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Dynamical Behavior of Coupled Chaotic Oscillators and its Control

耦合混沌振子的动力学行为及其控制

基本信息

批准号：
09650079
负责人：
FUNAKOSHI Mitsuaki
金额：
$ 1.98万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650079/
关键词：
Chaos Coupled Oscillators Coupled Map Controlling Chaos

项目摘要

As a model of coupled nonlinear oscillators, a periodic coupled map lattice (CML) composed of J lattice points are numerically examined. In this system, the logistic map is chosen as the local dynamics, and the nonlinearity parameter of this map is reduced to b for every Mth lattice points from 2 for other lattice points. These lattice points are diffusively coupled with the coupling constant epsilon. If J is large enough to satisfy the conditions J <greater than or equal> 5M the phase diagram on the (b, epsilon) plane depends on J only weakly except for a smalIn the phase diagrams, we find a few regions, called Regions A, B and C, in which the pattern selection is observed. Although Region A, found for small epsilon, extends from b = 0 to b = 2 which corresponds to the case of a homogeneous CML, Regions B and C, found for larger epsilon, extend only up to a certain b which is smaller than 2. Outside these regions, we usually observe the spatiotemporal chaos. Therefore, when M is not so large, the introduction of the periodicity can suppress the spatiotemporal chaos to the pattern selection for epsilon within Regions B and C if b is sufficiently small.It is also found that the transient length Nt, the time step at which a solution of the periodic CML reaches the pattern selection from a random initial state, increases with M roughly exponentially in Regions B and C and algebraically in Region A if b is sufficiently smaller than 2. Therefore, although the suppression of the spatiotemporal chaos is realized with smaller modification of the homogeneous CML if we choose larger M, the time step required for the attainment of this suppression from a random initial state becomes much larger.Furthermore, the pattern formation in Faraday waves is examined as a typical example of nonlinear extended system.

作为耦合非线性振子的模型，对由 J 个格点组成的周期耦合映射格子 (CML) 进行了数值研究。在该系统中，选择Logistic映射作为局部动力学，并且该映射的非线性参数对于每M个格点从其他格点的2减少到b。这些晶格点与耦合常数 epsilon 进行扩散耦合。如果 J 足够大以满足条件 J <大于或等于> 5M，则 (b, epsilon) 平面上的相图仅较弱地依赖于 J，除了较小的相图。在相图中，我们发现几个区域，称为区域 A、B 和 C，在其中观察到图案选择。虽然针对小 epsilon 发现的区域 A 从 b = 0 延伸到 b = 2（对应于同质 CML 的情况），但针对较大 epsilon 发现的区域 B 和 C 仅延伸到小于 2 的某个 b。在这些区域之外，我们通常观察到时空混沌。因此，当 M 不太大时，如果 b 足够小，则引入周期性可以抑制区域 B 和 C 内 epsilon 模式选择的时空混沌。还发现，瞬态长度 Nt（周期性 CML 的解从随机初始状态到达模式选择的时间步长）在区域 B 和 C 中随 M 大致呈指数增长，在区域 A 中随 M 增长，如果 b 为远小于2。因此，如果我们选择较大的M，虽然可以通过对齐次CML进行较小的修改来实现时空混沌的抑制，但从随机初始状态实现这种抑制所需的时间步长会变得更大。此外，法拉第波中的图案形成作为非线性扩展系统的典型例子进行了研究。