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1.
Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays 下载免费PDF全文
Jing-Jun Zhao Jing-Yu Xiao & Yang Xu 《advances in applied mathematics and mechanics.》2013,5(2):146-162
This paper is concerned with the Hopf bifurcation analysis of
tumor-immune system competition model with two delays. First, we
discuss the stability of state points with different kinds of
delays. Then, a sufficient condition to the existence of the Hopf
bifurcation is derived with parameters at different points.
Furthermore, under this condition, the stability and direction of
bifurcation are determined by applying the normal form method and
the center manifold theory. Finally, a kind of Runge-Kutta methods
is given out to simulate the periodic solutions numerically. At
last, some numerical experiments are given to match well with the
main conclusion of this paper. 相似文献
2.
The feedback control of a delayed dynamical system, which also includes various chaotic systems with time delays, is investigated. On the basis of stability analysis of a nonautonomous system with delays, some simple yet less conservative criteria are obtained for feedback control in a delayed dynamical system. Finally, the theoretical result is applied to a typical class of chaotic Lorenz system and Chua circuit with delays. Numerical simulations are also given to verify the theoretical results. 相似文献
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This paper undertakes a nonlinear analysis of a model for a maglev system with time-delayed feedback. Using linear analysis, we determine constraints on the feedback control gains and the time delay which ensure stability of the maglev system. We then show that a Hopf bifurcation occurs at the linear stability boundary. To gain insight into the periodic motion which arises from the Hopf bifurcation, we use the method of multiple scales on the nonlinear model. This analysis shows that for practical operating ranges, the maglev system undergoes both subcritical and supercritical bifurcations, which give rise to unstable and stable limit cycles respectively. Numerical simulations confirm the theoretical results and indicate that unstable limit cycles may coexist with the stable equilibrium state. This means that large enough perturbations may cause instability in the system even if the feedback gains are such that the linear theory predicts that the equilibrium state is stable. 相似文献
4.
Stability and bifurcation in a neural network model with two delays 总被引:38,自引:0,他引:38
A simple neural network model with two delays is considered. Linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. For the case without self-connection, it is found 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. An example is given and numerical simulations are performed to illustrate the obtained results. 相似文献
5.
Anna Zakharova Alexey Feoktistov Tatyana Vadivasova Eckehard Schöll 《The European physical journal. Special topics》2013,222(10):2481-2495
We analyze noise-induced phenomena in nonlinear dynamical systems near a subcritical Hopf bifurcation. We investigate qualitative changes of probability distributions (stochastic bifurcations), coherence resonance, and stochastic synchronization. These effects are studied in dynamical systems for which a subcritical Hopf bifurcation occurs. We perform analytical calculations, numerical simulations and experiments on an electronic circuit. For the generalized Van der Pol model we uncover the similarities between the behavior of a self-sustained oscillator characterized by a subcritical Hopf bifurcation and an excitable system. The analogy is manifested through coherence resonance and stochastic synchronization. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with hard excitation, can be partially synchronized even outside the oscillatory regime of the deterministic system. 相似文献
6.
This paper is concerned with the Hopf bifurcation control of a newhyperchaotic circuit system. The stability of the hyperchaotic circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. Animportant feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions. 相似文献
7.
J.C. JI 《Journal of sound and vibration》2003,259(4):845-856
The effect of time delays occurring in the feedback control loop on the linear stability of a simple magnetic bearing system is investigated by analyzing the associated characteristic transcendental equation. It is found that a Hopf bifurcation can take place when time delays pass certain values. The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method. It is also found that a codimension two bifurcation can occur through a Hopf and a steady state bifurcation interaction. Finally, numerical simulations are performed to verify the analytical predictions. 相似文献
8.
By means of an extended center-manifold reduction, we derive the nonlocal complex Ginzburg-Landau equation (NCGLE) valid for electrochemical systems with migration coupling. We carry out the stability analysis of the uniform oscillation, elucidating the role of the nonlocal coupling in electrochemical systems at the vicinity of a supercritical Hopf bifurcation. We apply the NCGLE to an experimental system, an N-type negative differential resistance electrochemical oscillator, which is shown to exhibit electrochemical turbulence for wide parameter ranges. 相似文献
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We find numerically small scale basic structures of homoclinic bifurcation curves in the parameter space of the Chua circuit. The distribution of these basic structures in the parameter space and their geometrical properties constitute a complete homoclinic bifurcation scenario of this system. Furthermore, these structures and the scenario are theoretically demonstrated to be generic to a large class of dynamical systems that presents, as the Chua circuit, Shilnikov homoclinic orbits. We classify the complexity of primary and subsidiary homoclinic orbits by their order given by the number of their returning loops. Our results confirm previous predictions of structures of homoclinic bifurcation curves and extend this study to high order primary orbits. Furthermore, we identify accumulations of bifurcation curves of subsidiary homoclinic orbits into bifurcation curves of both primary and subsidiary orbits. 相似文献
13.
We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model. 相似文献
14.
用平均模型分析了单周期控制Boost变换器的运行,分析表明在参考电压变化的情况下,单周期控制Boost变换器会出现Hopf分岔.Hopf分岔使得变换效率下降,器件应力增加.为了消除Hopf分岔,提出了采用washout滤波器的方法.建立了采用washout滤波器的单周期控制Boost变换器平均模型,对于washout滤波器中的两个新参数,可以用Routh-Hurwitz准则来确定.仿真和电路实验验证了所提方法的效果.
关键词:
washout滤波器
单周期控制
Boost变换器
Hopf分岔 相似文献
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针对控制无线网络拥塞控制系统中流体流模型的Hopf分岔的问题,提出一种状态反馈控制器.通过选择通信时延作为分岔参数,验证模型在加入状态反馈控制器后,①增加了分岔参数的临界值,扩大了稳定性区域,使系统的Hopf分岔延迟;②通过选择合适的参数,可以容易地改变分岔周期解的稳定性及其分岔方向.理论分析和数据仿真验证了该方法能够有效地控制系统的Hopf分岔. 相似文献
17.
TANG Fang WANG Ling 《理论物理通讯》2005,44(2):303-306
This paper considers the chaos synchronization of the modified Chua's circuit with x|x| function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be synchronized using active control when the values of parameters both in drive system and response system are known aforehand.Furthermore, based on Lyapunov stability theory we propose an adaptive active control approach to make the states of two identical Chua systems with unknown constant parameters asymptotically synchronized. Moreover the designed controller is independent of those unknown parameters. Numerical simulations are given to validate the proposed synchronization approach. 相似文献
18.
Results are provided here about the stability and bifurcation of periodic solutions for a (neural) network with n elements where delays between adjacent units and external inputs are included. The particular cases n = 2 and n = 3 are discussed in details, to explicitly illustrate the role of the delays in the corresponding bifurcation sets and the stability properties, like a Hopf bifurcation, a pitchfork bifurcation, and a Bogdanov-Takens bifurcation. 相似文献
19.
We investigate the steady-state solution and its bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed feedback. We show that the steady state is globally stable for small feedback gain and that local stability is lost, generically, through a Hopf bifurcation for larger feedback gain. We provide simple criteria that determine whether the Hopf bifurcation is supercritical or subcritical based on the knowledge of the first three terms in the Taylor-expansion of the nonlinearity. Furthermore, the presence of double-Hopf bifurcations of the steady state is shown, which indicates possible quasiperiodic and chaotic dynamics in these systems. As a result of this investigation, we find that AC-coupling introduces fundamental differences to systems of Ikeda-type [K. Ikeda, K. Matsumoto, High-dimensional chaotic behavior in systems with time-delayed feedback, Physica D 29 (1987) 223–235] already at the level of steady-state bifurcations, e.g. bifurcations exist in which limit cycles are created with periods other than the fundamental “period-2” mode found in Ikeda-type systems. 相似文献
20.
The effects of a tuned added mass on the aeroelastic stability of a single degree of freedom bluff body exposed to a steady flow are investigated. The model captures the essential aspects of the behaviour of flexible structures equipped with Tuned Mass Dampers undergoing galloping oscillations. The system exhibits simple as well double Hopf bifurcations, of non-resonant and 1:1 resonant type. Postcritical behaviour of the system in the neighbourhood of the 1:1 resonant type bifurcation is investigated. Employing the Multiple Scale Method, a second order bifurcation equation in the complex amplitude of motion is obtained. Analytical solutions are used to describe the bifurcation scenario in the cases of both undercritical and supercritical aerodynamic behaviour of the bluff body. The effectiveness of the Tuned Mass Damper even in the postcritical range is proved. 相似文献