extensive entropy bifurcation, manifest in different astrophysical environments, as particular core-halo patterns of solar wind velocity distributions, the probability distributions of the differences of the fluctuations in plasma turbulence as well as the structure of density distributions in stellar gravitational equilibrium are discussed. In all cases a lower entropy core is accompanied by a higher entropy halo state as compared to the standard BGS solution. Data analysis and comparison with high resolution observations significantly support the theoretical requirement of non-extensive entropy generalization when dealing with systems subject to long-range interactions and correlations.
Bifurcations in two-image photometric stereo for orthogonal illuminations
Kozera, R.; Prokopenya, A.; Noakes, L.; Śluzek, A.
2017-07-01
This paper discusses the ambiguous shape recovery in two-image photometric stereo for a Lambertian surface. The current uniqueness analysis refers to linearly independent light-source directions p = (0, 0, -1) and q arbitrary. For this case necessary and sufficient condition determining ambiguous reconstruction is governed by a second-order linear partial differential equation with constant coefficients. In contrast, a general position of both non-colinear illumination directions p and q leads to a highly non-linear PDE which raises a number of technical difficulties. As recently shown, the latter can also be handled for another family of orthogonal illuminations parallel to the OXZ-plane. For the special case of p = (0, 0, -1) a potential ambiguity stems also from the possible bifurcations of sub-local solutions glued together along a curve defined by an algebraic equation in terms of the data. This paper discusses the occurrence of similar bifurcations for such configurations of orthogonal light-source directions. The discussion to follow is supplemented with examples based on continuous reflectance map model and generated synthetic images.
CONTROL OF A SADDLE NODE BIFURCATION IN A POWER SYSTEM USING A PID CONTROLLER
Directory of Open Access Journals (Sweden)
J. Alvarez
2003-04-01
Full Text Available In this work, we present the elimination of a saddle-node bifurcation in a basic power system using a PIDcontroller. In addition, a stability analysis of the rotor angle and its frequency, which are directly related tovoltage collapse problem, is presented.
Experimental bifurcation analysis—Continuation for noise-contaminated zero problems
DEFF Research Database (Denmark)
Schilder, Frank; Bureau, Emil; Santos, Ilmar Ferreira
2015-01-01
Noise contaminated zero problems involve functions that cannot be evaluated directly, but only indirectly via observations. In addition, such observations are affected by a non-deterministic observation error (noise). We investigate the application of numerical bifurcation analysis for studying t...
Periodic-Orbit Bifurcation and Shell Structure in Reflection-Asymmetric Deformed Cavity
Sugita, A.; Arita, K.; Matsuyanagi, K.
1997-01-01
Shell structure of the single-particle spectrum for reflection-asymmetric deformed cavity is investigated. Remarkable shell structure emerges for certain combinations of quadrupole and octupole deformations. Semiclassical periodic-orbit analysis indicates that bifurcation of equatorial orbits plays an important role in the formation of this new shell structure.
Neimark-Sacker bifurcation for the discrete-delay Kaldor model
Dobrescu, Loretti Isabella; Opris, Dumitru
2007-01-01
We consider a discrete-delay time, Kaldor non-linear business cycle model in income and capital. Given an investment function, resembling the one discussed by Rodano, we use the linear approximation analysis to state the local stability property and local bifurcations, in the parameter space. Finally, we will give some numerical examples to justify the theoretical results.
Weijer, W.; Dijkstra, H.A.
2001-01-01
Within a low-resolution primitive-equation model of the three-dimensional ocean circulation, a bifurcation analysis is performed of double-hemispheric basin flows. Main focus is on the connection between results for steady two-dimensional flows in a non-rotating basin and those for
Weijer, W.; Dijkstra, Henk A.
2001-01-01
Within a low-resolution primitive-equation model of the three-dimensional ocean circulation, a bifurcation analysis is performed of double-hemispheric basin flows. Main focus is on the connection between results for steady two-dimensional flows in a nonrotating basin and those for
Cutting Balloon Angioplasty in the Treatment of Short Infrapopliteal Bifurcation Disease.
Iezzi, Roberto; Posa, Alessandro; Santoro, Marco; Nestola, Massimiliano; Contegiacomo, Andrea; Tinelli, Giovanni; Paolini, Alessandra; Flex, Andrea; Pitocco, Dario; Snider, Francesco; Bonomo, Lorenzo
2015-08-01
To evaluate the safety, feasibility, and effectiveness of cutting balloon angioplasty in the management of infrapopliteal bifurcation disease. Between November 2010 and March 2013, 23 patients (mean age 69.6±9.01 years, range 56-89; 16 men) suffering from critical limb ischemia were treated using cutting balloon angioplasty (single cutting balloon, T-shaped double cutting balloon, or double kissing cutting balloon technique) for 47 infrapopliteal artery bifurcation lesions (16 popliteal bifurcation and 9 tibioperoneal bifurcation) in 25 limbs. Follow-up consisted of clinical examination and duplex ultrasonography at 1 month and every 3 months thereafter. All treatments were technically successful. No 30-day death or adverse events needing treatment were registered. No flow-limiting dissection was observed, so no stent implantation was necessary. The mean postprocedure minimum lumen diameter and acute gain were 0.28±0.04 and 0.20±0.06 cm, respectively, with a residual stenosis of 0.04±0.02 cm. Primary and secondary patency rates were estimated as 89.3% and 93.5% at 6 months and 77.7% and 88.8% at 12 months, respectively; 1-year primary and secondary patency rates of the treated bifurcation were 74.2% and 87.0%, respectively. The survival rate estimated by Kaplan-Meier analysis was 82.5% at 1 year. Cutting balloon angioplasty seems to be a safe and effective tool in the routine treatment of short/ostial infrapopliteal bifurcation lesions, avoiding procedure-related complications, overcoming the limitations of conventional angioplasty, and improving the outcome of catheter-based therapy. © The Author(s) 2015.
Understanding a Period-Doubling Bifurcation in Cardiac Cells
Berger, Carolyn; Zhao, Xiaopeng; Schaeffer, David; Idriss, Salim; Gauthier, Daniel
2008-03-01
Bifurcations in the electrical response of cardiac tissue can destabilize spatio-temporal waves of electrochemical activity in the heart, leading to tachycardia or even fibrillation. Therefore, it is important to classify these bifurcations so that we can understand the mechanisms that cause instabilities in cardiac tissue. We have determined that the period-doubling bifurcation in paced myocardium is of the unfolded border-collision type. To understand how this new type of bifurcation manifest itself in cardiac tissue, we have also studied the role of calcium in inducing the bifurcation. We will discuss the nature of the unfolded border-collision bifurcation and present our results of dual voltage and calcium measurements in a frog ventricle preparation.
Roy, D.; Balanarayan, P.; Gadre, Shridhar R.
2008-11-01
The Poincaré-Hopf relation is studied for molecular electrostatic potentials (MESPs) of a few test systems such as cyclopropane, cyclobutane, pyridine, and benzene. Appropriate spheres centered at various points, including the center of mass of the system under study, are constructed and the MESP gradient is evaluated on the corresponding spherical grid. The change in directional nature of MESP gradient on the surface of these spheres gives indication of the critical points of the function. This is used for developing a method for locating the critical points of MESP. The strategy also enables a general definition of the Euler characteristic (EC) of the molecule, independent of any region or space. Further, the effect of basis set and level of theory on the EC is discussed.
Venturi, Daniele
2016-11-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics, quantum field theory and statistical physics. For example, in the context of fluid dynamics, the Hopf characteristic functional equation was deemed by Monin and Yaglom to be "the most compact formulation of the turbulence problem", which is the problem of determining the statistical properties of the velocity and pressure fields of Navier-Stokes equations given statistical information on the initial state. However, no effective numerical method has yet been developed to compute the solution to functional differential equations. In this talk I will provide a new perspective on this general problem, and discuss recent progresses in approximation theory for nonlinear functionals and functional equations. The proposed methods will be demonstrated through various examples.
Wiener-Hopf optimal control of a hydraulic canal prototype with fractional order dynamics.
Feliu-Batlle, Vicente; Feliu-Talegón, Daniel; San-Millan, Andres; Rivas-Pérez, Raúl
2017-06-26
This article addresses the control of a laboratory hydraulic canal prototype that has fractional order dynamics and a time delay. Controlling this prototype is relevant since its dynamics closely resembles the dynamics of real main irrigation canals. Moreover, the dynamics of hydraulic canals vary largely when the operation regime changes since they are strongly nonlinear systems. All this makes difficult to design adequate controllers. The controller proposed in this article looks for a good time response to step commands. The design criterium for this controller is minimizing the integral performance index ISE. Then a new methodology to control fractional order processes with a time delay, based on the Wiener-Hopf control and the Padé approximation of the time delay, is developed. Moreover, in order to improve the robustness of the control system, a gain scheduling fractional order controller is proposed. Experiments show the adequate performance of the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Bifurcation and stability for a nonlinear parabolic partial differential equation
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
Sequences of gluing bifurcations in an analog electronic circuit
Energy Technology Data Exchange (ETDEWEB)
Akhtanov, Sayat N.; Zhanabaev, Zeinulla Zh. [Physico-Technical Department, Al Farabi Kazakh National University, Al Farabi Av. 71, Almaty, 050038 Kazakhstan (Kazakhstan); Zaks, Michael A., E-mail: zaks@math.hu-berlin.de [Institute of Mathematics, Humboldt University, Rudower Chaussee 25, D-12489 Berlin (Germany)
2013-10-01
We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and replaces the Lorenz route to chaos by a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the irregular ones. Every single bifurcation “glues” in the phase space two stable periodic orbits and creates a new one, with the doubled length: a sequence of such bifurcations results in the birth of the chaotic attractor.
Energy Technology Data Exchange (ETDEWEB)
Ouattara, B; Khouzam, A; Mojtabi, A [Universite de Toulouse (France); INPT, UPS (France); IMFT (Institut de Mecanique des Fluides de Toulouse), Allee Camille Soula, F-31400 Toulouse (France); Charrier-Mojtabi, M C, E-mail: bouattar@imft.fr, E-mail: akhouzam@imft.fr, E-mail: mojtabi@imft.fr, E-mail: cmojtabi@cict.fr [PHASE, EA 810, UFR PCA, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex (France)
2012-06-01
The aim of this study was to investigate the effect of conducting boundaries on the onset of convection in a binary fluid-saturated porous layer. The isotropic saturated porous layer is bounded by two impermeable but thermally conducting plates, subjected to a constant heat flux. These plates have identical conductivity. Moreover, the conductivity of the plates is generally different from the porous layer conductivity. The overall layer is of large extent in both horizontal directions. The problem is governed by seven dimensionless parameters, namely the normalized porosity of the medium {epsilon}, the ratio of plates over the porous layer thickness {delta} and their relative thermal conductivities ratio d, the separation ratio {delta}, the Lewis number Le and thermal Rayleigh number Ra. In this work, an analytical and numerical stability analysis is performed. The equilibrium solution is found to lose its stability via a stationary bifurcation or a Hopf bifurcation depending on the values of the dimensionless parameters. For the long-wavelength mode, the critical Rayleigh number is obtained as Ra{sub cs}=12(1+2d{delta} )/[1+{psi} (2d{delta}Le+Le+1)] and k{sub cs}=0 for {psi}> {psi} {sub uni}> 0. This work extends an earlier paper by Mojtabi and Rees (2011 Int. J. Heat Mass Transfer 54 293-301) who considered a configuration where the porous layer is saturated by a pure fluid.
Spijkerboer, T.P.
2017-01-01
The externalization of European migration policy has resulted in a bifurcation of global human mobility, which is divided along a North/South axis. In two judgments, the EU Court of Justice was confronted with cases challenging the exclusion of Syrian refugees from Europe. These cases concern core
Periodic orbits near a bifurcating slow manifold
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2015-01-01
(\\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^{1/2}\\ln...
Filipce, Venko; Ammirati, Mario
2015-01-01
Basilar aneurisms are one of the most complex and challenging pathologies for neurosurgeons to treat. Endoscopy is a recently rediscovered neurosurgical technique that could lend itself well to overcome some of the vascular visualization challenges associated with this pathology. The purpose of this study was to quantify and compare the basilar artery (BA) bifurcation (tip of the basilar) working area afforded by the microscope and the endoscope using different approaches and image guidance. We performed a total of 9 dissections, including pterional (PT) and orbitozygomatic (OZ) approaches bilaterally in five whole, fresh cadaver heads. We used computed tomography based image guidance for intraoperative navigation as well as for quantitative measurements. We estimated the working area of the tip of the basilar, using both a rigid endoscope and an operating microscope. Operability was qualitatively assessed by the senior authors. In microscopic exposure, the OZ approach provided greater working area (160 ± 34.3 mm(2)) compared to the PT approach (129.8 ± 37.6 mm(2)) (P > 0.05). The working area in both PT and OZ approaches using 0° and 30° endoscopes was larger than the one available using the microscope alone (P approach, both 0° and 30° endoscopes provided a working area greater than a microscopic OZ approach (P approach (P > 0.05). Integration of endoscope and microscope in both PT and OZ approaches can provide significantly greater surgical exposure of the BA bifurcation compared to that afforded by the conventional approaches alone.
10th International Workshop on Bifurcation and Degradation in Geomaterials
Zhao, Jidong
2015-01-01
This book contains contributions to the 10th International Workshop on Bifurcation and Degradation in Geomaterials held in Hong Kong, May 28-30, 2014. This event marks the silver Jubilee anniversary of an international conference series dedicated to the research on localization, instability, degradation and failure of geomaterials since 1988 when its first workshop was organized in Germany. This volume of book collects the latest progresses and state-of-the-art research from top researchers around the world, and covers topics including multiscale modeling, experimental characterization and theoretical analysis of various instability and degradation phenomena in geomaterials as well as their relevance to contemporary issues in engineering practice. This book can be used as a useful reference for research students, academics and practicing engineers who are interested in the instability and degradation problems in geomechanics and geotechnical engineering.
Damped bead on a rotating circular hoop - a bifurcation zoo
Dutta, Shovan
2012-01-01
The evergreen problem of a bead on a rotating hoop shows a multitude of bifurcations when the bead moves with friction. This motion is studied for different values of the damping coefficient and rotational speeds of the hoop. Phase portraits and trajectories corresponding to all different modes of motion of the bead are presented. They illustrate the rich dynamics associated with this simple system. For some range of values of the damping coefficient and rotational speeds of the hoop, linear stability analysis of the equilibrium points is inadequate to classify their nature. A technique involving transformation of coordinates and order of magnitude arguments is presented to examine such cases. This may provide a general framework to investigate other complex systems.
Droplet Breakup Dynamics in Bi-Layer Bifurcating Microchannel
Directory of Open Access Journals (Sweden)
Yong Ren
2018-01-01
Full Text Available Breakup of droplets at bi-layer bifurcating junction in polydimethylsiloxane (PDMS microchannel has been investigated by experiments and numerical simulation. The pressure drop in bi-layer bifurcating channel was investigated and compared with single-layer bifurcating channel. Daughter droplet size variation generated in bi-layer bifurcating microchannel was analyzed. The correlation was proposed to predict the transition between breakup and non-breakup conditions of droplets in bi-layer bifurcating channel using a phase diagram. In the non-breakup regime, droplets exiting port can be switched via tuning flow resistance by controlling radius of curvature, and or channel height ratio. Compared with single-layer bifurcating junction, 3-D cutting in diagonal direction from bi-layer bifurcating junction induces asymmetric fission to form daughter droplets with distinct sizes while each size has good monodispersity. Lower pressure drop is required in the new microsystem. The understanding of the droplet fission in the novel microstructure will enable more versatile control over the emulsion formation, fission and sorting. The model system can be developed to investigate the encapsulation and release kinetics of emulsion templated particles such as drug encapsulated microcapsules as they flow through complex porous media structures, such as blood capillaries or the porous tissue structures, which feature with bifurcating junctions.
Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations
Bakri, Taoufik; Meijer, Hil Gaétan Ellart; Verhulst, Ferdinand
2009-01-01
Persistence and bifurcations of Lyapunov manifolds can be studied by a combination of averaging-normalization and numerical bifurcation methods. This can be extended to infinite-dimensional cases when using suitable averaging theorems. The theory is applied to the case of a parametrically excited
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
Quantum Localization near Bifurcations in Classically Chaotic Systems
Varga, I; Eckhardt, B
1999-01-01
We show that strongly localized wave functions occur around classical bifurcations. Near a saddle node bifurcation the scaling of the inverse participation ratio on Planck's constant and the dependence on the parameter is governed by an Airy function. Analytical estimates are supported by numerical calculations for the quantum kicked rotor.
Seasonal Variation of the North/South Equatorial Current Bifurcation
Chen, Z.
2016-02-01
The seasonal variation of the North/South Equatorial Current (NEC/SEC) bifurcation off the Philippine/Madagascar/Australian coast is investigated. It is shown that the seasonal cycles of the NEC/SEC bifurcation are generally analogous to each other, all of which shift synchronously back and forth seasonally and arrive at their southernmost positions in boreal late spring and early summer. It is demonstrated that the linear, reduced gravity, long Rossby model, which works well for the NEC bifurcation, is insufficient to reproduce the seasonal cycles of the SEC bifurcation off the Madagascar/Australian coast particularly in their south-north migrations. This can be attributed to the existence of the isolated island in the Madagascar case and the seasonally-varying wind forcing around the Australian coast, while they are almost absent in the NEC bifurcation case. Without considering the existence of an island and the alongshore winds, we propose a simple bifurcation model under the framework of linear Rossby wave dynamics. It is found that the seasonal bifurcation latitude is predominantly determined by the spatial pattern of the wind and baroclinic Rossby wave propagation. This model explains the roles of local/remote wind forcing and baroclinic adjustment in the south-north migration and peak seasons of the bifurcation latitude.
Bifurcation and chaos in high-frequency peak current mode Buck converter
Chang-Yuan, Chang; Xin, Zhao; Fan, Yang; Cheng-En, Wu
2016-07-01
Bifurcation and chaos in high-frequency peak current mode Buck converter working in continuous conduction mode (CCM) are studied in this paper. First of all, the two-dimensional discrete mapping model is established. Next, reference current at the period-doubling point and the border of inductor current are derived. Then, the bifurcation diagrams are drawn with the aid of MATLAB. Meanwhile, circuit simulations are executed with PSIM, and time domain waveforms as well as phase portraits in i L-v C plane are plotted with MATLAB on the basis of simulation data. After that, we construct the Jacobian matrix and analyze the stability of the system based on the roots of characteristic equations. Finally, the validity of theoretical analysis has been verified by circuit testing. The simulation and experimental results show that, with the increase of reference current I ref, the corresponding switching frequency f is approaching to low-frequency stage continuously when the period-doubling bifurcation happens, leading to the converter tending to be unstable. With the increase of f, the corresponding I ref decreases when the period-doubling bifurcation occurs, indicating the stable working range of the system becomes smaller. Project supported by the National Natural Science Foundation of China (Grant No. 61376029), the Fundamental Research Funds for the Central Universities, China, and the College Graduate Research and Innovation Program of Jiangsu Province, China (Grant No. SJLX15_0092).
A computational model of microbubble transport through a blood-filled vessel bifurcation
Calderon, Andres
2005-11-01
We are developing a novel gas embolotherapy technique to occlude blood vessels and starve tumors using gas bubbles that are produced by the acoustic vaporization of liquid perfluorocarbon droplets. The droplets are small enough to pass through the microcirculation, but the subsequent bubbles are large enough to lodge in vessels. The uniformity of tumor infarction depends on the transport the blood-borne bubbles before they stick. We examine the transport of a semi-infinite bubble through a single bifurcation in a liquid-filled two-dimensional channel. The flow is governed by the conservation of fluid mass and momentum equations. Reynolds numbers in the microcirculation are small, and we solve the governing equations using the boundary element method. The effect of gravity on bubble splitting is investigated and results are compared with our previous bench top experiments and to a quasi-steady one-dimensional analysis. The effects of daughter tube outlet pressures and bifurcation geometry are also considered. The findings suggest that slow moving bubbles will favor the upper branch of the bifurcation, but that increasing the bubble speed leads to more even splitting. It is also found that some bifurcation geometries and flow conditions result in severe thinning of the liquid film separating the bubble from the wall, suggesting the possibility bubble-wall contact. This work is supported by NSF grant BES-0301278 and NIH grant EB003541.
Zhou, Haoyin; Sun, Peng; Ha, Seongmin; Lundine, Devon; Xiong, Guanglei
2016-10-01
Image-based simulation of blood flow using computational fluid dynamics has been shown to play an important role in the diagnosis of ischemic coronary artery disease. Accurate extraction of complex coronary artery structures in a watertight geometry is a prerequisite, but manual segmentation is both tedious and subjective. Several semi- and fully automated coronary artery extraction approaches have been developed but have faced several challenges. Conventional voxel-based methods allow for watertight segmentation but are slow and difficult to incorporate expert knowledge. Machine learning based methods are relatively fast and capture rich information embedded in manual annotations. Although sufficient for visualization and analysis of coronary anatomy, these methods cannot be used directly for blood flow simulation if the coronary vasculature is represented as a loose combination of tubular structures and the bifurcation geometry is improperly modeled. In this paper, we propose a novel method to extract branching coronary arteries from CT imaging with a focus on explicit bifurcation modeling and application of machine learning. A bifurcation lumen is firstly modeled by generating the convex hull to join tubular vessel branches. Guided by the pre-determined centerline, machine learning based segmentation is performed to adapt the bifurcation lumen model to target vessel boundaries and smoothed by subdivision surfaces. Our experiments show the constructed coronary artery geometry from CT imaging is accurate by comparing results against the manually annotated ground-truths, and can be directly applied to coronary blood flow simulation. Copyright © 2016 Elsevier Ltd. All rights reserved.
Control of Bistability in a Delayed Duffing Oscillator
Directory of Open Access Journals (Sweden)
Mustapha Hamdi
2012-01-01
Full Text Available The effect of a high-frequency excitation on nontrivial solutions and bistability in a delayed Duffing oscillator with a delayed displacement feedback is investigated in this paper. We use the technique of direct partition of motion and the multiple scales method to obtain the slow dynamic of the system and its slow flow. The analysis of the slow flow provides approximations of the Hopf and secondary Hopf bifurcation curves. As a result, this study shows that increasing the delay gain, the system undergoes a secondary Hopf bifurcation. Further, it is indicated that as the frequency of the excitation is increased, the Hopf and secondary Hopf bifurcation curves overlap giving birth in the parameter space to small regions of bistability where a stable trivial steady state and a stable limit cycle coexist. Numerical simulations are carried out to validate the analytical finding.
Climate bifurcation during the last deglaciation?
Directory of Open Access Journals (Sweden)
T. M. Lenton
2012-07-01
Full Text Available There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer
Climate bifurcation during the last deglaciation?
Lenton, T. M.; Livina, V. N.; Dakos, V.; Scheffer, M.
2012-07-01
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 spliced record of the
Bifurcated intraarticular long head of biceps tendon
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Vivek Pandey
2014-01-01
Full Text Available Though rare, many anomalous origins of long head of the biceps tendon (LHBT have been reported in the literature. Anatomic variations commonly explained are a third humeral head, anomalous insertion, congenital absence and adherence to the rotator cuff. We report a rare case who underwent shoulder arthroscopy with impingement symptoms where in LHBT was found to be bifurcated with a part attached to superior labrum and the other part to the posterior capsule of joint. Furthermore, intraarticular portion of LHBT was adherent to the undersurface of the supraspinatus tendon. Awareness of such an anatomical aberration during the shoulder arthroscopy is of great importance as it can potentially avoid unnecessary confusion and surgery.
Bifurcated SEN with Fluid Flow Conditioners
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F. Rivera-Perez
2014-01-01
Full Text Available This work evaluates the performance of a novel design for a bifurcated submerged entry nozzle (SEN used for the continuous casting of steel slabs. The proposed design incorporates fluid flow conditioners attached on SEN external wall. The fluid flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through numerical simulations using the CFD technique. Numerical results were validated by means of physical simulations conducted on a scaled cold water model. Numerical and physical simulations confirmed that the performance of the proposed SEN is superior to a traditional one. Fluid flow conditioners reduce the liquid free surface fluctuations and minimize the occurrence of vortexes at the free surface.
Oscillatory bifurcation for semilinear ordinary differential equations
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Tetsutaro Shibata
2016-06-01
\\] where $f(u = u + (1/2\\sin^k u$ ($k \\ge 2$ and $\\lambda > 0$ is a bifurcation parameter. It is known that $\\lambda$ is parameterized by the maximum norm $\\alpha = \\Vert u_\\lambda\\Vert_\\infty$ of the solution $u_\\lambda$ associated with $\\lambda$ and is written as $\\lambda = \\lambda(k,\\alpha$. When we focus on the asymptotic behavior of $\\lambda(k,\\alpha$ as $\\alpha \\to \\infty$, it is natural to expect that $\\lambda(k, \\alpha \\to \\pi^2/4$, and its convergence rate is common to $k$. Contrary to this expectation, we show that $\\lambda(2n_1+1,\\alpha$ tends to $\\pi^2/4$ faster than $\\lambda(2n_2,\\alpha$ as $\\alpha \\to \\infty$, where $n_1\\ge 1,\\ n_2 \\ge 1$ are arbitrary given integers.
Clausius entropy for arbitrary bifurcate null surfaces
Baccetti, Valentina; Visser, Matt
2014-02-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation {\\rm{d}}S = \\unicode{x111} Q/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations.
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
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Brown Robert F
2004-01-01
Full Text Available The reduced Lefschetz number, that is, where denotes the Lefschetz number, is proved to be the unique integer-valued function on self-maps of compact polyhedra which is constant on homotopy classes such that (1 for and ; (2 if is a map of a cofiber sequence into itself, then ; (3 , where is a self-map of a wedge of circles, is the inclusion of a circle into the th summand, and is the projection onto the th summand. If is a self-map of a polyhedron and is the fixed point index of on all of , then we show that satisfies the above axioms. This gives a new proof of the normalization theorem: if is a self-map of a polyhedron, then equals the Lefschetz number of . This result is equivalent to the Lefschetz-Hopf theorem: if is a self-map of a finite simplicial complex with a finite number of fixed points, each lying in a maximal simplex, then the Lefschetz number of is the sum of the indices of all the fixed points of .
Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks.
Mincheva, Maya; Roussel, Marc R
2012-11-01
Network conditions for Turing instability in biochemical systems with two biochemical species are well known and involve autocatalysis or self-activation. On the other hand general network conditions for potential Turing instabilities in large biochemical reaction networks are not well developed. A biochemical reaction network with any number of species where only one species moves is represented by a simple digraph and is modeled by a reaction-diffusion system with non-mass action kinetics. A graph-theoretic condition for potential Turing-Hopf instability that arises when a spatially homogeneous equilibrium loses its stability via a single pair of complex eigenvalues is obtained. This novel graph-theoretic condition is closely related to the negative cycle condition for oscillations in ordinary differential equation models and its generalizations, and requires the existence of a pair of subnetworks, each containing an even number of positive cycles. The technique is illustrated with a double-cycle Goodwin type model. Copyright © 2012 Elsevier Inc. All rights reserved.
Gritli, Hassène; Belghith, Safya
2017-06-01
An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.
Pulsatile flow in coronary bifurcations for different stenting techniques
García García, Javier; Manuel Martín, Fernando Jaime; Doce Carrasco, Y.; Castro Ruiz, F.; Crespo Martínez, Antonio; Goicolea Marin, P.; Fernandez Diaz, J.A.
2012-01-01
The objective of this work is to analyze the local hem odynamic changes caused in a coronary bifurcation by three different stenting techniques: simple stenting of the main vessel, simple stenting of the main vessel with kissing balloon in the side branch and culotte. To carry out this study an idealized geometry of a coronary bifurcation is used, and two bifurcation angles, 45º and 90º, are chosen as representative of the wide variety of re al configurations. In order to quantify th...
The Persistence of a Slow Manifold with Bifurcation
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Kristiansen, Kristian Uldall; Palmer, P.; Robert, M.
2012-01-01
his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated...... by tethered satellites. It is shown that an almost full measure subset of a neighborhood of the slow manifold's normally elliptic branches persists in an adiabatic sense. We prove this using averaging and a blow-up near the bifurcation....
Bifurcation control in the Burgers-KdV equation
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Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, 00015 Monterotondo (Rome) (Italy)], E-mail: solitone@yahoo.it
2008-03-15
We consider the bifurcation control for the forced Burgers-KdV equation by means of delay feedback linear terms. We use a perturbation method in order to find amplitude and phase modulation equations as well as external force-response and frequency-response curves. We observe in the resonance response a saddle-node bifurcation that leads to jump and hysteresis phenomena. We compare the uncontrolled and controlled systems and demonstrate that control terms can delay or remove the occurrence of the saddle-node bifurcation and reduce the amplitude peak of the resonant response.
Bifurcations in biaxially stretched highly non-linear materials under normal electric fields
Diaz-Calleja, R.; Llovera-Segovia, P.; Quijano-López, A.
2014-10-01
A study of the effect of the combined action of mechanical and electrical force fields in biaxially stretched slabs has been carried out. Samples of VHB 4910, a dielectric elastomer whose stress-strain behaviour can be fitted well to an Ogden constitutive equation, have been chosen. The analysis show that bifurcation appearance crucially depends on both the configuration of the system sample-electrodes and the parameters of the empirical model.
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Bifurcation dynamics of the tempered fractional Langevin equation
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Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
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.
Bunch lengthening with bifurcation in electron storage rings
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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)
HIGH BIFURCATION OF THE BRACHIAL ARTERY - A COMMON VARIANT
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Sesi
2015-10-01
Full Text Available 28 cadavers were dissected for variations in the bifurcation of brachial artery bilaterally {n=56} at the department of anatomy, Rangaraya Medical College, Kakinada, A.P. from 2010 to 2015 . Found variations during routine dissections for first year MBBS students. The findings have thrown light on the common as well as rare variants in the anatomy of brachial artery bifurcation and the course of radial and ulnar arteries in current study
Grundeken, Maik J; Collet, Carlos; Ishibashi, Yuki; Généreux, Philippe; Muramatsu, Takashi; LaSalle, Laura; Kaplan, Aaron V; Wykrzykowska, Joanna J; Morel, Marie-Angèle; Tijssen, Jan G; de Winter, Robbert J; Onuma, Yoshinobu; Leon, Martin B; Serruys, Patrick W
2017-08-24
To compare visual estimation with different quantitative coronary angiography (QCA) methods (single-vessel versus bifurcation software) to assess coronary bifurcation lesions. QCA has been developed to overcome the limitations of visual estimation. Conventional QCA however, developed in "straight vessels," has proved to be inaccurate in bifurcation lesions. Therefore, bifurcation QCA was developed. However, the impact of these different modalities on bifurcation lesion severity classification is yet unknown METHODS: From a randomized controlled trial investigating a novel bifurcation stent (Clinicaltrials.gov NCT01258972), patients with baseline assessment of lesion severity by means of visual estimation, single-vessel QCA, 2D bifurcation QCA and 3D bifurcation QCA were included. We included 113 bifurcations lesions in which all 5 modalities were assessed. The primary end-point was to evaluate how the different modalities affected the classification of bifurcation lesion severity and extent of disease. On visual estimation, 100% of lesions had side-branch diameter stenosis (%DS) >50%, whereas in 83% with single-vessel QCA, 27% with 2D bifurcation QCA and 26% with 3D bifurcation QCA a side-branch %DS >50% was found (P < 0.0001). With regard to the percentage of "true" bifurcation lesions, there was a significant difference between visual estimate (100%), single-vessel QCA (75%) and bifurcation QCA (17% with 2D bifurcation software and 13% with 3D bifurcation software, P < 0.0001). Our study showed that bifurcation lesion complexity was significantly affected when more advanced bifurcation QCA software were used. "True" bifurcation lesion rate was 100% on visual estimation, but as low as 13% when analyzed with dedicated bifurcation QCA software. © 2017 Wiley Periodicals, Inc.
Grazing bifurcation in aeroelastic systems with freeplay nonlinearity
Vasconcellos, R.; Abdelkefi, A.; Hajj, M. R.; Marques, F. D.
2014-05-01
A nonlinear analysis is performed to characterize the effects of a nonsmooth freeplay nonlinearity on the response of an aeroelastic system. This system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The nonsmooth freeplay nonlinearity is associated with the pitch degree of freedom. The aerodynamic loads are modeled using the unsteady formulation. Linear analysis is first performed to determine the coupled damping and frequencies and the associated linear flutter speed. Then, a nonlinear analysis is performed to determine the effects of the size of the freeplay gap on the response of the aeroelastic system. To this end, two different sizes are considered. The results show that, for both considered freeplay gaps, there are two different transitions or sudden jumps in the system's response when varying the freestream velocity (below linear flutter speed) with the appearance and disappearance of quadratic nonlinearity induced by discontinuity. It is demonstrated that these sudden transitions are associated with a tangential contact between the trajectory and the freeplay boundaries (grazing bifurcation). At the first transition, it is demonstrated that increasing the freestream velocity is accompanied by the appearance of a superharmonic frequency of order 2 of the main oscillating frequency. At the second transition, the results show that an increase in the freestream velocity is followed by the disappearance of the superharmonic frequency of order 2 and a return to a simple periodic response (main oscillating frequency).
Editorial: at the bifurcation of the last frontiers.
Nguyen, Thach; Chen, Shao Liang; Xu, Bo; Kwan, Tak; Nguyen, Katrina; Nanjundappa, Aravinda; Van Ho, Bao; Gao, Run-Lin
2010-08-01
The concept of coronary angioplasty percutaneous coronary intervention (PCI) was pioneered by Andreas Gruntzig. Since then, several modifications, innovative devices, techniques, and advances have revolutionized the practice of interventional cardiology. Coronary bifurcation and chronic total occlusion are the last two frontiers that continue to challenge the skills of the interventional cardiologists. Proceedings of the second Bifurcation Summit held from November 26 to 28, 2009 in Nanjing, China are published in this symposium. In a general review, the state of the art in management of bifurcation lesion is summarized in the statement of the "Bifurcation Club in KOKURA." A new-presented concept was the "extension distance" between the main vessel and the sidebranch ostia and its association with restenosis. The results of two studies on shear stress (SS) after PCI showed that contradictory lower SS after stenting was associated with lower in-stent restenosis. There was better fractional flow reserve after double kissing crush technique than provisional one-stent technique. There was also lower rate of stent thrombosis after bifurcation stenting with excellent final angiographic results. In a negative note, the SYNTAX score had no predictive values on trifurcated left main stenting. In summary, different aspects of percutaneous management for bifurcated lesion are described seen from different perspectives and evidenced by novel techniques and strategies.
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...
Bifurcation Of Olfactory Bulb Neuron Biophysics During Odor-Evoked Subthreshold Oscillation.
Kubota, Yoshihisa; Bower, James
1998-03-01
The Role of odor-evoked subthreshold oscillations in the olfactory bulb was studied using bifurcation and impedance analysis in a mathematical model of mitral cells which are the primary neuron of the olfactory bulb. Mathematical analyses of a reduced realistic model of an olfactory mitral cell suggests that these cells undergo a bifurcation from nonspecific passive response to voltage-dependent, low-frequency specific resonance during subthreshold bulbar oscillations. We propose that a partial role of odor-evoked subthreshold oscillations may be to bring the biophysical state variables of mitral cells into region of phase space where neurons become highly resonant to peripheral afferent as well as centrifugal inputs despite of the heterogeneity in mitral cell biophysics prior to odor presentation.
Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System
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Chuanjun Dai
2013-01-01
Full Text Available We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.
Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold
Grafke, Tobias; Vanden-Eijnden, Eric
2017-09-01
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within the realm of large deviation theory. It is shown that these non-equilibrium transitions make use of a reaction channel created by the bifurcation structure of the slow manifold, leading to vastly increased transition rates. Several examples are used to illustrate these findings, including an insect outbreak model, a system modeling phase separation in the presence of evaporation, and a system modeling transitions in active matter self-assembly. The last example involves a spatially extended system modeled by a stochastic partial differential equation.
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Javier Benezet
2016-01-01
Full Text Available We present a complex bifurcation lesion treated with a new two-stent strategy combining a dedicated sirolimus eluting bifurcation stent, BiOSS Lim, with a bioresorbable vascular scaffold (BVS. The advantages of this strategy compared with the conventional two-stent approach are as follows: the dedicated stent protects the carina from being damaged, the large cell at the middle zone of the BiOSS Lim gives possibility to enter easily into the side branch (SB with any standard size conventional device, and, finally, the additional use of BVS in the SB could have a long-term benefit in terms of restenosis.
Porto, C. D. N.; Costa Filho, C. F. F.; Macedo, M. M. G.; Gutierrez, M. A.; Costa, M. G. F.
2017-03-01
Studies in intravascular optical coherence tomography (IV-OCT) have demonstrated the importance of coronary bifurcation regions in intravascular medical imaging analysis, as plaques are more likely to accumulate in this region leading to coronary disease. A typical IV-OCT pullback acquires hundreds of frames, thus developing an automated tool to classify the OCT frames as bifurcation or non-bifurcation can be an important step to speed up OCT pullbacks analysis and assist automated methods for atherosclerotic plaque quantification. In this work, we evaluate the performance of two state-of-the-art classifiers, SVM and Neural Networks in the bifurcation classification task. The study included IV-OCT frames from 9 patients. In order to improve classification performance, we trained and tested the SVM with different parameters by means of a grid search and different stop criteria were applied to the Neural Network classifier: mean square error, early stop and regularization. Different sets of features were tested, using feature selection techniques: PCA, LDA and scalar feature selection with correlation. Training and test were performed in sets with a maximum of 1460 OCT frames. We quantified our results in terms of false positive rate, true positive rate, accuracy, specificity, precision, false alarm, f-measure and area under ROC curve. Neural networks obtained the best classification accuracy, 98.83%, overcoming the results found in literature. Our methods appear to offer a robust and reliable automated classification of OCT frames that might assist physicians indicating potential frames to analyze. Methods for improving neural networks generalization have increased the classification performance.
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.
2013-01-01
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.
Mammalian evolution may not be strictly bifurcating.
Hallström, Björn M; Janke, Axel
2010-12-01
The massive amount of genomic sequence data that is now available for analyzing evolutionary relationships among 31 placental mammals reduces the stochastic error in phylogenetic analyses to virtually zero. One would expect that this would make it possible to finally resolve controversial branches in the placental mammalian tree. We analyzed a 2,863,797 nucleotide-long alignment (3,364 genes) from 31 placental mammals for reconstructing their evolution. Most placental mammalian relationships were resolved, and a consensus of their evolution is emerging. However, certain branches remain difficult or virtually impossible to resolve. These branches are characterized by short divergence times in the order of 1-4 million years. Computer simulations based on parameters from the real data show that as little as about 12,500 amino acid sites could be sufficient to confidently resolve short branches as old as about 90 million years ago (Ma). Thus, the amount of sequence data should no longer be a limiting factor in resolving the relationships among placental mammals. The timing of the early radiation of placental mammals coincides with a period of climate warming some 100-80 Ma and with continental fragmentation. These global processes may have triggered the rapid diversification of placental mammals. However, the rapid radiations of certain mammalian groups complicate phylogenetic analyses, possibly due to incomplete lineage sorting and introgression. These speciation-related processes led to a mosaic genome and conflicting phylogenetic signals. Split network methods are ideal for visualizing these problematic branches and can therefore depict data conflict and possibly the true evolutionary history better than strictly bifurcating trees. Given the timing of tectonics, of placental mammalian divergences, and the fossil record, a Laurasian rather than Gondwanan origin of placental mammals seems the most parsimonious explanation.
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Harry Pratt
2017-12-01
Full Text Available The analysis of retinal blood vessels present in fundus images, and the addressing of problems such as blood clot location, is important to undertake accurate and appropriate treatment of the vessels. Such tasks are hampered by the challenge of accurately tracing back problems along vessels to their source. This is due to the unresolved issue of distinguishing automatically between vessel bifurcations and vessel crossings in colour fundus photographs. In this paper, we present a new technique for addressing this problem using a convolutional neural network approach to firstly locate vessel bifurcations and crossings and then to classifying them as either bifurcations or crossings. Our method achieves high accuracies for junction detection and classification on the DRIVE dataset and we show further validation on an unseen dataset from which no data has been used for training. Combined with work in automated segmentation, this method has the potential to facilitate: reconstruction of vessel topography, classification of veins and arteries and automated localisation of blood clots and other disease symptoms leading to improved management of eye disease.
Bifurcation in epigenetics: Implications in development, proliferation, and diseases
Jost, Daniel
2014-01-01
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of biochemical marks on chromatin. Here, we develop a stochastic model that describes the dynamics of epigenetic marks along a given DNA region. Through mathematical analysis, we show the emergence of bistable and persistent epigenetic states from the cooperative recruitment of modifying enzymes. We also find that the dynamical system exhibits a critical point and displays, in the presence of asymmetries in recruitment, a bifurcation diagram with hysteresis. These results have deep implications for our understanding of epigenetic regulation. In particular, our study allows one to reconcile within the same formalism the robust maintenance of epigenetic identity observed in differentiated cells, the epigenetic plasticity of pluripotent cells during differentiation, and the effects of epigenetic misregulation in diseases. Moreover, it suggests a possible mechanism for developmental transitions where the system is shifted close to the critical point to benefit from high susceptibility to developmental cues.
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
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Robert F. Brown
2004-03-01
Full Text Available The reduced Lefschetz number, that is, L(Ã¢Â‹Â…Ã¢ÂˆÂ’1 where L(Ã¢Â‹Â… denotes the Lefschetz number, is proved to be the unique integer-valued function ÃŽÂ» on self-maps of compact polyhedra which is constant on homotopy classes such that (1 ÃŽÂ»(fg=ÃŽÂ»(gf for f:XÃ¢Â†Â’Y and g:YÃ¢Â†Â’X; (2 if (f1,f2,f3 is a map of a cofiber sequence into itself, then ÃŽÂ»(f1=ÃŽÂ»(f1+ÃŽÂ»(f3; (3 ÃŽÂ»(f=Ã¢ÂˆÂ’(deg(p1fe1+Ã¢Â‹Â¯+deg(pkfek, where f is a self-map of a wedge of k circles, er is the inclusion of a circle into the rth summand, and pr is the projection onto the rth summand. If f:XÃ¢Â†Â’X is a self-map of a polyhedron and I(f is the fixed point index of f on all of X, then we show that I(Ã¢Â‹Â…Ã¢ÂˆÂ’1 satisfies the above axioms. This gives a new proof of the normalization theorem: if f:XÃ¢Â†Â’X is a self-map of a polyhedron, then I(f equals the Lefschetz number L(f of f. This result is equivalent to the Lefschetz-Hopf theorem: if f:XÃ¢Â†Â’X is a self-map of a finite simplicial complex with a finite number of fixed points, each lying in a maximal simplex, then the Lefschetz number of f is the sum of the indices of all the fixed points of f.
Anatomical Considerations on Surgical Anatomy of the Carotid Bifurcation
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Adamantios Michalinos
2016-01-01
Full Text Available Surgical anatomy of carotid bifurcation is of unique importance for numerous medical specialties. Despite extensive research, many aspects such as precise height of carotid bifurcation, micrometric values of carotid arteries and their branches as their diameter, length, and degree of tortuosity, and variations of proximal external carotid artery branches are undetermined. Furthermore carotid bifurcation is involved in many pathologic processes, atheromatous disease being the commonest. Carotid atheromatous disease is a major predisposing factor for disabling and possibly fatal strokes with geometry of carotid bifurcation playing an important role in its natural history. Consequently detailed knowledge of various anatomic parameters is of paramount importance not only for understanding of the disease but also for design of surgical treatment, especially selection between carotid endarterectomy and carotid stenting. Carotid bifurcation paragangliomas constitute unique tumors with diagnostic accuracy, treatment design, and success of operative intervention dependent on precise knowledge of anatomy. Considering those, it becomes clear that selection and application of proper surgical therapy should consider anatomical details. Further research might ameliorate available treatment options or even lead to innovative ones.
Directory of Open Access Journals (Sweden)
Omid Arjmandi-Tash
2012-12-01
Full Text Available Introduction: Atherosclerosis is a focal disease that susceptibly forms near bifurcations, anastomotic joints, side branches, and curved vessels along the arterial tree. In this study, pulsatile blood flow in a bifurcation model with a non-planar branch is investigated. Methods: Wall shear stress (WSS distributions along generating lines on vessels for different bifurcation angles are calculated during the pulse cycle. Results: The WSS at the outer side of the bifurcation plane vanishes especially for higher bifurcation angles but by increasing the bifurcation angle low WSS region squeezes. At the systolic phase there is a high possibility of formation of a separation region at the outer side of bifurcation plane for all the cases. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these peaks drop as bifurcation angle is increased. Conclusion: It was found that non-planarity of the daughter vessel lowers the minimum WSS at the outer side of the bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky.
Shin, Susanna Hewon; Starnes, Benjamin Ware
2017-11-01
Up to 40% of abdominal aortic aneurysms (AAAs) have coexistent iliac artery aneurysms (IAAs). In the past, successful endovascular repair required internal iliac artery (IIA) embolization, which can lead to pelvic or buttock ischemia. This study describes a technique that uses a readily available solution with a minimally altered off-the-shelf bifurcated graft in the IAA to maintain IIA perfusion. From August 2009 to May 2015, 14 patients with AAAs and coexisting IAAs underwent repair with a bifurcated-bifurcated approach. A 22-mm or 24-mm bifurcated main body device was used in the IAA with extension of the "contralateral" limb into the IIA. Intraoperative details including operative time, fluoroscopy time, and contrast agent use were recorded. Outcome measures assessed were operative technical success and a composite outcome measure of IIA patency, freedom from reintervention, and clinically significant endoleak at 1 year. Fourteen patients underwent bifurcated-bifurcated repair during the study period. Technical success was achieved in 93% of patients, with successful treatment of the AAA and IAA and preservation of flow to at least one IIA. The procedure was performed with a completely percutaneous bilateral femoral approach in 92% of patients. Three patients had a type II endoleak on initial follow-up imaging, but none were clinically significant. There were no cases of bowel ischemia or erectile dysfunction. One patient had buttock claudication ipsilateral to IIA coil embolization (contralateral to bifurcated iliac repair and preserved IIA) that resolved by 6-month follow-up. Two patients required reinterventions. One patient presented to his first follow-up visit on postoperative day 25 with thrombosis of the right external iliac limb ipsilateral to the bifurcated iliac repair, which was successfully treated with thrombectomy and stenting of the limb. This same patient presented at 83 months with growth of the preserved IIA to 3.9 cm and underwent coil
Noisy zigzag transition, fluctuations, and thermal bifurcation threshold
Delfau, Jean-Baptiste; Coste, Christophe; Saint Jean, Michel
2013-06-01
We study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory.
Local bifurcation of electrohydrodynamic waves on a conducting fluid
Lin, Zhi; Zhu, Yi; Wang, Zhan
2017-03-01
We are concerned with progressive waves propagating on a two-dimensional conducting fluid when a uniform electric field is applied in the direction perpendicular to the undisturbed free surface. The competing effects of gravity, surface tension, and electrically induced forces are investigated using both analytical and numerical techniques for an inviscid and incompressible fluid flowing irrotationally. We simplify the full Euler equations by expanding and truncating the Dirichlet-Neumann operators in the Hamiltonian formulation of the problem. The numerical results show that when the electric parameter is in a certain range, the bifurcation structure near the minimum of the phase speed is rich with Stokes, solitary, generalized solitary, and dark solitary waves. In addition to symmetric solutions, asymmetric solitary waves featuring a multi-packet structure are found to occur along a branch of asymmetric generalized solitary waves that itself bifurcates from Stokes waves of finite amplitude. The detailed bifurcation diagrams, together with typical wave profiles, are presented.
Spike-train bifurcation scaling in two coupled chaotic neurons
Energy Technology Data Exchange (ETDEWEB)
Huerta, R.; Rabinovich, M.I. [Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402 (United States); Abarbanel, H.D. [Department of Physics and Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093-0402 (United States); Bazhenov, M. [Howard Hughes Medical Institute, The Salk Institute, Computational Neurobiology Laboratory, La Jolla, California 92037 (United States)
1997-03-01
We investigate the variation of the out-of-phase periodic rhythm produced by two chaotic neurons {bold (}Hindmarsh-Rose neurons [J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London B {bold 221}, 87 (1984)]{bold )} coupled by electrical and reciprocally synaptic connections. The exploration of a two-parametric bifurcation diagram, as a function of the strength of the electrical and inhibitory coupling, reveals that the periodic rhythms associated to the limit cycles bounded by saddle-node bifurcations, undergo a strong variation as a function of small changes of electrical coupling. We found that there is a scaling law for the bifurcations of the limit cycles as a function of the strength of both couplings. From the functional point of view of this mixed typed of coupling, the small variation of electrical coupling provides a high sensitivity for period regulation inside the regime of out-of-phase synchronization. {copyright} {ital 1997} {ital The American Physical Society}
Dynamical systems V bifurcation theory and catastrophe theory
1994-01-01
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of w...
Bifurcations in the optimal elastic foundation for a buckling column
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Rayneau-Kirkhope, Daniel, E-mail: ppxdr@nottingham.ac.u [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom); Farr, Robert [Unilever R and D, Olivier van Noortlaan 120, AT3133, Vlaardingen (Netherlands); London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London (United Kingdom); Ding, K. [Department of Physics, Fudan University, Shanghai, 200433 (China); Mao, Yong [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
2010-12-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
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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
Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge.
Li, Juan; Song, Yongzhong; Wan, Hui
2017-04-01
To study the impacts of toxin produced by phytoplankton and refuges provided for phytoplankton on phytoplankton-zooplankton interactions in lakes, we establish a simple phytoplankton-zooplankton system with Holling type II response function. The existence and stability of positive equilibria are discussed. Bifurcation analyses are given by using normal form theory which reveals reasonably the mechanisms and nonlinear dynamics of the effects of toxin and refuges, including Hopf bifurcation, Bogdanov-Takens bifurcation of co-dimension 2 and 3. Numerical simulations are carried out to intuitively support our analytical results and help to explain the observed biological behaviors. Our findings finally show that both phytoplankton refuge and toxin have a significant impact on the occurring and terminating of algal blooms in freshwater lakes.
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Lóczi, Lajos
2015-01-07
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.
Bifurcation in tidal streams of Sagittarius Dwarf Galaxy: Numerical Simulations
Camargo Camargo, Y.; Casas-Miranda, R.
2018-01-01
We performed N-body simulations between Sagittarius dwarf galaxy and the Milky Way. The Sagittarius galaxy is modeled with two components: dark matter halo and stellar disc. The Milky Way is modeled with three components: dark matter halo, stellar disc and bulge. The goal of this work is to reproduce the bifurcations in the tidal tails and the physical properties of the Sagittarius dwarf galaxy. For it, we simulated the interaction of the progenitor of this galaxy with the Milky Way. Although bifurcations could be reproduced, the position and physical properties of Sagittarius remnant could not be obtained simultaneously.
Wall shear stress evolution in carotid artery bifurcation
Bernad, S. I.; Bosioc, A. I.; Totorean, A. F.; Petre, I.; Bernad, E. S.
2017-07-01
The steady flow in an anatomically realistic human carotid bifurcation was simulated numerically. Main parameters such as wall shear stress (WSS), velocity profiles and pressure distributions are investigated in the carotid artery, namely in bifurcation and sinusoidal enlargement regions. Flow in the carotid sinus is dominated by a single secondary vortex motion accompanied by a strong helical flow. This type of flow is induced primarily by the curvature and asymmetry of the in vivo geometry. Low wall shear stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb.
A gravel-sand bifurcation : a simple model and the stability of the equilibrium states
Schielen, Ralph M.J.; Blom, Astrid
2017-01-01
A river bifurcation, can be found in, for instance, a river delta, in braided or anabranching reaches, and in manmade side channels in restored river reaches. Depending on the partitioning of water and sediment over the bifurcating branches, the bifurcation develops toward (a) a stable state with
Iterative Controller Tuning for Process with Fold Bifurcations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
2007-01-01
Processes involving fold bifurcation are notoriously difficult to control in the vicinity of the fold where most often optimal productivity is achieved . In cases with limited process insight a model based control synthesis is not possible. This paper uses a data driven approach with an improved...
Bifurcation diagrams in relation to synchronization in chaotic systems
Indian Academy of Sciences (India)
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 ...
Improved homoclinic predictor for Bogdanov-Takens bifurcation
Kuznetsov, Yuri; Meijer, Hil; Al Hdaibat, Bashir; Govaerts, Willy
2014-01-01
An improved homoclinic predictor at a generic codim 2 Bogdanov-Takens (BT) bifucation is derived. We use the classical ‘blow-up’ technique to reduce the canonical smooth normal form near a generic BT bifurcation to a perturbed Hamiltonian system. With a simple perturbation method, we derive explicit
Coronary bifurcation lesions treated with simple or complex stenting
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; de Belder, Adam J
2016-01-01
AIMS: Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data...
Bifurcations of phase portraits of pendulum with vibrating suspension point
Neishtadt, A. I.; Sheng, K.
2017-06-01
We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two parameters. We give a complete description of bifurcations of phase portraits of this averaged system.
AEROSOL TRANSPORT AND DEPOSITION IN SEQUENTIALLY BIFURCATING AIRWAYS
Deposition patterns and efficiencies of a dilute suspension of inhaled particles in three-dimensional double bifurcating airway models for both in-plane and 90 deg out-of-plane configurations have been numerically simulated assuming steady, laminar, constant-property air flow wit...
Bifurcations of phase portraits of pendulum with vibrating suspension point
Neishtadt, Anatoly; Sheng, Kaicheng
2016-01-01
We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two parameters. We give complete description of bifurcations of phase portraits of this averaged system.
Percutaneous transluminal angioplasty and stenting for carotid bifurcation stenosis
Vos, J.A.
2009-01-01
Carotid Endartectomy (CEA) has been proven to benefit patients with carotid bifurcation stenosis. For patients unfit for this therapy an alternative has been developed, namely Carotid Angioplasty and Stenting (CAS). No anesthesia or neck dissection is necessary in this procedure. In this thesis
Low-crosstalk bifurcation detectors for coupled flux qubits
De Groot, P.C.; Van Loo, A.F.; Lisenfeld, J.; Schouten, R.N.; Lupa?cu, A.; Harmans, C.J.P.M.; Mooij, J.E.
2010-01-01
We present experimental results on the crosstalk between two ac-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning
Numerical computation of bifurcations in large equilibrium systems in MATLAB.
Bindel, David; Friedman, Mark; Govaerts, Willy; Hughes, Jeremy; Kuznetsov, Yuri
2014-01-01
The Continuation of Invariant Subspaces (CIS) algorithm produces a smoothly-varying basis for an invariant subspace R(s) of a parameter-dependent matrix A(s). We have incorporated the CIS algorithm into Cl_matcont, a Matlab package for the study of dynamical systems and their bifurcations. Using
Perturbed period-doubling bifurcation. II. Experiments on Josephson junctions
DEFF Research Database (Denmark)
Eriksen, Gert Friis; Hansen, Jørn Bindslev
1990-01-01
We present experimental results on the effect of periodic perturbations on a driven, dynamic system that is close to a period-doubling bifurcation. In the preceding article a scaling law for the change of stability of such a system was derived for the case where the perturbation frequency ω...
Post-Treatment Hemodynamics of a Basilar Aneurysm and Bifurcation
Energy Technology Data Exchange (ETDEWEB)
Ortega, J; Hartman, J; Rodriguez, J; Maitland, D
2008-01-16
Aneurysm re-growth and rupture can sometimes unexpectedly occur following treatment procedures that were initially considered to be successful at the time of treatment and post-operative angiography. In some cases, this can be attributed to surgical clip slippage or endovascular coil compaction. However, there are other cases in which the treatment devices function properly. In these instances, the subsequent complications are due to other factors, perhaps one of which is the post-treatment hemodynamic stress. To investigate whether or not a treatment procedure can subject the parent artery to harmful hemodynamic stresses, computational fluid dynamics simulations are performed on a patient-specific basilar aneurysm and bifurcation before and after a virtual endovascular treatment. The simulations demonstrate that the treatment procedure produces a substantial increase in the wall shear stress. Analysis of the post-treatment flow field indicates that the increase in wall shear stress is due to the impingement of the basilar artery flow upon the aneurysm filling material and to the close proximity of a vortex tube to the artery wall. Calculation of the time-averaged wall shear stress shows that there is a region of the artery exposed to a level of wall shear stress that can cause severe damage to endothelial cells. The results of this study demonstrate that it is possible for a treatment procedure, which successfully excludes the aneurysm from the vascular system and leaves no aneurysm neck remnant, to elevate the hemodynamic stresses to levels that are injurious to the immediately adjacent vessel wall.
The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
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Farsad, Vanda
2017-06-14
This thesis is concerned with ''N pairs of symplectic fermions'' which are examples of logarithmic conformal field theories in two dimensions. The mathematical language of two-dimensional conformal field theories (on Riemannian surfaces of genus zero) are vertex operator algebras. The representation category of the even part of the symplectic fermion vertex operator super-algebra Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category. This determines an isomorphism of projective representations between two SL(2,Z)-actions associated to V{sub ev}. The first action is obtained by modular transformations on the space of so-called pseudo-trace functions of a vertex operator algebra. For V{sub ev} this was developed by A.M.Gaberdiel and I. Runkel. For the action one uses that Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category and thus carries a projective SL(2,Z)-action on a certain Hom-space [Ly1,Ly2,KL]. To do so we calculate the SL(2,Z)-action on the representation category of a general factorisable quasi-Hopf algebras. Then we show that Rep V{sub ev} is conjecturally ribbon equivalent to Rep Q, for Q a factorisable quasi-Hopf algebra, and calculate the SL(2,Z)-action explicitly on Rep Q. The result is that the two SL(2,Z)-action indeed agree. This poses the first example of such comparison for logarithmic conformal field theories.
Directory of Open Access Journals (Sweden)
Kirillov O.N.
2007-01-01
Full Text Available Paradoxical effect of small dissipative and gyroscopic forces on the stability of a linear non-conservative system, which manifests itself through the unpredictable at first sight behavior of the critical non-conservative load, is studied. By means of the analysis of bifurcation of multiple roots of the characteristic polynomial of the non-conservative system, the analytical description of this phenomenon is obtained. As mechanical examples two systems possessing friction induced oscillations are considered: a mass sliding over a conveyor belt and a model of a disc brake describing the onset of squeal during the braking of a vehicle.
Bifurcation and Feedback Control of an Exploited Prey-Predator System
Directory of Open Access Journals (Sweden)
Uttam Das
2014-01-01
Full Text Available This paper makes an attempt to highlight a differential algebraic model in order to investigate the dynamical behavior of a prey-predator system due to the variation of economic interest of harvesting. In this regard, it is observed that the model exhibits a singularity induced bifurcation when economic profit is zero. For the purpose of stabilizing the proposed model at the positive equilibrium, a state feedback controller is therefore designed. Finally, some numerical simulations are carried out to show the consistency with theoretical analysis and to illustrate the effectiveness of the proposed controller.
Fuzzy Responses and Bifurcations of a Forced Duffing Oscillator with a Triple-Well Potential
Hong, Ling; Jiang, Jun; Sun, Jian-Qiao
Responses and bifurcations of a forced triple-well potential system with fuzzy uncertainty are studied by means of the Fuzzy Generalized Cell Mapping (FGCM) method. A rigorous mathematical foundation of the FGCM is established as a discrete representation of the fuzzy master equation for the possibility transition of continuous fuzzy processes. The FGCM offers a very effective approach for solutions to the fuzzy master equation based on the min-max operator of fuzzy logic. A fuzzy response is characterized by its topology in the state space and its possibility measure of membership distribution functions (MDFs). A fuzzy bifurcation implies a sudden change both in the topology and in the MDFs. The response topology is obtained based on the qualitative analysis of the FGCM involving the Boolean operation of 0 and 1. The MDFs are determined by the quantitative analysis of the FGCM with the min-max calculations. With an increase of the intensity of fuzzy noise, noise-induced escape from each of the potential wells defines two types of bifurcations, namely catastrophe and explosion. This paper focuses on the evolution of transient and steady-state MDFs of the fuzzy response. As the intensity of fuzzy noise increases, steady-state MDFs cover a bigger area in the state space with higher membership values spreading out to a larger area. The previous conjectures are further confirmed that steady-state MDFs are dependent on initial possibility distributions due to the nonsmooth and nonlinear nature of the min-max operation. It is found that as time goes on, transient MDFs spread around three potential wells. The evolutionary orientation of transient MDFs aligns with unstable invariant manifolds leading to stable invariant sets. Two examples of additive and multiplicative fuzzy noise are given.
Luzzatto-Fegiz, Paolo
2011-11-01
Steady fluid solutions play a special role in the dynamics of a flow: stable states may be realized in practice, while unstable ones may act as attractors. Unfortunately, determining stability is often a process far more laborious than finding steady states; indeed, even for simple vortex or wave flows, stability properties have often been the subject of debate. We consider here a stability idea originating with Lord Kelvin (1876), which involves using the second variation of the energy, δ2 E , to establish bounds on a perturbation. However, for numerically obtained flows, computing δ2 E explicitly is often not feasible. To circumvent this issue, Saffman & Szeto (1980) proposed an argument linking changes in δ2 E to turning points in a bifurcation diagram, for families of steady flows. Later work has shown that this argument is unreliable; the two key issues are associated with the absence of a formal turning-point theory, and with the inability to detect bifurcations (Dritschel 1995, and references therein). In this work, we build on ideas from bifurcation theory, and link turning points in a velocity-impulse diagram to changes in δ2 E ; in addition, this diagram delivers the direction of the change of δ2 E , thereby providing information as to whether stability is gained or lost. To detect hidden solution branches, we introduce to these fluid problems concepts from imperfection theory. The resulting approach, involving ``imperfect velocity-impulse'' diagrams, leads us to new and surprising results for a wide range of fundamental vortex and wave flows; we mention here the calculation of the first steady vortices without any symmetry, and the uncovering of the complete solution structure for vortex pairs. In addition, we find precise agreement with available results from linear stability analysis. Doctoral work advised by C.H.K. Williamson at Cornell University.
Bondarenko, V. E.; Doedel, E. J.; Rasmusson, R. L.
2000-02-01
We applied bifurcation analysis to the Luo-Rudy model of the guinea pig cardiac ventricular cell to investigate the behavior of repolarization in response to a simulated form of inherited arrhythmia, long QT syndrome. In this paper, we simulate pathological changes in cardiac repolarization through reductions in IKr. Decreased expression of this current has been linked to an inherited form of long QT syndrome which results in a high mortality, presumably due to sudden cardiac death from ventricular fibrillation.
Bifurcations and Crises in a Shape Memory Oscillator
Directory of Open Access Journals (Sweden)
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.
Local bifurcations in differential equations with state-dependent delay.
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
Power-dependent internal loss in Josephson bifurcation amplifiers
Watanabe, Michio; Inomata, Kunihiro; Yamamoto, Tsuyoshi; Tsai, Jaw-Shen
2009-11-01
We have studied nonlinear superconducting resonators: λ/2 coplanar-waveguide (CPW) resonators with Josephson junctions (JJs) placed in the middle and λ/4 CPW resonators terminated by JJs, which can be used for the qubit readout as “bifurcation amplifiers.” The nonlinearity of the resonators arises from the Josephson junctions, and because of the nonlinearity, the resonators with appropriate parameters are expected to show a hysteretic response to the frequency sweep, or “bifurcation,” when they are driven with a sufficiently large power. We designed and fabricated resonators whose resonant frequencies were around 10 GHz. We characterized the resonators at low temperatures, Tresonators with increasing drive power in the relevant power range. As a possible origin of the power-dependent loss, the quasiparticle channel of conductance of the JJs is discussed.
Local bifurcations in differential equations with state-dependent delay
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
Ferona, Aaron M.; Camley, Robert E.
2017-03-01
The behavior of a uniformly magnetized domain of ellipsoidal shape subject to a static external field and oscillatory external driving field is analyzed near bifurcation events. The analysis includes the effects of both linear and circularly polarized driving fields and is performed using numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equation. Under a linearly polarized driving field, the LLG equation is a nonautonomous differential equation which can lead to complex magnetization motions, such as bistability, multiperiodic orbits, quasiperiodicity, and chaos. Under a circularly polarized driving field, the LLG equation can be written in autonomous form by transforming to the frame rotating with the driving field. The autonomous nature allows one to perform a fixed-point analysis of the system for select demagnetization factors. Similarities and differences between the driven systems are highlighted through bifurcation diagrams, phase portraits, basins of attraction, and Lyapunov exponents. Magnetization switching, prolonged transients, quasiperiodicity, and chaos are observed with both linearly and circularly polarized driving fields in the magnetic systems investigated.
Application of the bifurcation method to the modified Boussinesq equation
Directory of Open Access Journals (Sweden)
Shaoyong Li
2014-08-01
Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
Time-Periodic Einstein-Klein-Gordon Bifurcations of Kerr
Chodosh, Otis; Shlapentokh-Rothman, Yakov
2017-12-01
We construct one-parameter families of solutions to the Einstein-Klein-Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-periodic. An immediate corollary is that for these Klein-Gordon masses, the Kerr family is not asymptotically stable as a solution to the Einstein-Klein-Gordon equations.
Bifurcation of solutions of nonlinear Sturm–Liouville problems
Directory of Open Access Journals (Sweden)
Gulgowski Jacek
2001-01-01
Full Text Available A global bifurcation theorem for the following nonlinear Sturm–Liouville problem is given Moreover we give various versions of existence theorems for boundary value problems The main idea of these proofs is studying properties of an unbounded connected subset of the set of all nontrivial solutions of the nonlinear spectral problem , associated with the boundary value problem , in such a way that .
Stability and bifurcation for Marchuk's model of an immune system
Marzuki, Ira Syazwani Mohamad; Roslan, Ummu'Atiqah Mohd
2017-08-01
The investigation of an immune system has long been and will continue to be one of dominant themes in both ecology and biology due to its importance. In this paper, we consider Marchuk's model of an immune system where this model is governed by a system of three differential equations with time. This model has two equilibrium states which are healthy state and chronic state. It is healthy state when the antigen reproduction is small while chronic state is when antigen reproduction rate is large. The objectives of this paper are to analyse the stability of this model, to summarize this stability using bifurcation diagram and to discuss interaction between the healthy and chronic states at stationary solution. The methods involved are stability theory and bifurcation theory. Our results show that healthy states are saddle and only one chronic state is asymptotically stable for a region of parameter considered. For the bifurcation's case, as we increase the value of a parameter in this model, the chronic state shows that there are increment in the number of antigen, plasma cell and the antibody production.
Bifurcation in autonomous and nonautonomous differential equations with discontinuities
Akhmet, Marat
2017-01-01
This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for beginners and experts in the field. For the former group o...
Intermittency and bifurcation in SEPICs under voltage-mode control
Liu, Fang
2010-08-01
A stroboscopic map for voltage-controlled single ended primary inductor converter (SEPIC) with pulse width modulation (PWM) is presented, where low-frequency oscillating phenomena such as quasi-periodic and intermittent quasi-periodic bifurcations occurring in the system are captured by numerical and experimental methods. According to bifurcation diagrams and nonlinear dynamical theory, the characteristics of the low-frequency oscillation and the mechanism for the appearance of the low-frequency oscillation are investigated. It is shown that as the controller parameter varies, the change in the conduction mode takes place from the continuous conduction mode (CCM) under the originally stable period one and high periodic orbits to the intermittent changes between CCM and discontinuous conduction mode (DCM), which may be related to the losing stability of the system and brought the system to exhibiting low-frequency oscillating behaviour in the time domain. Moreover, the occurrence of the intermittent quasi-periodic oscillation reflects that the system undergoes a Neimark-Sacker bifurcation.
Reverse bifurcation and fractal of the compound logistic map
Wang, Xingyuan; Liang, Qingyong
2008-07-01
The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.
Bifurcation control for the Zakharov-Kusnetsov equation
Energy Technology Data Exchange (ETDEWEB)
Maccari, Attilio, E-mail: solitone@yahoo.i [Via Alfredo Casella 3, 00013 Mentana (Rome) (Italy)
2010-05-01
We consider the bifurcation control for the forced Zakharov-Kusnetsov (ZK) equation by means of delay feedback linear control terms. Using a perturbation method, we obtain two slow flow equations on the amplitude and phase of the response as well as external force-response and frequency-response curves for the fundamental resonance. We observe in the resonance response for the uncontrolled system a saddle-center bifurcation, jumps and hysteresis phenomena and, using energy considerations, we show the existence of closed orbits of the slow flow equations. A limit cycle corresponds to a two-period quasi-periodic modulated motion for the ZK equation and we demonstrate that, in certain cases, a second low frequency appears in addition to the forcing frequency and then stable two-period quasi-periodic motions are present with amplitudes depending on the initial conditions. The value of the low frequency depends on the amplitude of the external excitation. Subsequently, we compare the uncontrolled and controlled systems and, to reduce the amplitude peak of the fundamental resonance and to remove saddle-center bifurcations and two-period quasi-periodic motions, we find appropriate choices of the feedback gains and time delay.
Bifurcation of solutions of separable parameterized equations into lines
Directory of Open Access Journals (Sweden)
Yun-Qiu Shen
2010-09-01
Full Text Available Many applications give rise to separable parameterized equations of the form $A(y, muz+b(y, mu=0$, where $y in mathbb{R}^n$, $z in mathbb{R}^N$ and the parameter $mu in mathbb{R}$; here $A(y, mu$ is an $(N+n imes N$ matrix and $b(y, mu in mathbb{R}^{N+n}$. Under the assumption that $A(y,mu$ has full rank we showed in [21] that bifurcation points can be located by solving a reduced equation of the form $f(y, mu=0$. In this paper we extend that method to the case that $A(y,mu$ has rank deficiency one at the bifurcation point. At such a point the solution curve $(y,mu,z$ branches into infinitely many additional solutions, which form a straight line. A numerical method for reducing the problem to a smaller space and locating such a bifurcation point is given. Applications to equilibrium solutions of nonlinear ordinary equations and solutions of discretized partial differential equations are provided.
Grundeken, Maik J; Lesiak, Maciej; Asgedom, Solomon; Garcia, Eulogio; Bethencourt, Armando; Norell, Michael S; Damman, Peter; Woudstra, Pier; Koch, Karel T; Vis, M Marije; Henriques, Jose P; Tijssen, Jan G; Onuma, Yoshinobu; Foley, David P; Bartorelli, Antonio L; Stella, Pieter R; de Winter, Robbert J; Wykrzykowska, Joanna J
2014-03-01
We evaluated differences in clinical outcomes between patients who underwent final kissing balloon inflation (FKBI) and patients who did not undergo FKBI in bifurcation treatment using the Tryton Side Branch Stent (Tryton Medical, Durham, North Carolina, USA). Clinical outcomes were defined as target vessel failure (composite of cardiac death, any myocardial infarction and clinically indicated target vessel revascularisation), cardiac death, myocardial infarction (MI), clinically indicated target vessel revascularisation and stent thrombosis. Cumulative event rates were estimated using the Kaplan-Meier method. A multivariable logistic regression analysis was performed to evaluate which factors were potentially associated with FKBI performance. Follow-up data was available in 717 (96%) patients with a median follow-up of 190 days. Cardiac death at 1 year occurred more often in the no-FKBI group (1.7% vs 4.6%, respectively, p=0.017), although this difference was no longer observed after excluding patients presenting with ST segment elevation MI (1.6% vs 3.3%, p=0.133). No significant differences were observed concerning the other clinical outcomes. One-year target vessel failure rates were 10.1% in the no-FKBI group and 9.2% in the FKBI group (p=0.257). Multivariable logistic regression analysis identified renal dysfunction, ST segment elevation MI as percutaneous coronary intervention indication, narrow (<30°) bifurcation angle and certain stent platforms as being independently associated with unsuccessful FKBI. A lower cardiac death rate was observed in patients in whom FKBI was performed compared with a selection of patients in whom FKBI could not be performed, probably explained by an unbalance in the baseline risk profile of the patients. No differences were observed regarding the other clinical outcomes.
Harikrishnan, K. P.
2018-02-01
We consider the simplest model in the family of discrete predator-prey system and introduce for the first time an environmental factor in the evolution of the system by periodically modulating the natural death rate of the predator. We show that with the introduction of environmental modulation, the bifurcation structure becomes much more complex with bubble structure and inverse period doubling bifurcation. The model also displays the peculiar phenomenon of coexistence of multiple limit cycles in the domain of attraction for a given parameter value that combine and finally gets transformed into a single strange attractor as the control parameter is increased. To identify the chaotic regime in the parameter plane of the model, we apply the recently proposed scheme based on the correlation dimension analysis. We show that the environmental modulation is more favourable for the stable coexistence of the predator and the prey as the regions of fixed point and limit cycle in the parameter plane increase at the expense of chaotic domain.
The effect of incidence function in backward bifurcation for malaria model with temporary immunity.
Roop-O, Pariyaporn; Chinviriyasit, Wirawan; Chinviriyasit, Settapat
2015-07-01
This paper addresses the effect of the choice of the incidence function for the occurrence of backward bifurcation in two malaria models, namely, malaria model with standard incidence rate and malaria model with nonlinear incidence rate. Rigorous qualitative analyzes of the models show that the malaria model with standard incidence rate exhibits the phenomenon of backward bifurcation whenever a certain epidemiological threshold, known as the basic reproduction number, is less than unity. The epidemiological consequence of this phenomenon is that the classical epidemiological requirement of making the reproductive number less than unity is no longer sufficient, although necessary, for effectively controlling the spread of malaria in a community. For the malaria model with nonlinear incidence rate, it is shown that this phenomenon does not occur and the disease-free equilibrium of the model is globally-asymptotically stable whenever the reproduction number is less than unity. When the associated basic reproduction number is greater than unity, the models have a unique endemic equilibrium which is globally asymptotically stable under certain conditions. The sensitivity analysis based on the mathematical technique has been performed to determine the importance of the epidemic model parameters in making strategies for controlling malaria. Copyright © 2015. Published by Elsevier Inc.
Detecting space-time alternating biological signals close to the bifurcation point.
Jia, Zhiheng; Bien, Harold; Entcheva, Emilia
2010-02-01
Time-alternating biological signals, i.e., alternans, arise in variety of physiological states marked by dynamic instabilities, e.g., period doubling. Normally, a sequence of large-small-large transients, they can exhibit variable patterns over time and space, including spatial discordance. Capture of the early formation of such alternating regions is challenging because of the spatiotemporal similarities between noise and the small-amplitude alternating signals close to the bifurcation point. We present a new approach for automatic detection of alternating signals in large noisy spatiotemporal datasets by exploiting quantitative measures of alternans evolution, e.g., temporal persistence, and by preserving phase information. The technique specifically targets low amplitude, relatively short alternating sequences and is validated by combinatorics-derived probabilities and empirical datasets with white noise. Using high-resolution optical mapping in live cardiomyocyte networks, exhibiting calcium alternans, we reveal for the first time early fine-scale alternans, close to the noise level, which are linked to the later formation of larger regions and evolution of spatially discordant alternans. This robust method aims at quantification and better understanding of the onset of cardiac arrhythmias and can be applied to general analysis of space-time alternating signals, including the vicinity of the bifurcation point.
Schomerus, H
1997-01-01
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. We derive uniform approximations to be used in semiclassical trace formulas and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction catastrophe integrals.
National Research Council Canada - National Science Library
Luo, Kang; Yi, Hong-Liang; Tan, He-Ping
2014-01-01
Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct...
Nieuwenhuys, Rudolf; Broere, Cees A J
2017-01-01
During the period extending from 1910 to 1970, Oscar and Cécile Vogt and their numerous collaborators published a large number of myeloarchitectonic studies on the cortex of the various lobes of the human cerebrum. In a previous publication [Nieuwenhuys et al (Brain Struct Funct 220:2551-2573, 2015; Erratum in Brain Struct Funct 220: 3753-3755, 2015)], we used the data provided by the Vogt-Vogt school for the composition of a myeloarchitectonic map of the entire human neocortex. Because these data were derived from many different brains, a standard brain had to be introduced to which all data available could be transferred. As such the Colin 27 structural scan, aligned to the MNI305 template was selected. The resultant map includes 180 myeloarchitectonic areas, 64 frontal, 30 parietal, 6 insular, 17 occipital and 63 temporal. Here we present a supplementary map in which the overall density of the myelinated fibers in the individual architectonic areas is indicated, based on a meta-analysis of data provided by Adolf Hopf, a prominent collaborator of the Vogts. This map shows that the primary sensory and motor regions are densely myelinated and that, in general, myelination decreases stepwise with the distance from these primary regions. The map also reveals the presence of a number of heavily myelinated formations, situated beyond the primary sensory and motor domains, each consisting of two or more myeloarchitectonic areas. These formations were provisionally designated as the orbitofrontal, intraparietal, posterolateral temporal, and basal temporal dark clusters. Recently published MRI-based in vivo myelin content mappings show, with regard to the primary sensory and motor regions, a striking concordance with our map. As regards the heavily myelinated clusters shown by our map, scrutiny of the current literature revealed that correlates of all of these clusters have been identified in in vivo structural MRI studies and appear to correspond either entirely or
Energy Technology Data Exchange (ETDEWEB)
Kolesnikov, R.A.; Krommes, J.A.
2005-09-22
The collisionless limit of the transition to ion-temperature-gradient-driven plasma turbulence is considered with a dynamical-systems approach. The importance of systematic analysis for understanding the differences in the bifurcations and dynamics of linearly damped and undamped systems is emphasized. A model with ten degrees of freedom is studied as a concrete example. A four-dimensional center manifold (CM) is analyzed, and fixed points of its dynamics are identified and used to predict a ''Dimits shift'' of the threshold for turbulence due to the excitation of zonal flows. The exact value of that shift in terms of physical parameters is established for the model; the effects of higher-order truncations on the dynamics are noted. Multiple-scale analysis of the CM equations is used to discuss possible effects of modulational instability on scenarios for the transition to turbulence in both collisional and collisionless cases.
A note on tilted Bianchi type VIh models: the type III bifurcation
Coley, A. A.; Hervik, S.
2008-10-01
In this note we complete the analysis of Hervik, van den Hoogen, Lim and Coley (2007 Class. Quantum Grav. 24 3859) of the late-time behaviour of tilted perfect fluid Bianchi type III models. We consider models with dust, and perfect fluids stiffer than dust, and eludicate the late-time behaviour by studying the centre manifold which dominates the behaviour of the model at late times. In the dust case, this centre manifold is three-dimensional and can be considered a double bifurcation as the two parameters (h and γ) of the type VIh model are varied. We therefore complete the analysis of the late-time behaviour of tilted ever-expanding Bianchi models of types I VIII.
Phylogenetic Evidence for H2 based Electron Bifurcation In Early Life
Adams, M. W.; Boyd, E. S.; Schut, G.; Peters, J.
2012-12-01
most simple forms of ATP production supporting life. This finding is consistent with phylogenetic analyses which indicate a close phylogenetic relationship between Ech/Eha and Nuo/Fpo, with [NiFe]-hydrogenase typically involved in H2 oxidation forming divergent lineages. This suggests that Ech/Eha are most likely to represent an ancestor of the Complex I family and the [NiFe]-hydrogenase family. A concatenation and phylogenetic analysis of the large and small subunits of Ech and Nuo was performed and and additional modules enabling coupling with CO2 (Eha), CO (Ech-CODH), and formate (Ech-Fdh) through H2-based electron bifurcation were overlaid on this phylogeny. The results suggest an origin for H2-based electron bifurcation via Ech/Eha among CO2 reducing hydrogenotrophic methanogenic Archaea or sulfur-reducing Archaea, with evolution towards coupling with formate and CO. These results provide insight into the evolutionary relationships between electron bifurcation-enabled ionic gradients capable of driving phosphorylation and electron transport-based phosphorylation. Moreover, these observations suggest that electron bifurcation may have been important in overcoming key metabolic bottlenecks and may have enabled life to access small energetic gradients to support metabolism on early Earth.
Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings
Jansons, Kalvis M.; Lythe, G. D.
1998-01-01
For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level ∈ and the rate of change of the parameter μ. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density, and last crossing time of zero are compared with results from numerical generation of paths.
Plastic bottle oscillator: Rhythmicity and mode bifurcation of fluid flow
Kohira, Masahiro I.; Magome, Nobuyuki; Kitahata, Hiroyuki; Yoshikawa, Kenichi
2007-01-01
The oscillatory flow of water draining from an upside-down plastic bottle with a thin pipe attached to its head is studied as an example of a dissipative structure generated under far-from-equilibrium conditions. Mode bifurcation was observed in the water/air flow: no flow, oscillatory flow, and counter flow were found when the inner diameter of the thin pipe was changed. The modes are stable against perturbations. A coupled two-bottle system exhibits either in-phase or anti-phase self-synchr...
Bifurcation in the chemotactic behavior of Physarum plasmodium
Shirakawa, Tomohiro; Gunji, Yukio-Pegio; Sato, Hiroshi; Tsubakino, Hiroto
2017-07-01
The plasmodium of true slime mold Physarum polycephalum is a unicellular and multinuclear giant amoeba. Since the cellular organism has some computational abilities, it is attracting much attention in the field of information science. However, previous studies have mainly focused on the optimization behavior of the plasmodium for a single-modality stimulus, and there are few studies on how the organism adapts to multi-modal stimuli. We stimulated the plasmodium with mixture of attractant and repellent stimuli, and we observed bifurcation in the chemotactic behavior of the plasmodium.
Experimental Bifurcation Analysis Using Control-Based Continuation
DEFF Research Database (Denmark)
Bureau, Emil; Starke, Jens
and unstable equilibria under variation of parameters. As a test case we demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator with hardening spring nonlinearity, controlled by electromagnetic actuators. The method...
Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa
Camacho, Erika T.; Radulescu, Anca; Wirkus, Stephen
2016-09-01
Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.
Experimental Bifurcation Analysis By Control-based Continuation - Determining Stability’
DEFF Research Database (Denmark)
Bureau, Emil; Santos, Ilmar; Thomsen, Jon Juel
2012-01-01
stable and unstable equilibrium states. We present the ongoing work of developing and applying the control-based continuation method to an experimental mechanical test-rig, consisting of a harmonically forced nonlinear impact oscillator controlled by electromagnetic actuators. Furthermore we propose...
Bifurcation Analysis of a Spatially Extended Laser with Optical Feedback
Green, K.; Krauskopf, B.; Marten, F.; Lenstra, D.
2009-01-01
Vertical cavity surface-emitting lasers (VCSELs) are a new type of semiconductor laser characterized by the spatial extent of their disk-shaped output apertures. As a result, a VCSEL supports several optical modes (patterns of light) transverse to the direction of light propagation. When any laser
Llibre, Jaume; Spinetti-Rivera, Mario; Colina-Morles, Eliezer
2015-06-01
This paper uses the qualitative theory of differential equations to analyse/design the dynamic behaviour of control systems. In particular, the Poincaré compactification and the Poincaré--Hopf theorem are used for analysing the local dynamics near the finite and infinite equilibrium points. As an application, a large signal characterisation of a Boost type power converter in closed loop, including its equilibrium/bifurcation points and its global dynamics, which depends upon the value of the load resistance, is studied.
Partitioning of red blood cell aggregates in bifurcating microscale flows
Kaliviotis, E.; Sherwood, J. M.; Balabani, S.
2017-03-01
Microvascular flows are often considered to be free of red blood cell aggregates, however, recent studies have demonstrated that aggregates are present throughout the microvasculature, affecting cell distribution and blood perfusion. This work reports on the spatial distribution of red blood cell aggregates in a T-shaped bifurcation on the scale of a large microvessel. Non-aggregating and aggregating human red blood cell suspensions were studied for a range of flow splits in the daughter branches of the bifurcation. Aggregate sizes were determined using image processing. The mean aggregate size was marginally increased in the daughter branches for a range of flow rates, mainly due to the lower shear conditions and the close cell and aggregate proximity therein. A counterintuitive decrease in the mean aggregate size was apparent in the lower flow rate branches. This was attributed to the existence of regions depleted by aggregates of certain sizes in the parent branch, and to the change in the exact flow split location in the T-junction with flow ratio. The findings of the present investigation may have significant implications for microvascular flows and may help explain why the effects of physiological RBC aggregation are not deleterious in terms of in vivo vascular resistance.
Dynamics of Surfactant Liquid Plugs at Bifurcating Lung Airway Models
Tavana, Hossein
2013-11-01
A surfactant liquid plug forms in the trachea during surfactant replacement therapy (SRT) of premature babies. Under air pressure, the plug propagates downstream and continuously divides into smaller daughter plugs at continuously branching lung airways. Propagating plugs deposit a thin film on airway walls to reduce surface tension and facilitate breathing. The effectiveness of SRT greatly depends on the final distribution of instilled surfactant within airways. To understand this process, we investigate dynamics of splitting of surfactant plugs in engineered bifurcating airway models. A liquid plug is instilled in the parent tube to propagate and split at the bifurcation. A split ratio, R, is defined as the ratio of daughter plug lengths in the top and bottom daughter airway tubes and studied as a function of the 3D orientation of airways and different flow conditions. For a given Capillary number (Ca), orienting airways farther away from a horizontal position reduced R due to the flow of a larger volume into the gravitationally favored daughter airway. At each orientation, R increased with 0.0005 < Ca < 0.05. This effect diminished by decrease in airways diameter. This approach will help elucidate surfactant distribution in airways and develop effective SRT strategies.
Bifurcation to forward flapping flight at intermediate Reynolds number.
Vandenberghe, Nicolas; Zhang, Jun; Childress, Stephen
2003-11-01
The locomotion of most fish and birds is realized by flapping wings or fins transverse to the direction of travel. According to early theoretical studies, a flapping wing translating at finite speed in an inviscid fluid experiences a propulsive force. In steady forward flight this thrust is balanced by drag. Such "lift-based mechanisms" of thrust production are characteristic of the Eulerian realm, where discrete vortical structures are shed. But, when the Reynolds number is small, viscous forces dominate and reciprocal flapping motions are ineffective. A flapping wing experiences a net drag and cannot be used to propel an organism. We have devised an experiment to bridge the two regimes, and to examine the transition to forward flight at intermediate Reynolds numbers. We study the dynamics of an horizontal wing that is flapped up and down and is free to move either forwards or backwards. This very simple kinematics emphasizes the demarcation between low and high Reynolds number because it is effective in the Eulerian realm but has no effect in the Stokesian realm. We show that flapping flight occurs abruptly as a symmetry breaking bifurcation at a critical flapping frequency. Beyond the bifurcation the forward speed increases linearly with the flapping frequency. The experiment establishes a clear demarcation between the different strategies of locomotion at large and small Reynolds number.
Prediction of fibre architecture and adaptation in diseased carotid bifurcations.
LENUS (Irish Health Repository)
Creane, Arthur
2011-12-01
Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.
Directory of Open Access Journals (Sweden)
Souayeh Saoussen
2014-01-01
Full Text Available The collective nonlinear dynamics of a coupled array of nanocantilevers is investigated while taking into account the main sources of nonlinearities. The amplitude and phase equations of this device, subject to parametric and internal resonances, are analytically derived by means of a multi-modal Galerkin discretization coupled with a multiscale analysis. Based on the steady-state solutions of these equations, the frequency responses are numerically computed for a two-beam array. The effects of different parameters are investigated and several dynamical aspects are confirmed by numerical simulations. Particularly, we have demonstrated that the bifurcation topology transfer is imposed by the first nanocantilever and it can be general to the collective nonlinear dynamics of the NEMS array.
Rusov, V; Vaschenko, V; Mihalys, O; Kosenko, S; Mavrodiev, S; Vachev, B
2008-01-01
The possible physical linkage between galactic cosmic rays intensity and the Earth's cloud cover is discussed using the analysis of the first indirect aerosol effect (Twomey effect) and its experimental representation as the dependence of average cloud droplet effective radius on aerosol index characterizing the aerosol concentration in the atmospheric air column of unit section. It is shown that the basic kinetic equation of the Earth's climate energy-balance model is described by the bifurcation equation (with respect to the temperature of the Earth's surface) in the form of fold catastrophe with two governing parameters defining the variations of insolation and Earth's magnetic field (or galactic cosmic rays intensity in the atmosphere), respectively. The principle of hierarchical climatic models construction, which consists in the structural invariance of balance equations of these models evolving on the different time scales, is described. It means that if the system of equations of multizonal weather mo...
Quantifying the role of noise on droplet decisions in bifurcating microchannels
Norouzi Darabad, Masoud; Vaughn, Mark; Vanapalli, Siva
2017-11-01
While many aspects of path selection of droplets flowing through a bifurcating microchannel have been studied, there are still unaddressed issues in predicting and controlling droplet traffic. One of the more important is understanding origin of aperiodic patterns. As a new tool to investigate this phenomena we propose monitoring the continuous time response of pressure fluctuations at different locations. Then we use time-series analysis to investigate the dynamics of the system. We suggest that natural system noise is the cause of irregularity in the traffic patterns. Using a mathematical model, we investigate the effect of noise on droplet decisions at the junction. Noise can be derived from different sources including droplet size variation, droplet spacing, and pump induced velocity fluctuation. By analyzing different situations we explain system behavior. We also investigate the ``memory'' of a microfluidic system in terms of the resistance to perturbations that quantify the allowable deviation in operating condition before the system changes state.
Detecting the onset of bifurcations and their precursors from noisy data
Energy Technology Data Exchange (ETDEWEB)
Omberg, Larsson [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Royal Institute of Technology (KTH), Stockholm, (Sweden); Dolan, Kevin [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Neiman, Alexander [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Moss, Frank [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States)
2000-05-01
We study the problem of the detection of noise-induced precursors of periodic motion instabilities in stochastic dynamical systems. In particular, we concentrate on the period-doubling bifurcation. We have developed a statistical method to detect the onset of bifurcations and their precursors based on the previously established topological recurrence technique. (c) 2000 The American Physical Society.
Generic Hopf–Neĭmark–Sacker bifurcations in feed-forward systems
Broer, Henk W.; Vegter, Gert
2008-01-01
We show that generic Hopf–Neĭmark–Sacker bifurcations occur in the dynamics of a large class of feed-forward coupled cell networks. To this end we present a framework for studying such bifurcations in parametrized families of perturbed forced oscillators near weak resonance points. Our approach is
$\\Delta I=4$ and $\\Delta I=8$ bifurcations in rotational bands of diatomic molecules
Bonatsos, Dennis; Lalazissis, G A; Drenska, S B; Minkov, N; Raychev, P P; Roussev, R P; Bonatsos, Dennis
1996-01-01
It is shown that the recently observed $\\Delta I=4$ bifurcation seen in superdeformed nuclear bands is also occurring in rotational bands of diatomic molecules. In addition, signs of a $\\Delta I=8$ bifurcation, of the same order of magnitude as the $\\Delta I=4$ one, are observed both in superdeformed nuclear bands and rotational bands of diatomic molecules.
Qualitatively different bifurcation scenarios observed in the firing of identical nerve fibers
Energy Technology Data Exchange (ETDEWEB)
Zheng Qiaohua; Liu Zhiqiang; Yang Minghao; Wu Xiaobo [College of Life Science, Shaanxi Normal University, Xi' an 710062 (China); Gu Huaguang [College of Life Science, Shaanxi Normal University, Xi' an 710062 (China)], E-mail: guhuaguang@263.net; Ren Wei [College of Life Science, Shaanxi Normal University, Xi' an 710062 (China)], E-mail: renwei1964@vip.sina.com
2009-01-26
This Letter reports various bifurcation scenarios, including period-adding bifurcations with chaos and those with stochastic firing patterns, generated by identical neural pacemakers. The scenarios are studied by properly adjusting two physiological parameters, one is 4-aminopyridine sensitive potassium conductance and the other is extracellular calcium concentration, in both experimentation and simulation.
The anatomy of the bifurcated neural spine and its occurrence within Tetrapoda.
Woodruff, D Cary
2014-09-01
Vertebral neural spine bifurcation has been historically treated as largely restrictive to sauropodomorph dinosaurs; wherein it is inferred to be an adaptation in response to the increasing weight from the horizontally extended cervical column. Because no extant terrestrial vertebrates have massive, horizontally extended necks, extant forms with large cranial masses were examined for the presence of neural spine bifurcation. Here, I report for the first time on the soft tissue surrounding neural spine bifurcation in a terrestrial quadruped through the dissection of three Ankole-Watusi cattle. With horns weighing up to a combined 90 kg, the Ankole-Watusi is unlike any other breed of cattle in terms of cranial weight and presence of neural spine bifurcation. Using the Ankole-Watusi as a model, it appears that neural spine bifurcation plays a critical role in supporting a large mobile weight adjacent to the girdles. In addition to neural spine bifurcation being recognized within nonavian dinosaurs, this vertebral feature is also documented within many members of temnospondyls, captorhinids, seymouriamorphs, diadectomorphs, Aves, marsupials, artiodactyls, perissodactyls, and Primates, amongst others. This phylogenetic distribution indicates that spine bifurcation is more common than previously thought, and that this vertebral adaptation has contributed throughout the evolutionary history of tetrapods. Neural spine bifurcation should now be recognized as an anatomical component adapted by some vertebrates to deal with massive, horizontal, mobile weights adjacent the girdles. © 2014 Wiley Periodicals, Inc.
Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters
DEFF Research Database (Denmark)
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2017-01-01
-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation...
Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation
Hesse, Janina; Schleimer, Jan-Hendrik; Schreiber, Susanne
2017-05-01
Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to induce even more drastic changes in synchronization than the BT transition. This result arises from a direct effect of the saddle-node-loop bifurcation on the limit cycle and hence spike dynamics. In contrast, the BT bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node-loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails an increase in synchronization range in pulse-coupled oscillators, such as neurons. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators.
Sun, Zhonghua; Chaichana, Thanapong
2017-10-01
To investigate the correlation between left coronary bifurcation angle and coronary stenosis as assessed by coronary computed tomography angiography (CCTA)-generated computational fluid dynamics (CFD) analysis when compared to the CCTA analysis of coronary lumen stenosis and plaque lesion length with invasive coronary angiography (ICA) as the reference method. Thirty patients (22 males, mean age: 59±6.9 years) with calcified plaques at the left coronary artery were included in the study with all patients undergoing CCTA and ICA examinations. CFD simulation was performed to analyze hemodynamic changes to the left coronary artery models in terms of wall shear stress, wall pressure and flow velocity, with findings correlated to the coronary stenosis and degree of bifurcation angle. Calcified plaque length was measured in the left coronary artery with diagnostic value compared to that from coronary lumen and bifurcation angle assessments. Of 26 significant stenosis at left anterior descending (LAD) and 13 at left circumflex (LCx) on CCTA, only 14 and 5 of them were confirmed to be >50% stenosis at LAD and LCx respectively on ICA, resulting in sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) of 100%, 52%, 49% and 100%. The mean plaque length was measured 5.3±3.6 and 4.4±1.9 mm at LAD and LCx, respectively, with diagnostic sensitivity, specificity, PPV and NPV being 92.8%, 46.7%, 61.9% and 87.5% for extensively calcified plaques. The mean bifurcation angle was measured 83.9±13.6º and 83.8±13.3º on CCTA and ICA, respectively, with no significant difference (P=0.98). The corresponding sensitivity, specificity, PPV and NPV were 100%, 78.6%, 84.2% and 100% based on bifurcation angle measurement on CCTA, 100%, 73.3%, 78.9% and 100% based on bifurcation angle measurements on ICA, respectively. Wall shear stress was noted to increase in the LAD and LCx models with significant stenosis and wider angulation (>80º), but
Stability analysis of an HIV/AIDS epidemic model with treatment
Cai, Liming; Li, Xuezhi; Ghosh, Mini; Guo, Baozhu
2009-07-01
An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number [real]0. If [real]01. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.
Targeted particle tracking in computational models of human carotid bifurcations.
Marshall, Ian
2011-12-01
A significant and largely unsolved problem of computational fluid dynamics (CFD) simulation of flow in anatomically relevant geometries is that very few calculated pathlines pass through regions of complex flow. This in turn limits the ability of CFD-based simulations of imaging techniques (such as MRI) to correctly predict in vivo performance. In this work, I present two methods designed to overcome this filling problem, firstly, by releasing additional particles from areas of the flow inlet that lead directly to the complex flow region ("preferential seeding") and, secondly, by tracking particles both "downstream" and "upstream" from seed points within the complex flow region itself. I use the human carotid bifurcation as an example of complex blood flow that is of great clinical interest. Both idealized and healthy volunteer geometries are investigated. With uniform seeding in the inlet plane (in the common carotid artery (CCA)) of an idealized bifurcation geometry, approximately half the particles passed through the internal carotid artery (ICA) and half through the external carotid artery. However, of those particles entering the ICA, only 16% passed directly through the carotid bulb region. Preferential seeding from selected regions of the CCA was able to increase this figure to 47%. In the second method, seeding of particles within the carotid bulb region itself led to a very high proportion (97%) of pathlines running from CCA to ICA. Seeding of particles in the bulb plane of three healthy volunteer carotid bifurcation geometries led to much better filling of the bulb regions than by particles seeded at the inlet alone. In all cases, visualization of the origin and behavior of recirculating particles led to useful insights into the complex flow patterns. Both seeding methods produced significant improvements in filling the carotid bulb region with particle tracks compared with uniform seeding at the inlet and led to an improved understanding of the complex
LENUS (Irish Health Repository)
Creane, Arthur
2012-07-01
Many soft biological tissues contain collagen fibres, which act as major load bearing constituents. The orientation and the dispersion of these fibres influence the macroscopic mechanical properties of the tissue and are therefore of importance in several areas of research including constitutive model development, tissue engineering and mechanobiology. Qualitative comparisons between these fibre architectures can be made using vector plots of mean orientations and contour plots of fibre dispersion but quantitative comparison cannot be achieved using these methods. We propose a \\'remodelling metric\\' between two angular fibre distributions, which represents the mean rotational effort required to transform one into the other. It is an adaptation of the earth mover\\'s distance, a similarity measure between two histograms\\/signatures used in image analysis, which represents the minimal cost of transforming one distribution into the other by moving distribution mass around. In this paper, its utility is demonstrated by considering the change in fibre architecture during a period of plaque growth in finite element models of the carotid bifurcation. The fibre architecture is predicted using a strain-based remodelling algorithm. We investigate the remodelling metric\\'s potential as a clinical indicator of plaque vulnerability by comparing results between symptomatic and asymptomatic carotid bifurcations. Fibre remodelling was found to occur at regions of plaque burden. As plaque thickness increased, so did the remodelling metric. A measure of the total predicted fibre remodelling during plaque growth, TRM, was found to be higher in the symptomatic group than in the asymptomatic group. Furthermore, a measure of the total fibre remodelling per plaque size, TRM\\/TPB, was found to be significantly higher in the symptomatic vessels. The remodelling metric may prove to be a useful tool in other soft tissues and engineered scaffolds where fibre adaptation is also present.
Ojeda, Soledad; Azzalini, Lorenzo; Chavarría, Jorge; Serra, Antonio; Hidalgo, Francisco; Benincasa, Susanna; Gheorghe, Livia L; Diletti, Roberto; Romero, Miguel; Bellini, Barbara; Gutiérrez, Alejandro; Suárez de Lezo, Javier; Mazuelos, Francisco; Segura, José; Carlino, Mauro; Colombo, Antonio; Pan, Manuel
2017-11-08
There is little evidence on the optimal strategy for bifurcation lesions in the context of a coronary chronic total occlusion (CTO). This study compared the procedural and mid-term outcomes of patients with bifurcation lesions in CTO treated with provisional stenting vs 2-stent techniques in a multicenter registry. Between January 2012 and June 2016, 922 CTO were recanalized at the 4 participating centers. Of these, 238 (25.8%) with a bifurcation lesion (side branch ≥ 2mm located proximally, distally, or within the occluded segment) were treated by a simple approach (n=201) or complex strategy (n=37). Propensity score matching was performed to account for selection bias between the 2 groups. Major adverse cardiac events (MACE) consisted of a composite of cardiac death, myocardial infarction, and clinically-driven target lesion revascularization. Angiographic and procedural success were similar in the simple and complex groups (94.5% vs 97.3%; P=.48 and 85.6% vs 81.1%; P=.49). However, contrast volume, radiation dose, and fluoroscopy time were lower with the simple approach. At follow-up (25 months), the MACE rate was 8% in the simple and 10.8% in the complex group (P=.58). There was a trend toward a lower MACE-free survival in the complex group (80.1% vs 69.8%; P=.08). After propensity analysis, there were no differences between the groups regarding immediate and follow-up results. Bifurcation lesions in CTO can be approached similarly to regular bifurcation lesions, for which provisional stenting is considered the technique of choice. After propensity score matching, there were no differences in procedural or mid-term clinical outcomes between the simple and complex strategies. Copyright © 2017 Sociedad Española de Cardiología. Published by Elsevier España, S.L.U. All rights reserved.
Waiting times and output process of a server computed via Wiener-Hopf factorization
Hasslinger, Gerhard
1998-10-01
Non-renewal processes are relevant in queueing analysis to include various types of traffic arising in integrated services communication networks. We consider a workload based approach to the single server queue in discrete time domain with semi-Markov arrivals (SMP/G/1). Starting from a subdivision of the busy periods, we generalize a computationally attractive algorithm for the discrete time GI/G/1 queue. The stationary distributions of the waiting and idle time as well as the moments of the busy period are computed. Performance results are given for deterministic servers with autoregressive input and the output process of a server is modeled by adapting a SMP of small size.
Sheathless electrokinetic particle separation in a bifurcating microchannel
Li, Di; Lu, Xinyu; Song, Yongxin; Wang, Junsheng; Li, Dongqing
2016-01-01
Particle separation has found practical applications in many areas from industry to academia. Current electrokinetic particle separation techniques primarily rely on dielectrophoresis, where the electric field gradients are generated by either active microelectrodes or inert micro-insulators. We develop herein a new type of electrokinetic method to continuously separate particles in a bifurcating microchannel. This sheath-free separation makes use of the inherent wall-induced electrical lift to focus particles towards the centerline of the main-branch and then deflect them to size-dependent flow paths in each side-branch. A theoretical model is also developed to understand such a size-based separation, which simulates the experimental observations with a good agreement. This electric field-driven sheathless separation can potentially be operated in a parallel or cascade mode to increase the particle throughput or resolution. PMID:27703590
Plastic bottle oscillator: Rhythmicity and mode bifurcation of fluid flow
Kohira, Masahiro I.; Magome, Nobuyuki; Kitahata, Hiroyuki; Yoshikawa, Kenichi
2007-10-01
The oscillatory flow of water draining from an upside-down plastic bottle with a thin pipe attached to its head is studied as an example of a dissipative structure generated under far-from-equilibrium conditions. Mode bifurcation was observed in the water/air flow: no flow, oscillatory flow, and counter flow were found when the inner diameter of the thin pipe was changed. The modes are stable against perturbations. A coupled two-bottle system exhibits either in-phase or anti-phase self-synchronization. These characteristic behaviors imply that the essential features of the oscillatory flow in a single bottle system can be described as a limit-cycle oscillation.
Wake-sleep transition as a noisy bifurcation
Yang, Dong-Ping; McKenzie-Sell, Lauren; Karanjai, Angela; Robinson, P. A.
2016-08-01
A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.
Phase dynamics of edge transport bifurcation induced by external biasing
Li, B.; Wang, X. Y.; Xie, Z. J.; Li, P. F.; Gentle, K. W.
2018-02-01
Edge transport bifurcation induced by external biasing is explored with self-consistent turbulence simulations in a flux-driven system with both closed and open magnetic field lines. Without bias, the nonlinear evolution of interchange turbulence produces large-scale turbulent eddies, leading to the high levels of radial transport in the edge region. With sufficiently strong biasing, a strong suppression of turbulence is found. The plasma potential structures are strongly modified with the generation of sheared mean flows at the plasma edge. Consequently, the turbulence-driven flux is decreased to a much lower level, indicating a transition to a state of reduced transport. The simulations show that the dynamics of the phase and amplitude of fluctuations play a crucial role in the mechanism of transport suppression driven by biasing.
Bifurcations in a Generalization of the ZAD Technique: Application to a DC-DC Buck Power Converter
Directory of Open Access Journals (Sweden)
Ludwing Torres
2012-01-01
Full Text Available A variation of ZAD technique is proposed, which is to extend the range of zero averaging of the switching surface (in the classic ZAD it is taken in a sampling period, to a number of sampling periods. This has led to a technique that has been named -ZAD. Assuming a specific value for =2, we have studied the 2-ZAD technique. The latter has presented better results in terms of stability, regarding the original ZAD technique. These results can be demonstrated in different state space graphs and bifurcation diagrams, which have been calculated based on the analysis done about the behavior of this new strategy.
Bifurcations of periodic motion in a three-degree-of-freedom vibro-impact system with clearance
Liu, Yongbao; Wang, Qiang; Xu, Huidong
2017-07-01
The smooth bifurcation and grazing non-smooth bifurcation of periodic motion of a three-degree-of-freedom vibro-impact system with clearance are studied in this paper. Firstly, a periodic solution of vibro-impact system is solved and a six-dimensional Poincaré map is established. Then, for the six-dimensional Poincaré map, the analytic expressions of all eigenvalues of Jacobi matrix with respect to parameters are unavailable. This implies that with application of the classical critical criterion described by the properties of eigenvalues, we have to numerically compute eigenvalues point by point and check their properties to search for the bifurcation points. Such the numerical calculation is a laborious job in the process of determining bifurcation points. To overcome the difficulty that originates from the classical bifurcation criteria, the explicit critical criteria without using eigenvalues calculation of high-dimensional map are applied to determine bifurcation points of Co-dimension-one period doubling bifurcation and Co-dimension-one Neimark-Sacker bifurcation and Co-dimension-two Flip-Neimark-Sacker bifurcation, and then local dynamical behaviors of these bifurcations are analyzed. Moreover, the directions of period doubling bifurcation and Neimark-Sacker bifurcation are analyzed by center manifold reduction theory and normal form approach. Finally, the existence of the grazing periodic motion of the vibro-impact system is analyzed and the grazing bifurcation point is obtained, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and co-existing multiple solutions near the grazing bifurcation point are revealed.
Non normal modal analysis of oscillations in boiling water reactors
Energy Technology Data Exchange (ETDEWEB)
Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.uy [Ministerio de Industria, Energia y Mineria (MIEM), Montevideo (Uruguay); Flores-Godoy, Jose-Job, E-mail: job.flores@ibero.mx [Universidad Iberoamericana (UIA), Mexico, DF (Mexico). Dept. de Fisica Y Matematicas
2013-07-01
The first objective of the present work is to construct a simple reduced order model for BWR stability analysis, combining a two nodes nodal model of the thermal hydraulics with a two modes modal model of the neutronics. Two coupled non-linear integral-differential equations are obtained, in terms of one global (in phase) and one local (out of phase) power amplitude, with direct and cross feedback reactivities given as functions of thermal hydraulics core variables (void fractions and temperatures). The second objective is to apply the effective life time approximation to further simplify the nonlinear equations. Linear approximations for the equations of the amplitudes of the global and regional modes are derived. The linearized equation for the amplitude of the global mode corresponds to a decoupled and damped harmonic oscillator. An analytical closed form formula for the damping coefficient, as a function of the parameters space of the BWR, is obtained. The coefficient changes its sign (with the corresponding modification in the decay ratio) when a stability boundary is crossed. This produces a supercritical Hopf bifurcation, with the steady state power of the reactor as the bifurcation parameter. However, the linearized equation for the amplitude of the regional mode corresponds always to an over-damped and always coupled (with the amplitude of the global mode) harmonic oscillator, for every set of possible values of core parameters (including the steady state power of the reactor) in the framework of the present mathematical model. The equation for the above mentioned over damped linear oscillator is closely connected with a non-normal operator. Due to this connection, there could be a significant transient growth of some solutions of the linear equation. This behavior allows a significant shrinking of the basin of attraction of the equilibrium state. The third objective is to apply the above approach to partially study the stability of the regional mode and
Braided River Evolution and Bifurcation Dynamics During Floods and Low Flow in the Jamuna River
Marra, W. A.; Kleinhans, M. G.; Addink, E.
2010-12-01
River bifurcations have become recognised over the last decade as being critical but poorly understood elements in many channel systems, including braided and anastomosing rivers, fluvial lowland plains and deltas. They control the partitioning of both water and sediment with consequences for the downstream evolution and for river and coastal management. Avulsion studies and bifurcation modelling suggest that symmetrical bifurcations are inherently unstable. However, the simultaneous activity of channels in deltas, anastomosing rivers and large braided rivers such as the Jamuna suggest that symmetrical bifurcations are stable in agreement with sediment transport optimisation theories. These theories are still a matter of debate. Our objective is to understand the stability and evolution of the braid pattern through studying the dynamics of the bifurcations under natural discharge conditions: both during floods and low flow. Using a series of Landsat TM images taken at irregular intervals showing inter-annual variation, we studied the evolution of a large number of bifurcations in the Jamuna river between 1999 and 2004. The images were first classified into water, bare sediment and vegetation. The contiguous water body of the river was then selected and translated into a network description with bifurcations and confluences at the nodes and interconnecting channels. Channel width is a crucial attribute of the network channels as this allows the calculation of bifurcation asymmetry. The key step here is to describe river network evolution by identifying the same node in multiple subsequent images as well as new and abandoned nodes, in order to distinguish migration of bifurcations from avulsion processes. Nodes in two subsequent images were linked through distance and angle of the downstream connected channels. Once identified through time, the changes in node position and the changes in the connected channels can be quantified Along the entire river the well
Bifurcation boundary conditions for current programmed PWM DC-DC converters at light loading
Fang, Chung-Chieh
2012-10-01
Three types of bifurcations (instabilities) in the PWM DC-DC converter at light loading under current mode control in continuous-conduction mode (CCM) or discontinuous-conduction mode (DCM) are analysed: saddle-node bifurcation (SNB) in CCM or DCM, border-collision bifurcation during the CCM-DCM transition, and period-doubling bifurcation in CCM. Different bifurcations occur in some particular loading ranges. Bifurcation boundary conditions separating stable regions from unstable regions in the parametric space are derived. A new methodology to analyse the SNB in the buck converter based on the peak inductor current is proposed. The same methodology is applied to analyse the other types of bifurcations and converters. In the buck converter, multiple stable/unstable CCM/DCM steady-state solutions may coexist. Possibility of multiple solutions deserves careful study, because an ignored solution may merge with a desired stable solution and make both disappear. Understanding of SNB can explain some sudden disappearances or jumps of steady-state solutions observed in switching converters.
Bifurcation of Vortex Breakdown Patterns in a Circular Cylinder with two Rotating Covers
DEFF Research Database (Denmark)
Brøns, Morten; Bisgaard, Anders
2006-01-01
We analyse the topology of vortex breakdown in a closed cylindrical container in the steady domain under variation of three parameters, the aspect ratio of the cylinder, the Reynolds number, and the ratio of the angular velocities of the covers. We develop a general post-processing method to obtain...... topological bifurcation diagrams from a database of simulations of two-dimensional flows and apply the method to axisymmetric simulations of the flow in the cylinder. Interpreting the diagrams with the aid of bifurcation theory, we obtain complete topological bifurcation diagrams for the rotation ratio...