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.     

Genesio混沌系统的线性反馈控制实验

构建了Genesio混沌系统的硬件实现电路,采用线性反馈对该系统进行控制,根据Hurwitz稳定性判据,得到将系统控制到稳定状态的反馈增益的取值范围.通过硬件电路实验对理论分析进行验证,结果表明线性反馈可以将Genesio混沌系统有效地控制到不动点和稳定的周期态.     

一类新混沌系统的线性状态反馈控制

研究了一类新混沌系统的控制问题.利用Routh-Hurwitz准则对受控系统进行了稳定性分析，结合线性状态反馈方法理论上严格证明了达到控制目标反馈系数的选择原则.数值研究证明了该方法能够有效地控制混沌系统到失稳的平衡点或周期解，同时控制效果在弱噪声干扰下具有很强的鲁棒性. 关键词： 新混沌系统 线性状态反馈控制 Routh-Hurwitz准则 噪声     

Hopf Bifurcation in a Nonlinear Wave System

Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.     

再入飞行器失稳的分叉理论分析与数值仿真验证

飞行器再入大气层时的姿态稳定性事关飞行安全, 是气动设计的关键问题之一.文章采用非线性自治动力系统分叉理论, 耦合求解非定常Navier-Stokes方程和俯仰运动方程, 研究了钝体和细长体两类航天飞行器再入过程单自由度俯仰运动失稳问题.研究表明, 航天飞行器再入时, 如果仅有1个配平攻角, 随Mach数降低, 其配平攻角处的俯仰姿态失稳一般对应于Hopf分叉, 并存在亚临界Hopf分叉和超临界Hopf分叉两种失稳形态; 如果再入时随着Mach数的降低, 其配平攻角由1个演化至多个(一般为3个), 其配平攻角处的俯仰姿态失稳形态将更为复杂, 可能发生鞍结点分叉形态的刚性失稳行为;随Mach数的进一步降低, 其俯仰运动还可能进一步发生Hopf分叉和同宿分叉.      

双稳系统随机共振的反馈控制

将双稳系统的输出反馈到输入端再作用于系统,提出了采用反馈来控制随机共振的方法.以典型双稳系统为对象,并以信噪比和功率谱放大率作为度量随机共振效应的可观察变量,分别研究了采用线性或非线性反馈函数所产生的随机共振现象.理论分析和数值仿真结果表明随机共振是可控制的.该方法特别适用于系统参数固定或难以改变的系统. 关键词： 双稳系统 随机共振 反馈控制 共振效应     

陈氏混沌系统的非反馈控制

通过对陈氏混沌系统施加非共振参数激励实现非反馈混沌控制.将远大于系统特征频率的周期信号作为控制输入，利用平均法和Lyapunov方法证明控制方案的可行性，并得出控制参数应满足的条件.数值研究表明此方法可以使受控系统迅速达到稳定状态，且具有较强的抗干扰性能.     

混沌系统的注入反馈控制与动态控制方法研究

提出了注入反馈控制混沌的方法,把蔡氏电路混沌系统控制到指定的平衡态和希望的振荡周期轨道上.通过改变控制参数,研究了几个典型物理状态变化现象,丰富了蔡氏电路混沌系统的应用方法 关键词： 混沌 平衡态 极限环     

Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system

Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.     

Hopf bifurcation analysis of Chen circuit with direct time delay feedback

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.     

Hopf bifurcation control via a dynamic state-feedback control

To relocate two Hopf bifurcation points, simultaneously, to any desired locations in n-dimensional nonlinear systems, a novel dynamic state-feedback control law is proposed. Analytical schemes to determine the control gains according to the conditions for the emergence of Hopf bifurcation are derived. To verify the effectiveness of the proposed control law, numerical examples are provided.     

Equilibrium points and bifurcation control of a chaotic system

Based on the Routh--Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.     

Equilibrium points and bifurcation control of a chaotic system

Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.     

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     

Hopf bifurcation and chaos control in a new chaotic system via hybrid control strategy

In this paper, we investigate the problem of Hopf bifurcation and chaos control in a new chaotic system. A hybrid control strategy using both state feedback and parameter control is proposed. Theoretical analysis shows that the Hopf bifurcation critical value can be changed via hybrid control. Meanwhile, this control strategy can also control the chaos state. The direction and stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out to illustrate the effectiveness of the main theoretical results.