物理学报2016，Vol.65Issue(10)：100501-1-100501-10,10.DOI:10.7498/aps.65.100501
耦合不连续系统同步转换过程中的多吸引子共存∗
Synchronization transition with co existence of attractors in coupled discontinuous system
摘要
Abstract
The studies of extended dynamics systems are relevant to the understanding of spatiotemporal patterns observed in diverse fields. One of the well-established models for such complex systems is the coupled map lattices, and several fea-tures of pattern formation including synchronization, unsynchronization, traveling waves and clustering synchronization are found. Among the above-mentioned patterns, chaotic synchronization has been intensively investigated in recent years. It has been demonstrated that two or more chaotic systems can be synchronized by linking them with mutual coupling or a common signal or some signals. Over the last decade, a number of theoretical methods have been presented to deal with this problem, such as the methods of master stability functions and eigenvalue analysis. While much effort has been devoted to the networks with different topological structures in continuous systems. The coupled discontinuous maps have been investigated with increasing interest in recent years, they showed that the complete synchronization in coupled discontinuous systems is more complicated than in coupled continuous systems. However, a similar problem of synchronization transition in coupled discontinuous systems is much less known. <br> The synchronization transition in coupled discontinuous map lattices is studied. The average order parameter and maximal Lyapunov exponent are calculated to diagnose the synchronization of coupled piecewise maps. The results indicate that there exist the periodic clusters and the synchronization state, and a new transition style from periodic cluster states to complete synchronization states is found. The periodic cluster states consist of two kinds of periodic orbits: symmetric periodic orbits and asymmetric periodic orbits. <br> Based on the pattern analysis, the common features of the patterns are constructed by the two periodic attractors, and the periodic orbit is an unstable periodic orbit of the isolate map. The discontinuities in a system can divide the phase space into individual zones of different dynamical features. The interactions between the local nonlinearity and the spatial coupling confine orbit into certain spaces and form a dynamic balance between two periodic clusters. The system can reach complete synchronization states when the balance is off. It is shown that synchronization transition of the coupled discontinuous map can exhibit the different processes, which depends on coupling strength. Four transition modes are found in coupled discontinuous map: 1) the transition, from the coexistence of chaotic synchronization and chaotic un-synchronization states to the coexistence of chaotic synchronization, chaotic un-synchronization, symmetric periodic orbits and asymmetric periodic orbits;2) the transition from the coexistence of chaotic synchronization, chaotic un-synchronization, symmetric periodic orbits and asymmetric periodic orbits to the coexistence of chaotic synchro-nization, symmetric periodic orbits and asymmetric periodic orbits; 3) the transition from the coexistence of chaotic synchronization, symmetric periodic orbits and asymmetric periodic orbits to the coexistence of chaotic synchronization and symmetric periodic orbits;4) the transition from the coexistence of chaotic synchronization and symmetric periodic orbits to the chaotic synchronization. Because the local dynamics has discontinuous points, the coupled system shows a riddle basin characteristic in the phase space, and the synchronization transition of coupled piecewise maps looks more complex than continuous system.关键词
同步转换/不连续系统/吸引子共存Key words
synchronization transition/discontinuous system/coexistence of attractors引用本文复制引用
杨科利..耦合不连续系统同步转换过程中的多吸引子共存∗[J].物理学报,2016,65(10):100501-1-100501-10,10.基金项目
国家自然科学基金(批准号:11547247)、陕西省教育厅科研计划项目(批准号:15JK1045)和宝鸡文理学院重点科研项目(批准号:ZK15028)资助的课题 （批准号:11547247）
