共查询到16条相似文献,搜索用时 109 毫秒
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基于数学上延迟(时滞)系统Hopf分支理论及分析方法,解析地确定出 用延迟反馈法可控制三阶自治混沌系统的一般条件.利用这种分析方法,着重从理论上 讨论了在控制意义下系统出现稳定周期解及由Hopf分支产生周期解的分支方向的判据.将这 些理论应用到三阶自治混沌系统的控制实例中,解析地得到使系统可控的参量区域.在该区 域内选择控制参量,通过数值模拟也得到控制系统从混沌到周期态的结果.
关键词:
延迟反馈
Hopf分支
控制混沌 相似文献
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针对R(o)ssler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. 相似文献
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分析一个简单二阶延迟系统的Hopf分支和混沌特性, 包括分支点、分支方向和分支周期解的稳定性, 解析求出退延迟情况下, 这个系统的相轨线方程; 通过数值计算并绘制分岔图, 揭示系统存在由倍周期通向混沌的道路; 利用单路线性组合信号, 反馈控制实现系统的部分完全同步; 利用主动-被动与线性反馈的联合, 实现系统的完全同步; 设计和搭建系统的电子实验线路, 并从实验中观测到与理论分析或数值计算相一致的结果.
关键词:
延迟非线性系统
电路实验
Hopf分支
混沌 相似文献
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针对Rssler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NormalForm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. 相似文献
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利用荷控忆阻器和一个电感串联设计一种新型浮地忆阻混沌电路.用常规动力学分析方法研究该系统的基本动力学特性,发现系统可以产生一对关于原点对称的"心"型吸引子.将观察混沌吸引子时关注的电压、电流推广到功率和能量信号,观察到蝴蝶结型奇怪吸引子的产生.理论分析Hopf分岔行为并通过数值仿真进行验证,结果表明系统随电路参数变化能产生Hopf分岔、反倍周期分岔两种分岔行为.相对于其它忆阻混沌电路该电路采用的是一个浮地型忆阻器,并且在初始状态改变时,能产生共存吸引子和混沌吸引子与周期极限环共存现象. 相似文献
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讨论了快慢两时间尺度下超混沌Lorenz系统原点的稳定性问题,分析了原点的Hopf分岔,包括Hopf分岔的存在性,分岔方向以及分岔周期解的稳定性等问题,并用数值例子对所得到的结果加以验证.在一定的参数条件下,快慢系统会产生对称簇发并能达到超混沌状态.基于快慢分析法,揭示了对称簇发中沉寂态与激发态相互转迁的不同分岔模式,并进一步分析了耦合强度对慢过效应的影响.
关键词:
超混沌Lorenz系统
Hopf分岔
对称式fold/subHopf簇发
慢过效应 相似文献
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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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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
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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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Jinmei Liu 《Optik》2014
Many four-wing chaotic systems have been developed based on cross product or quadratic operations. Differently, we construct a three-dimensional chaotic system generating four-wing or double-wing attractors by virtue of sign function. Dynamical properties such as equilibrium points, Poincaré map, Lyapunov exponent spectra, Hopf bifurcations and bifurcation diagrams of the system are theoretically and numerically analyzed. Results of mathematical analyses and simulation tests indicate that the proposed chaotic system can keep chaotic to generate four-wing or double-wing attractors within a large scope of parameters. The system also shows hyperchaotic behaviors in some parameter range. Besides, circuit implementation of the chaotic system is studied. That proves the system is physically realizable. 相似文献
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In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilibria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps. There is little difference between this chaotic system without equilibria and other chaotic systems with equilibria shown by phase portraits and Lyapunov exponents. But the bifurcation diagram shows that the chaotic systems without equilibria do not have characteristics such as pitchfork bifurcation, Hopf bifurcation etc. which are common to the normal chaotic systems. The Poincaré maps show that this system is a four-wing chaotic system with more complicated dynamics. Moreover, the physical existence of the four-wing chaotic attractor without equilibria is verified by an electronic circuit. 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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Direct time delay feedback can make non-chaotic Chen
circuit chaotic. The chaotic Chen circuit with direct time delay
feedback possesses rich and complex dynamical behaviours. To reach a
deep and clear understanding of the dynamics of such circuits
described by delay differential equations, Hopf bifurcation in the
circuit is analysed using the Hopf bifurcation theory and the
central manifold theorem in this paper. Bifurcation points and
bifurcation directions are derived in detail, which prove to be
consistent with the previous bifurcation diagram. Numerical
simulations and experimental results are given to verify the
theoretical analysis. Hopf bifurcation analysis can explain and
predict the periodical orbit (oscillation) in Chen circuit with
direct time delay feedback. Bifurcation boundaries are derived using
the Hopf bifurcation analysis, which will be helpful for determining
the parameters in the stabilisation of the originally chaotic
circuit. 相似文献