Botella-Soler V, Glendinning P
IST Austria (Institute of Science and Technology Austria), Am Campus 1, A-3400 Klosterneuburg, Austria.
School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA),University of Manchester, Manchester M13 9PL, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062809. doi: 10.1103/PhysRevE.89.062809. Epub 2014 Jun 16.
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be nontrivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: Nodes can be divided in differently synchronized classes but, contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behavior can evolve from undifferentiated nodes.
我们描述了一个由耦合混沌映射组成的简单自适应网络。尽管网络节点处映射的动力学可能很复杂，但对于耦合参数的所有值，该网络都会达到一个稳定状态（冻结拓扑）。网络结构呈现出有趣的层次特性，并且在某些参数区域中，动力学是多同步的：节点可以被划分为不同的同步类，但与簇同步不同的是，同一类中的节点不必相互连接。据推测，这些复杂的同步模式在系统生物学和电路中发挥作用。我们研究的自适应系统描述了这种行为如何从无差异的节点演化而来。
