Sinha Sudeshna
Institute of Mathematical Sciences, Taramani, Chennai 600 113, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Jul;66(1 Pt 2):016209. doi: 10.1103/PhysRevE.66.016209. Epub 2002 Jul 18.
We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbor coupling never allows spatiotemporal synchronization in our system, randomly rewiring some of those connections stabilizes entire networks at x*, where x* is the strongly unstable fixed point solution of the local chaotic map. In fact, the smallest degree of randomness in spatial connections opens up a window of stability for the synchronized fixed point in coupling parameter space. Further, the coupling epsilon(bifr) at which the onset of spatiotemporal synchronization occurs, scales with the fraction of rewired sites p as a power law, for 0.1<p<1. We also show that the regularizing effect of random connections can be understood from stability analysis of the probabilistic evolution equation for the system, and approximate analytical expressions for the range and epsilon(bifr) are obtained.
我们研究了耦合混沌映射网络的时空动力学,其耦合连接具有不同程度的随机性。虽然严格的最近邻耦合在我们的系统中永远不会实现时空同步,但随机重新连接其中一些连接会使整个网络在x处稳定下来,其中x是局部混沌映射的强不稳定不动点解。事实上,空间连接中最小程度的随机性为耦合参数空间中的同步不动点打开了一个稳定窗口。此外,对于0.1 < p < 1,发生时空同步起始时的耦合ε(bifr)与重新布线位点的比例p成幂律关系。我们还表明,随机连接的正则化效应可以从系统概率演化方程的稳定性分析中得到理解,并获得了范围和ε(bifr)的近似解析表达式。