基于Washout滤波器的Rssler系统Hopf分岔控制

针对R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.     

基于Washout滤波器的R(o)ssler系统Hopf分岔控制

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.     

基于Washout滤波器的Rössler系统Hopf分岔控制

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     

线性延时反馈Josephson结的Hopf分岔和混沌化

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌. 关键词： 约瑟夫森结 线性延时反馈 Hopf分岔 混沌     

一类相对转动系统Hopf分岔的非线性反馈控制

研究一类非线性摩擦阻尼力作用下的相对转动系统的Hopf分岔现象,给出系统产生Hopf分岔的充要条件,提出一种非线性反馈控制方法对系统的Hopf分岔点进行转移,并控制极限环的稳定性和幅值,数值模拟说明该方法对一类相对转动系统的Hopf分岔控制是有效的. 关键词： 相对转动 非线性反馈控制 Hopf分岔 极限环     

一类简化Lang-Kobayashi方程的Hopf分岔及其稳定性

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     

Langford系统Hopf分岔极限环幅值控制

系统地研究了Langford 系统Hopf分岔极限环幅值非线性反馈控制问题.根据中心流形定理和规范型降维理论, 推导含控制增益项的非线性曲率系数控制公式和幅值近似解,通过数值仿真验证并绘制极限环幅控关系曲线. 所推导的控制公式为Langford 系统极限环幅值控制提供了方便有效的控制方法.     

一个三时滞生物捕食被捕食系统分岔的混合控制

针对多时滞捕食被捕食系统的Hopf分岔控制问题,提出一种基于状态反馈和参数调节的混合控制方法,这种混合控制方法可以延迟有害Hopf分岔的发生或使Hopf分岔消失.分析了该控制系统的稳定性和Hopf分岔的存在性,并通过规范型理论和中心流形定理,给出了分岔周期解的稳定性和分岔方向的计算公式.最后通过数值模拟验证了该理论的正确性. 关键词： 时滞 捕食被捕食系统 Hopf分岔 混合控制     

Rijke管热声不稳定非线性动力学研究——分岔分析

建立了水平Rijke管热声模型,利用Galerkin方法对控制方程组进行展开,实现数值求解。确定了Galerkin模态收敛阶数为10,利用非线性动力学理论对系统进行分岔分析。Rijke管热声系统分岔行为属于亚临界Hopf分岔。系统稳定性区域分为全局稳定、全局不稳定及双稳态区域。获得了无量纲加热功率K,加热器位置x_f,阻尼系数c_1和时间延迟τ等参数的分岔图谱,发现加热器位置x_f的分岔图谱存在两个Hopf分岔点。在线性不稳定区域内,振荡幅值随时间延迟τ的增大呈现先增大后减小的趋势。     

三自由度含间隙碰撞振动系统Neimark-Sacker分岔的反控制

分岔反控制作为传统分岔控制的逆问题, 其目的是在预先指定的系统参数点通过控制主动设计出具有所期望特性的分岔解. 以一类三自由度含间隙双面碰撞振动系统为研究对象, 在不改变原系统平衡解结构的前提下, 考虑到在碰撞振动系统反控制过程中由Poincaré映射的隐式特点和传统的映射Neimark-Sacker分岔临界准则带来的困难, 通过对原系统施加线性反馈控制器并利用不直接依赖于特征值计算的Neimark-Sacker分岔显式临界准则研究了此系统的分岔反控制问题. 首先对原系统施加线性反馈控制, 建立闭环控制系统的六维Poincaré映射. 由于六维映射的雅克比矩阵的特征值没有解析的表达式, 利用高维映射Neimark-Sacker分岔的显式临界准则, 获得了系统出现拟周期碰撞振动运动的控制参数区域. 然后采用中心流形-正则形方法分析了拟周期分岔解的稳定性. 数值仿真结果表明本文方法可以在指定的系统参数点通过控制设计出稳定的拟周期碰撞运动.     

Nonlinear analysis of a maglev system with time-delayed feedback control

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.     

Langford系统Hopf分叉的线性反馈控制

分析Langford系统的Hopf分叉现象，并研究采用线性反馈控制方法控制该系统的Hopf分叉.从理论上推导出受控系统产生Hopf分叉的条件，给出了某些极限环的解析表达式，对该系统进行了分叉点的转移与极限环的稳定性控制.数值模拟说明本文采用的方法对Langford系统的Hopf分叉控制是有效的. 关键词： Langford系统 反馈控制 Hopf分叉 极限环     

一个简单延迟非线性系统的动力学行为及混沌同步

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     

Hopf Bifurcation Control of a Hyperchaotic Circuit System

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.     

Dynamic analysis and synchronization control of an unusual chaotic system with exponential term and coexisting attractors

This paper reports a new four-dimensional chaotic system consisting of an exponential nonlinear term, two quadratic nonlinear terms and five linear terms. The system has only one equilibrium and performs stability, periodicity and chaos with the variation of the parameters. It losses its stability with the occurrence of Hopf bifurcation and goes into chaos via period-doubling bifurcation. One more interesting feature of the system is that it can generate multiple coexisting attractors for different initial conditions, such as two strange attractors with one limit cycle, one strange attractor with two limit cycles, etc. The dynamic properties of the system are presented by numerical simulation includes bifurcation diagrams, Lyapunov exponent spectrum and phase portraits. An electronic circuit is constructed to implement the chaotic attractor of the system. Based on the linear quadratic regulator (LQR) method, the synchronization control of the system is investigated.     

Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback

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.     

一类耦合非线性相对转动系统的Hopf分岔控制

建立一类耦合非线性相对转动系统的动力学方程,研究系统在主共振和1∶1内共振情况下的Hopf分岔行为,设计非线性反馈控制器,控制系统Hopf分岔的发生、极限环的稳定性和幅值,数值模拟证明了该方法的有效性.     

Dynamics of solitary waves generated by subcritical instability under the action of delayed feedback control

We consider the influence of a global delayed feedback control which acts on a system governed by a subcritical Ginzburg–Landau equation. The method based on a variational principle is applied for the derivation of a low-dimensional evolution model. In the framework of this model a one-pulse solution is found, and its linear and nonlinear stability analysis is carried out. The existence region for a stable time-periodic pulse solution is found between the boundaries in the parameter space corresponding to a Hopf bifurcation and a saddle-node bifurcation. The obtained results are compared with the results of an analytical linear theory and direct numerical simulations of the original problem.