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     

一类惯性神经网络的分岔与控制

本文讨论了一类三阶惯性神经网络的稳定性和分岔问题. 利用灵敏度理论,确定了合适的Hopf 分岔参数. 基于Routh-Hurwitz判据和分岔理论,给出了系统稳定性、发生Hopf分岔以及产生静态分岔的条件. 数值模拟不仅验证了理论分析的正确性,还说明了所设计的单节点时滞反馈控制器不仅能延迟网络分岔的发生,还能改变极限环的振幅. 关键词： 惯性神经网络 稳定性 时滞反馈控制 Hopf分岔     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 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.     

用多凹槽滤波器控制混沌系统

提出了一种施加多个凹槽滤波器反馈控制混沌系统的方法,使混沌运动转化为规则的运动.多凹槽滤波器控制是一种具有固定参数的线性反馈控制方法,它不影响原系统的参数,截断了系统从倍周期分叉通向混沌的道路.同时,用Melnikov方法进行理论分析,给出了合适的反馈控制器的参数.将多凹槽滤波器应用于典型的混沌系统,其仿真结果表明了该控制方法的有效性与可行性 关键词： 混沌 多凹槽滤波器 Melnikov方法     

单模激光Haken-Lorenz系统的振荡解析解

研究了单模激光Haken-Lorenz系统在Hopf 分歧点处的动力学行为.求出了Haken-Lorenz系统的定态解，采用线性稳定性原理对定态解进行了稳定性分析，获得了本征值方程，进而确定了系统的Hopf 分歧点μc.利用级数法求出了系统在分歧点处的时间周期振荡解的解析表达式.通过计算机对系统分歧点处的动力学行为进行了数值模拟，结果表明，系统在分歧点处存在一个极限环，即时间周期振荡解.与理论分析的解析结果相一致.     

基于状态反馈控制的无线网络拥塞控制流体流模型的Hopf分岔

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.     

增强型延迟反馈法控制低维混沌系统的解析研究

基于时间延迟反馈控制混沌系统的方法,提出一种增强型控制方案,并利用分析延迟系统产生Hopf分支条件的方法,给出这种方案控制低维连续自治混沌系统时,在达到控制目标的条件下,控制参数的一般解析关系.将这一方案和分析方法应用到两个混沌模型中,结果表明:采用修正的方案可以明显地改善控制混沌的效果和质量;解析分析的结果与实际数值计算的结果一致. 关键词： 延迟反馈 混沌控制 Hopf分支     

基于延时干扰的感应电能传输系统分岔频率输送控制

本文针对感应电能传输系统分岔频率的输送控制问题, 提出一种基于延时干扰的变轨控制方法. 该方法在反馈控制环节中加入一段延时干扰, 通过调节延时参数, 可使系统相轨迹流在各稳定极限环吸引子间自由切换. 文中以原副边均为串联谐振的感应电能传输系统为例, 对该方法的机理及实现方案进行了研究, 并通过仿真和实验验证了其有效性. 论文的研究结果对类似多吸引子分岔行为的输送控制可提供一定的理论参考. 关键词： 感应电能传输 频率分岔 输送控制 延时干扰     

Amplitude control of limit cycle in a van der Pol Duffing system

This paper applies washout filter technology to amplitude control of limit cycles emerging from Hopf bifurcation of the van der Pol–Duffing system.The controlling parameters for the appearance of Hopf bifurcation are given by the Routh–Hurwitz criteria.Noticeably,numerical simulation indicates that the controllers control the amplitude of limit cycles not only of the weakly nonlinear van der Pol–Duffing system but also of the strongly nonlinear van der Pol–Duffing system.In particular,the emergence of Hopf bifurcation can be controlled by a suitable choice of controlling parameters.Gain-amplitude curves of controlled systems are also drawn.     

Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser

A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.     

Dynamical Analysis of a Fractional Order Rosenzweig-MacArthur Model Incorporating Herbivore Induced Plant Volatile

Plants send signals through releasing Volatile Organic Compounds (VOCs), to attract beneficial natural carnivorous insects as reinforcement against harmful herbivorous insects which are responsible for hampering the growth of plants. In this work, we explore the dynamical behavior of a volatile mediated plant-herbivore-carnivore system with fractional order differential equations. Basic results on the existence, uniqueness, non-negativity and boundedness of the solutions, local and global stability of coexistence equilibrium points and limit cycles emerging through Hopf bifurcation are investigated. Stability behavior around coexistence equilibrium point changes with varying fractional order (α). Also the existence of Hopf bifurcation is established by considering the fractional order α as a bifurcation parameter. Moreover, the attraction factor of plant volatile to carnivore and predation rate for plant-herbivore are responsible for changing the system dynamics. Numerical simulations using matlab software are performed to support the analytical findings.     

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.     

Routes to bursting in a periodically driven oscillator

The dynamical behaviors of a periodic excited oscillator with multiple time scales in the form that order gap exists between the frequency of the excitation and the natural frequency, are investigated in this Letter. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamics. Different types of bursting phenomena, such as fold/Hopf bursting, fold/Hopf/homoclinic bursting and Hopf/homoclinic bursting, are presented, the mechanism of which is obtained based on the bifurcations of the generalized autonomous system as well as the introduction of the so-called transformed phase portraits. Furthermore, the evolution of the bursting is discussed in details, in which one may find that when the two limit cycles caused by the Hopf bifurcations of the two related equilibrium points interact with each other, homoclinic bifurcation may occur, leading to the merge of the two cycles to form a large amplitude cycle. The homoclinic bifurcation may cause the two asymmetric bursters to merge into a symmetric enlarged burster, in which the large amplitude of the spiking state agrees well with the amplitude of the cycle caused by the homoclinic bifurcation.     

四维Qi系统零平衡点的Hopf分岔反控制

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     

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     

Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation

This Letter is concerned with bifurcation and chaos control in scalar delayed differential equations with delay parameter τ. By linear stability analysis, the conditions under which a sequence of Hopf bifurcation occurs at the equilibrium points are obtained. The delayed feedback controller is used to stabilize unstable periodic orbits. To find the controller delay, it is chosen such that the Hopf bifurcation remains unchanged. Also, the controller feedback gain is determined such that the corresponding unstable periodic orbit becomes stable. Numerical simulations are used to verify the analytical results.