LATTIS-Institut National des Sciences Appliquées de Toulouse, Université de Toulouse, Toulouse, France.
Chaos. 2011 Jun;21(2):023110. doi: 10.1063/1.3540319.
It is widely believed that when two discrete time chaotic systems are coupled together then there is a contraction in the phase space (where the essential dynamics takes place) when compared with the phase space in the uncoupled case. Contrary to such a popular belief, we produce a counter example--we consider two discrete time chaotic systems both with an identical attractor A, and show that the two systems could be nonlinearly coupled in a way such that the coupled system's attractor persists strongly, i.e., it is A × A despite the coupling strength is varied from zero to a nonzero value. To show this, we prove robust topological mixing on A × A. Also, it is of interest that the studied coupled system can exhibit a type of synchronization called generalized partial synchronization which is also robust.
人们普遍认为，当两个离散时间混沌系统耦合在一起时，与未耦合情况下的相空间相比，相空间会发生收缩。与这种普遍观点相反，我们给出了一个反例——我们考虑两个离散时间混沌系统都具有相同的吸引子 A，并表明这两个系统可以以一种非线性的方式耦合，使得耦合系统的吸引子保持不变，即尽管耦合强度从 0 变化到非零值，它仍然是 A×A。为了证明这一点，我们证明了 A×A 上的鲁棒拓扑混合。此外，有趣的是，所研究的耦合系统可以表现出一种称为广义部分同步的同步类型，这种同步也是鲁棒的。
