二维耦合映射系统中的吸引域和冒泡吸引盆

Attraction Domain and Riddled Basins in Two-Dimensional Coupled Mapping Systems

摘要: 混沌同步问题在多个领域都有重要的应用。比如：卫星运动中的混沌同步和反同步问题，分数阶金融系统中的混沌同步问题，不确定混沌系统的自适应同步问题。本文以二维耦合映射系统为例，讨论了混沌同步状态的弱稳定性，冒泡吸引盆的形成。同时利用临界曲线构造吸引域，分析吸引域在局部和全局冒泡出现中的作用。

Abstract: Chaotic Synchronization has significant applications in many fields. Examples include chaotic synchronization and desynchronization in the motion of satellites, chaotic synchronization in fractional order financial systems, and adaptive synchronization in uncertain chaotic systems. The purpose of this paper is to discuss the weak stability of chaotic synchronization and the formation of riddled basins using the two-dimensional coupled mapping system. The critical curve is simultaneously used to construct the attraction domain, and the role of the attraction domain in the emergence of local and global riddling is analysed.