From lag synchronization to pattern formation in networked dynamics |
| |
Authors: | Zhiyong Zhang Jigui Luo Zengrong Liu |
| |
Institution: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China;2. College of Science, Shanghai University, Shanghai 200444, China;3. Institute of Systems Biology, Shanghai University, Shanghai 200444, China |
| |
Abstract: | The relationship between lag synchronization and pattern formation is investigated in this article by taking networked dynamics as spatio–temporal models. Firstly some results in two-dimensional open flow models with unidirectional coupling term are presented, and sufficient conditions for globally asymptotically stable lag synchronization in discrete and continuous cases are revealed by analytic method to elucidate the wave pattern evoked by the lag synchronization in such models. Then, an ad hoc network topology, a so-called “tier-network”, is introduced, which is an acyclic digraph with one center node and all the directed pathways from any other node to the center node are equal in length. And the dynamics in tier-networks is investigated. Some similarly sufficient conditions for globally asymptotically stable lag synchronization is obtained by analytic method, and the wave pattern in tier-networks evoked by lag synchronization is illustrated. The above results are supported by the numerical simulation in discrete case. |
| |
Keywords: | Lag synchronization Pattern formation Chaotic wave Time-delayed coupling Tier-network |
本文献已被 ScienceDirect 等数据库收录! |
|