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1.
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
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Qiang Lai 《Chinese Journal of Physics (Taipei)》2018,56(3):1064-1073
This paper studies the stability and bifurcation of three cases of bidirectional gene regulatory networks with negative feedback loops and time delays. The uniqueness of the positive equilibrium point of the gene regulatory networks is verified. The delay independent stability conditions of the networks are established by analyzing their corresponding characteristic equations. The existence of the Hopf bifurcation of the networks with or without time delays is presented. Numerical simulations demonstrate the correctness of the obtained theoretical results. 相似文献
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Rank-1 attractors play a vital role in biological systems and the circuit systems.In this paper,we consider a periodically kicked Chua model with two delays in a circuit system.We first analyze the local stability of the equilibria of the Chua system and obtain the existence conditions of supercritical Hopf bifurcations.Then,we derive some explicit formulas about Hopf bifurcation,which could help us find the form of Hopf bifurcation and the stability of bifurcating period solutions through the Hassards method.Also,we show that rank-1 chaos occurs when the Chua model with two delays undergoes a supercritical Hopf bifurcation and encounters a periodic kick,which shows the effect of two delays on the circuit system.Finally,we illustrate the theoretical analysis by simulations and try to explain the mechanism of delay in our system. 相似文献
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Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays
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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
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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
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This letter puts forward an ingenious feedback control method with parametric delay to manipulate bifurcation control for a delayed fractional dual congestion model. By employing time delay as a bifurcation parameter, the local dynamics involving stability and Hopf bifurcation is examined. The control efforts can be realized with or without time delay in the strength of feedback control. It suggests that the stability performance is consumedly elevated by exploiting the parametric delay feedback controller, yet Hopf bifurcation engenders ahead of time in the event of the absence of the controller. Moreover, the impact of the order or linear feedback gain on the bifurcation point is numerically discussed via aborative calculation. Numerical simulations are eventually actualized to corroborate the proposed scheme. 相似文献
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针对Rössler系统平衡点的Hopf分岔,以Washout滤波器为控制器,详细讨论了控制器参数对Hopf分岔点位置、分岔类型以及周期解振幅的控制问题.首先根据Routh-Hurwitz判据计算了受控系统的参数空间稳定域,找出了对应的Hopf分岔边界,并由此分析了滤波器时间常数、线性控制增益对分岔点位置的影响.然后,引入Normal Form直接法方便地求出系统Hopf分岔Normal Form系数,由此确定出改变分岔类型和周期解振幅的控制器非线性增益选择原则.最后用数值计算验证了本文的结论.
关键词:
Rö
ssler系统
Washout滤波器
Hopf分岔
Normal Form 相似文献
11.
Bifurcation is investigated with the full velocity difference traffic model. Applying the Hopt theorem, an analytical Hopf bifurcation calculation is performed and the critical road length is determined for arbitrary numbers of vehicles. It is found that the Hopf bifurcation critical points locate on the boundary of the linear instability region. Crossing the boundary, the uniform traffic flow loses linear stability via Hopf bifurcation and the oscillations appear. 相似文献
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Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback
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The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied.By considering the energy in the air-gap field of the AC motor,the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system.The characteristic roots and the stable regions of time delay are determined by the direct method,and the relationship between the feedback gain and the length summation of stable regions is analyzed.Choosing the time delay as a bifurcation parameter,we find that the Hopf bifurcation occurs when the time delay passes through a critical value.A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem.Numerical simulations are also performed,which confirm the analytical results. 相似文献
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This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf bifurcation depending on selected values of the system parameters are studied. The region of the stability for the Hopf bifurcation is investigated.By the hybrid control method, a nonlinear controller is designed for changing the Hopf bifurcation point and expanding the range of the stability. Discussions show that with the change of parameters of the controller, the Hopf bifurcation emerges at an expected location with predicted properties and the range of the Hopf bifurcation stability is expanded. Finally,numerical simulation is provided to confirm the analytic results. 相似文献
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The stability and bifurcation in a voltage controlled negative-output KY Boost converter is studied in this Letter. A glimpse at the stability and bifurcation from the power electronics simulator (PSIM) software are given. And then, its mathematical model and corresponding discrete model are derived. The stability and bifurcation of the converter are determined with the help of the loci of eigenvalues of the Jacobian matrix. It is found that the Hopf bifurcation is easy to come in this converter when the value of its energy-transferring capacitor increases. Finally, the analytical results are confirmed by the circuit experiment. 相似文献
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讨论了一类简化Lang-Kobayashi方程的Hopf 分岔的性质.根据分岔理论,给出了系统产生Hopf 分岔的临界时滞条件,然后利用中心流形定理和规范型理论得到了确定Hopf分岔方向和分岔周期解的稳定性计算公式.最后,用数值模拟对理论结果进行了验证.
关键词:
Lang-Kobayashi方程
时滞
Hopf分岔
稳定性 相似文献
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针对一类多项式形式的Hopf分岔系统, 提出了一种鲁棒稳定的控制器设计方法. 使用该方法设计控制器时不需要求解出系统在分岔点处的分岔参数值, 只需要估算出分岔参数的上下界, 然后设计一个参数化的控制器, 并通过Hurwitz判据和柱形代数剖分技术求解出满足上下界条件的控制器参数区域, 最后在得到的这个区域内确定出满足鲁棒稳定的控制器参数值. 该方法设计的控制器是由包含系统状态的多项式构成, 形式简单, 具有通用性, 且添加控制器后不会改变原系统平衡点的位置. 本文首先以Lorenz系统为例说明了控制器的推导和设计过程, 然后以van der Pol振荡系统为例, 进行了工程应用. 通过对这两个系统的控制器设计和仿真, 说明了文中提出的控制器设计方法能够有效地应用于这类Hopf分岔系统的鲁棒稳定控制, 并且具有通用性. 相似文献
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P. Pepo̵wski 《Physica D: Nonlinear Phenomena》1983,6(3):364-374
We investigate a Hopf bifurcation at complex conjugate double eigenvalues in semiclassical equations of a laser with saturable absorber where the degeneracy of eigenvalues is implied by a symmetry. The bifurcation analysis is undertaken within a more general system of nonlinear ordinary differential equations invariant under the same transformations as laser equations. It is proved that three periodic solutions exist and their stability criteria are found. 相似文献
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通过线性与非线性状态反馈, 实现了对四维Qi系统零平衡点的Hopf分岔反控制.首先确定产生Hopf分岔的线性控制项,得到线性控制增益的选取原则.然后,利用稳定性分析,借助于对线性受控Qi系统的Jordan标准型的直接控制以及适当的变换,确定影响Hopf分岔稳定性的非线性控制项,得到非线性控制增益的选取原则.针对所考虑分岔参数的不同,给出不同的控制方案.最后通过数值模拟验证了理论分析结果的正确性.
关键词:
Qi系统
Hopf分岔
反控制
稳定性 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