非线性系统混沌运动的神经网络控制

设计前馈反传神经网络控制非线性系统混沌运动的新方法.根据扰动参数模型输入输出数据,按照非线性学习算法训练网络产生系统稳定所需的小扰动控制信号,去镇定混沌运动,使嵌入在混沌吸引子中的不稳定周期轨道回到稳定不动点上.Hnon映射数值仿真结果表明,这种方法控制非线性混沌系统响应速度快、控制精度高 关键词： 混沌控制 神经网络 吸引子 非线性     

基于自适应脉冲微扰实现混沌控制的研究

提出了自适应脉冲微扰控制混沌系统的方法.在参量脉冲微扰中引入自适应控制策略，设计出可以产生合适的脉冲强度的自适应控制器来实现混沌控制.采取这种方法对混沌的Rssle r连续系统和Hnon离散映射实施仿真控制，能够将系统稳定到不同的周期轨道或不动点上 ；并且，数值仿真结果还表明该控制方法具有较强的鲁棒性. 关键词： 自适应 脉冲微扰 混沌控制 鲁棒性     

一种改进的谐振参数扰动法及其在DC/DC变换器混沌控制中的应用

种改进的谐振参数扰动法来控制混沌，该混沌控制方法引入了基于非线性映射的调制，其控制目标可以是任意周期的轨道，而不是原混沌吸引子中的嵌入轨道。作为一个应用实例，文中描述了该方法在电流模式控制dc/dc变换器中的应用结果。     

用自适应脉冲微扰引导混沌系统到周期解

用自适应脉冲微扰方法控制的系统的某个系统变量作为驱动,设计了一种自适应控制器方法对两个或多个响应混沌系统进行脉冲微扰,引导这些系统从混沌运动到低周期运动,实现同时控制多个混沌系统到不同的周期态. 当选择相同的自适应控制器输入变量实施脉冲微扰时,还可控制两个或多个混沌系统达到不同的周期态同步. 通过对R?ssler混沌系统的仿真研究证实了方法的有效性. 关键词： 混沌控制 系统参量 自适应控制器 脉冲微扰 周期态同步     

基于参数切换算法的混沌系统吸引子近似及其电路设计

基于参数切换算法和离散混沌系统, 设计一种新的混沌系统参数切换算法, 给出了两算法的原理. 采用混沌吸引子相图观测法, 研究了不同算法下统一混沌系统和Rössler混沌系统参数切换结果, 最后引入方波发生器, 设计了Rössler混沌系统参数切换电路. 结果表明, 采用参数切换算法可以近似出指定参数下的系统, 其吸引子与该参数下吸引子一致; 基于离散系统的参数切换结果更为复杂, 当离散序列分布均匀时, 只可近似得到指定参数下的系统; 相比传统切换混沌电路, 参数切换电路不用修改原有系统电路结构, 设计更为简单, 输出结果受方波频率影响, 通过加入合适频率的方波发生器, 数值仿真与电路仿真结果一致.     

周期参数扰动的T混沌系统同宿轨道分析

针对一类周期参数扰动的T混沌系统, 通过变换将系统转化为具有广义Hamilton结构的周期参数扰动的慢变系统, 运用Melnikov方法对系统的同宿轨道进行了分析计算, 并给出了系统的同宿轨道参数分支条件. 同时, 通过数值实验, 对周期参数扰动控制策略及同宿轨道进行了仿真, 验证了文中理论分析的正确性. 关键词： Hamilton系统 Melnikov方法 同宿轨道 周期参数扰动     

Cubic映象的瞄准与控制

实现了沿参数轴对不稳定周期轨道的连续控制,通过同时应用调节参数与变量微扰可实现对混沌区与分岔区中任一点的瞄准。给出的方法具有抗干扰性     

平移法控制离散系统的倍周期分岔和混沌

利用平移系统的方法,实现了对离散非线性动力学系统的倍周期分岔的控制和混沌吸引子不稳定周期轨道的控制.只要选择适当的平移参数,使系统平移到不同位置,就可将系统控制在不同的预期轨道.将此方法应用到Logistic映射和Henon映射中取得了很好的控制效果.     

Bifurcation analysis of the logistic map via two periodic impulsive forces

The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincare′ map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map.     

Controlling chaos in a high dimensional system with periodic parametric perturbations

The effect of applying a periodic perturbation to an accessible parameter of a high-dimensional (coupled-Lorenz) chaotic system is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic system can result in limit cycles or significantly reduced dimension for relatively small perturbations.     

用数字有限脉冲响应滤波器控制混沌

利用数字有限脉冲响应滤波器稳定微分动力系统和二维离散映象混沌吸引子中不稳定周期轨道的方法，实现了高周期轨道的稳定控制.分别研究了Lorenz系统和Henon映象，给出了初步的分析和数值模拟结果.这种方法的主要特点是不需要获取混沌系统中不稳定周期轨道的任何信息，控制参数的选择与被控混沌系统无关. 关键词：     

Chaotic Solutions of a Typical Nonlinear Oscillator in a Double Potential Trap

We have obtained a general unstable chaotic solution of a typical nonlinear oscillator in a double potential trap with weak periodic perturbations by using the direct perturbation method. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding chaotic region and orbits in parameter space are described by numerical simulations.     

Feedback control of canards

We present a control mechanism for tuning a fast-slow dynamical system undergoing a supercritical Hopf bifurcation to be in the canard regime, the tiny parameter window between small and large periodic behavior. Our control strategy uses continuous feedback control via a slow control variable to cause the system to drift on average toward canard orbits. We apply this to tune the FitzHugh-Nagumo model to produce maximal canard orbits. When the controller is improperly configured, periodic or chaotic mixed-mode oscillations are found. We also investigate the effects of noise on this control mechanism. Finally, we demonstrate that a sensor tuned in this way to operate near the canard regime can detect tiny changes in system parameters.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

Clustering of Periodic Orbits and Ensembles of Truncated Unitary Matrices

In present article we consider a combinatorial problem of counting and classification of periodic orbits in dynamical systems on an example of the baker’s map. Periodic orbits of a chaotic system can be organized into a set of clusters, where orbits from a given cluster traverse approximately the same points of the phase space but in a different time-order. We show that counting of cluster sizes in the baker’s map can be turned into a spectral problem for matrices from truncated unitary ensemble (TrUE). We formulate a conjecture of universality of the spectral edge in the eigenvalues distribution of TrUE and utilize it to derive asymptotics of the second moment of cluster distribution in the regime when both the orbit lengths and the parameter controlling closeness of the orbit actions tend to infinity. The result obtained allows to estimate the size of average cluster for various numbers of encounters in periodic orbit.     

广义Hénon混沌系统的自适应双模控制与同步

提出一种广义Hénon映射的自适应双模控制与同步方法.广义Hénon映射的混沌吸引子比Hénon映射的混沌吸引子更复杂,控制与同步困难,对于保密通信来说具有更高的安全性.该方法采用自适应双模控制,实现了广义Hénon映射的追踪控制与同步,提高了受控系统抑制参数摄动和随机扰动的能力,改善系统的鲁棒性.仿真结果验证了该方法的有效性.