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     

Phase synchronization of chaotic oscillations in terms of periodic orbits

We consider phase synchronization of chaotic continuous-time oscillator by periodic external force. Phase-locking regions are defined for unstable periodic cycles embedded in chaos, and synchronization is described in terms of these regions. A special flow construction is used to derive a simple discrete-time model of the phenomenon. It allows to describe quantitatively the intermittency at the transition to phase synchronization. (c) 1997 American Institute of Physics.     

Estimating generating partitions of chaotic systems by unstable periodic orbits

An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.     

周期轨迹与不可积体系的量子化：Henon-Heiles体系的一个研究例子

研究了两个振子耦合的Henon-Heiles体系的周期轨迹与量子化问题.结果表明，周期轨迹的 作用量积分与体系的能量有着简单的线性关系.可以利用那些是整数值的周期轨迹的作用量 积分对不可积体系进行半经典量子化.由周期轨迹的物理内涵出发，揭示混沌体系的残余周 期轨迹具有与量子化有关的性质.这对于认识和理解经典力学与量子体系的联系关系及其物 理内涵有着深刻而重要的意义. 关键词： 周期轨迹 半经典量子化 混沌     

Computable chaotic orbits

We contrast analytic properties of chaotic maps with the results of fixed-precision computation and then use Turing's ideas of computable irrational numbers to illustrate the computation of chaotic orbits to arbitrary N-bit precision. This leads to the study of chaos theory via integer maps that are automata with long-range site interactions. We also explain why the β-shadowing lemma is not a justification for the use of fixed-precision arithmetic in chaos theory.     

Energy distribution in strongly perturbed chaotic system

The analytical expression for the energy distribution for the Duffing oscillator that moves chaotically under the strong harmonic perturbation is obtained as a function of the perturbation amplitude and frequency.     

Topological classification of periodic orbits in Lorenz system

We systematically investigate the periodic orbits of the Lorenz flow up to certain topological length. As an alternative to Poincare′ section map analysis, we propose a new approach for establishing one-dimensional symbolic dynamics based on the topological structure of the orbit. A newly designed variational method is stable numerically for cycle searching,and two orbital fragments can be used as basic building blocks for initialization. The topological classification based on the entire orbital structure is revealed to be effective. The deformation of periodic orbits with the change of parameters provides a chart to the periods of cycles. The current research may provide a methodology for finding and systematically classifying periodic orbits in other similar chaotic flows.     

Dynamics of periodic pulse collisions in a strongly dissipative-dispersive system

We report on the dynamics of the periodic collision process occurring between different pulse bound states in a stretched-pulse erbium-doped fiber laser. The acquisition of a large number of second-order correlation traces allows us to reconstruct the dynamics of a single collision event. The measurements clearly demonstrate that, unlike true solitons in the case of integrable systems, the pulses do not fully overlap in the course of a collision. Instead, the collision proceeds through the exchange of bonds between the individual pulses constituting the bound states.     

动力学变换法探测连续系统不稳定周期轨道

本文利用动力学变换方法和庞加莱截面方法对两种连续混沌动力学系统进行不稳定周期轨道探测研究, 并对Lorenz系统进行了替代数据法检验.结果表明:基于庞加莱截面的动力学变换改进算法 可有效探测连续混沌动力学系统中的不稳定周期轨道.     

Generalized synchronization in the action of a chaotic signal on a periodic system

Generalized synchronization is observed during the action of a chaotic signal on generators of periodic oscillations. The features in the behavior of the synchronous regime threshold upon a change in the chaotic signal parameters are investigated. The possibility of using such devices for concealed information transfer is demonstrated.     

Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

An increase of the coupling strength in the system of two coupled R?ssler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of phase synchronization is related to phase-lockings on the surfaces of unstable tori, whereas transition from phase to lag synchronization is preceded by a decrease in the number of unstable periodic orbits.     

On the evaluation of the quantum corrections to periodic TDHF orbits

The evaluation of the leading order quantum correction to periodic mean-fields within the path integral approach is reinvestigated. The corresponding gaussian functional integral is well defined only after restoring the time-translation invariance broken by the time-dependent meanfield approximation. The particular structure of the action function permits one to restore the invariance in two different ways, that seem to exhibit an ambiguity in the evaluation of the leading order quantum correction. We prove, however, that both ways of restoring the time-translation invariance yield the same result, showing that the leading order quantum correction is uniquely defined within the path integral approach.