耦合哈密顿系统中测度同步的研究

测度同步现象是耦合哈密顿系统的一种重要性质.对规则系统和混沌系统的测度同步性 质作了深入研究，重点讨论了耦合哈密顿系统处于混沌状态时，系统测度同步的特点及系统 的相位关系.提出了一种定量判断测度同步的简单方法，考虑了高斯白噪声对系统中测度同 步性质的影响. 关键词： 耦合哈密顿系统 测度同步 相锁定 高斯白噪声     

探究耦合双摆系统测度同步的影响因素

同步是自然界中普遍存在的一种现象,是许多复杂系统实现功能的动力学基础.本文首先对无耗散耦合双摆系统进行建模,然后利用Matlab软件对影响测度同步的因素进行分析,包括横梁和摆锤之间的质量比、两个摆的长度差和质量差等.研究发现,随着横梁和摆锤的质量比的减小,两个摆之间的耦合强度逐渐增大;当质量比达到某一阈值时,两个摆达到测度同步并且相位相反.同时发现,随着两个摆的摆长差和质量差的增加,两个摆之间的同步能力将会变弱,系统将出现退同步现象.     

理论力学中混沌内容的讲授

介绍一种在理论力学教学中讲授非线性混沌的方法.这个方法的特点是混沌内容与理论力学内容不脱节,只占用6～8学时,但可以把混沌动力学的最基本概念在理论力学框架内讲清楚.     

电场中里德伯原子动力学性质的半经典理论研究

利用闭合轨道理论和Poincaré截面两种方法研究了鞍点附近电场中高里德伯态Li原子的动力学性质.由于原子实的作用,体系是混沌的,闭合轨道和周期轨道在混沌体系中并存,但二者在Poincaré截面上的反映是不同的.讨论了两种半经典理论在研究混沌体系时的联系,得到了仅靠闭合轨道理论得不到的信息. 关键词： Poincaré截面 回归谱 Stark效应     

端口受控哈密顿系统的混沌反控制研究

对端口受控哈密顿系统能量变化和动力学特性进行了分析，采用了分段线性输出反馈对其进行混沌反控制，给出了构造分段线性输出反馈矩阵的方法.此方法具有物理概念明确，不需计算李雅普诺夫指数，易于实现等特点.数值计算和仿真研究表明了此方法的有效性 关键词： 哈密顿系统 混沌 反控制     

统一混沌系统的耦合同步

对线性耦合的两个统一混沌系统同步进行研究.基于线性时变连续系统的稳定性理论，得到初始值不同的两个统一混沌系统全局渐进同步的一种新的充分条件.另外，与已经提出的判定统一混沌系统同步的方法进行比较，发现这里得到的充分条件的约束关系少、缺少保守性，而且满足的耦合系数范围更广.将该方法应用于统一混沌系统，数值仿真表明了该法的有效性与可行性. 关键词： 统一混沌系统 耦合同步 线性时变连续系统     

利用随机相位实现Duffing系统的混沌控制

基于线性随机系统Khasminskii球面坐标变换, 计算了谐和激励中含有随机相位的Duffing 方程的最大Lyapunov指数. 依据平均最大Lyapunov指数符号的变化, 分析随机相位对非线性系统动力学行为的影响.说明随机相位可以产生混沌亦可抑制混沌, 从而可以作为混沌控制的一种方法. 结合对相图、Poincaré截面、时间历程图的分析, 说明上述方法是有效的. 关键词： 随机相位 混沌控制 最大Lyapunov指数 Poincaré截面     

一个一维周期驱动哈密顿系统的实例及混沌控制

提出一种新的周期驱动非线性不可积哈密顿系统模型,并对其特性进行了讨论.通过简单的非反馈控制装置对这一系统进行混沌控制,将其混沌轨道分别控制在周期,准周期及指定混沌轨道上.与以往的控制方法不同的是,控制项仅是一结构简单、可调节的限位装置.为保守系统混沌控制的实际应用提供可供选择的途径     

Hénon混沌系统的预测控制与同步

用带有终端滑模等式约束的模型预测控制方法,对Hénon映象和Logistic映象的追踪控制和同步进行研究.由于滑动模态的引入,提高了受控系统抑制参数摄动和随机扰动的能力,改善了控制系统的鲁棒性,实现了系统对参考信号的追踪控制.数值仿真表明了该方法的有效性. 关键词： Hénon系统 预测控制 混沌同步     

一个一维周期驱动哈密顿系统的实例及混沌控制

提出一种新的周期驱动非线性不可积哈密顿系统模型,并对其特性进行了讨论.通过简单的非反馈控制装置对这一系统进行混沌控制,将其混沌轨道分别控制在周期,准周期及指定混沌轨道上.与以往的控制方法不同的是,控制项仅是一结构简单、可调节的限位装置.为保守系统混沌控制的实际应用提供可供选择的途径.     

级联功率因数校正变换器的级间耦合非线性动力学行为分析

级联功率因数校正(PFC)变换器是一个由PFC变换器和直流-直流(DC-DC)变换器级联而成的非线性系统.建立了级联PFC变换器的非线性模型,据此对系统的级间耦合非线性动力学行为进行了数值仿真,并进行了实验验证和分析.结果表明:PFC级输出电容减小会使系统出现分岔,引起DC-DC级输出电压的变化;DC-DC级负载电阻变化会改变PFC级的非线性动力学行为;当DC-DC级出现占空比饱和时,PFC级与DC-DC级之间会出现复杂的相互耦合影响过程.     

耦合电路系统的分岔研究

研究了由两个非线性电路系统耦合所构成的系统,给出高维系统平衡点的存在性条件和具体解析形式,分析了平衡点的余维1和余维2分岔,并对极限环进行了延拓,得到比较复杂的分岔形式.两个周期运动的子系统在不同的耦合参数下相互作用时,可能导致周期运动、混沌等丰富的动力学行为,通过对耦合前后平衡点的定性分析,得到了在弱耦合情况下平衡点变为中立型鞍点与分岔图出现的不连续现象之间的联系.     

Chaotic synchronization in Hamiltonian systems

It is shown that Hamiltonian systems can exhibit the phenomenon of chaotic synchronization. Specific attention is paid to the standard map. Analytic synchronization conditions are derived and numerically verified for the standard map. We report on experimental studies of an analog electronic circuit realization of a "piecewise linear standard map." When coupled appropriately to a duplicate circuit, chaotic synchronization is observed. The relevance of this study to synchronization in other Hamiltonian systems is discussed.     

Partial synchronization in linearly and symmetrically coupled ordinary differential systems

In this paper, we discuss partial synchronization of linearly and symmetrically coupled ordinary differential equations (LSCODEs). The synchronization phenomena are investigated via invariant synchronization manifolds. On the basis of geometrical analysis of the synchronization manifold, several criteria for the global attractivity of the invariant synchronization manifold are obtained. Combining these criteria with some numerical examples, we investigate how topological structure affects partial synchronization, and give a valuable discussion about the possibility of partial synchronization with increasing coupling strength.     

单向耦合下两个不同Lorenz系统的广义同步

对单向耦合下两个不同的Lorenz系统的广义同步进行了研究,利用辅助系统方法,基于稳定性理论和响应系统的有界性,得到了它们达到广义同步时的充分条件,并根据响应系统的修正系统具有零渐近稳定平衡点、非零渐近稳定平衡点和轨道渐近稳定周期解的情况,将广义同步分为第一类、第二类和第三类;利用Routh-Hurwitz定理,对修正系统平衡点的稳定性进行了分析,给出了单向耦合下两个不同Lorenz系统具有第一类、第二类广义同步的充分条件.数值仿真表明了该方法的有效性与可行性.     

Visibility graph similarity: A new measure of generalized synchronization in coupled dynamic systems

Synchronization is defined as interdependencies among coupled dynamic systems. In most coupled systems the intrinsic and internal variants, and the interdependencies among their subsystems are not accessible. Therefore, in order to quantify the interdependencies among the coupled systems, attempts have been made through measuring the synchronization between their outputs represented mostly as time series. In this paper a new method, called Visibility Graph Similarity (VGS), is presented as a method of measuring Generalized Synchronization. First, each time series is reconstructed as a trajectory in a state space. Next, a Distance Time Series (DTS) is created from a sequence of relative distances of the states to a reference state. Subsequently, a visibility graph (VG) is constructed using DTS. Then, a sequence of degrees of the VG, called Degree Sequence (DS), is obtained. Correlation of the DSs of two coupled systems is called VGS and is presented as a measurement of similarity of dynamics of the coupled systems. The synchronization measurement performance of the VGS is compared with synchronization likelihood (SL) and the classical cross correlation method using two identical and non-identical models of two coupled Henon map over the entire time domain. Also, it is compared with SL for tracing temporal synchronization using both models. It is shown that VGS provides a more accurate measure of the overall synchronization compared with SL. It is more reliable for measuring weak couplings compared with the cross correlation method. Moreover, VGS uses fewer parameters and detects the temporal synchronization sooner than the SL.     

Multiobjective synchronization of coupled systems

In this paper, multiobjective synchronization of chaotic systems is investigated by especially simultaneously minimizing optimization of control cost and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach that includes a hybrid chromosome representation. The hybrid encoding scheme combines binary representation with real number representation. The constraints on the coupling form are also considered by converting the multiobjective synchronization into a multiobjective constraint problem. In addition, the performances of the adaptive learning method and non-dominated sorting genetic algorithm-II as well as the effectiveness and contributions of the proposed approach are analyzed and validated through the Ro?ssler system in a chaotic or hyperchaotic regime and delayed chaotic neural networks.     

Bursting synchronization in non-locally coupled maps

Neuron activity presents two timescales, a fast one related to action-potential spiking, and a slow timescale in which bursting takes place. Bursting activity in neuron ensembles can be synchronized, meaning the adjustment of the bursting phases due to coupling. We investigated bursting synchronization in a non-locally coupled lattice using a two-dimensional map to describe neuron activity. The coupling involves all sites in a lattice, the corresponding strength decreasing with the lattice distance in a power-law fashion. We observed bursting synchronization for wide intervals of the coupling parameters. We also investigated the bursting synchronization of the ensemble with an external time-periodic signal applied to one or more selected neurons.     

Phase synchronization in bi-directionally coupled chaotic ratchets

We show the existence of phase synchronization in bi-directionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states. A transition from a regime where the phases rotate with different velocities to a synchronous state where the phase difference is bounded was observed as the coupling was increased. In addition, the region of synchronization in which the system is permanently phase locked was identified. In this regime, the transverse Lyapunov exponent corresponding to both phases remain positive. Our calculations show that the transition to a synchronized state occurs via a crisis transition to an attractor filling the whole phase space.