一个全局耦合不连续映像格子中的冻结化随机图案模式

本文研究了一类既不连续又不可逆分段线性映像构成的全局耦合映像格子系统中的一类典型集体动力学行为, 即冻结化随机图案模式. 计算了平均同步序参量和最大李雅普诺夫指数随耦合强度的变化. 结果显示, 当耦合强度超过某个阈值后, 在给定动力学变量的初始下, 系统几乎都能达到完全或部分同步状态, 出现冻结化随机图案. 这些现象表明, 耦合映像格子系统中存在着多个共存的吸引子. 因此, 其冻结化图案的结构和分布敏感地依赖于格点动力学变量初始值的选取. 感兴趣地是, 即使当单映像处于混沌状态时, 格点间的耦合仍能将系统调制到规则的运动状态, 这种特征对于混沌控制具有重要的利用价值. 上述丰富动力学行为的出现是由于单映像中不连续性和不可逆性相互作用的结果.

Frozen random patterns in a globally coupled discontinuous map lattices system

A class of the characteristic collective dynamic behaviors, i.e., the frozen random patterns, in a globally coupled both-discontinuous-and-non-invertible-map lattices are studied. The coupling-strength dependences of the mean order parameters and the largest Lyapunov exponents are calculated and analyzed. The result shows that, given the initial values for the dynamical variables, the system will reach its complete or partial synchronization state when the coupling strength is beyond some critical value, where the frozen random pattern appears. These phenomena reveal that there are coexisting attractors in the system, and thus the structure and the distribution of the frozen random patterns sensitively depend on the choice of the initial dynamics variables. The interesting event is that the system can be modulated to some regular states of motion by the coupling among lattices even when the single maps are in the chaotic states, which may have some important applications in controlling chaos. The rich dynamical behaviors mentioned above are due to the interplay between the discontinuity and the non-invertibility in the map.