Wang Sheng-Jun, Du Ru-Hai, Jin Tao, Wu Xing-Sen, Qu Shi-Xian
Institute of Theoretical &Computational Physics, Shaanxi Normal University, Xi'an 710062, China.
School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
Sci Rep. 2016 Mar 29;6:23448. doi: 10.1038/srep23448.
The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down of synchronization process is observed, which is a novel phenomenon. The result shows that there are two typical kinds of transient process before the system reaches complete synchronization, which is demonstrated by both the coupled multiple-period maps and the coupled multiple-band chaotic maps. When the coupling is weak, the evolution of the system is governed mainly by the local dynamic, i.e., the node states are attracted by the stable orbits or chaotic attractors of the single map and evolve toward the synchronized orbit in a less coherent way. When the coupling is strong, the node states evolve in a high coherent way toward the stable orbit on the synchronized manifold, where the collective dynamics dominates the evolution. In a mediate coupling strength, the interplay between the two paths is responsible for the slowing down. The existence of different synchronization paths is also proven by the finite-time Lyapunov exponent and its distribution.
同步的速度和路径在系统功能中起着关键作用，而这一点至今尚未得到足够的关注。在这项工作中，我们研究了耦合逻辑斯谛映射的同步过程，该过程揭示了低维耗散系统的共同特征。我们观察到同步过程出现了减慢，这是一个新现象。结果表明，在系统达到完全同步之前存在两种典型的瞬态过程，这在耦合多周期映射和耦合多带混沌映射中均得到了证明。当耦合较弱时，系统的演化主要由局部动力学支配，即节点状态被单个映射的稳定轨道或混沌吸引子吸引，并以不太相干的方式向同步轨道演化。当耦合较强时，节点状态以高度相干的方式向同步流形上的稳定轨道演化，此时集体动力学主导演化。在中等耦合强度下，两条路径之间的相互作用导致了减慢。有限时间李雅普诺夫指数及其分布也证明了不同同步路径的存在。
