Xu Li, Zhang Guang, Cui Haoyue
School of Science, Tianjin University of Commerce, Tianjin, China.
PLoS One. 2016 Jul 6;11(7):e0158591. doi: 10.1371/journal.pone.0158591. eCollection 2016.
The logistic coupled map lattices (LCML) have been widely investigated as well as their pattern dynamics. The patterns formation may depend on not only fluctuations of system parameters, but variation of the initial conditions. However, the mathematical discussion is quite few for the effect of initial values so far. The present paper is concerned with the pattern formation for a two-dimensional Logistic coupled map lattice, where any initial value can be linear expressed by corresponding eigenvectors, and patterns formation can be determined by selecting the corresponding eigenvectors. A set of simulations are conducted whose results demonstrate the fact. The method utilized in the present paper could be applied to other discrete systems as well.
逻辑耦合映射格子（LCML）及其模式动力学已得到广泛研究。模式的形成不仅可能取决于系统参数的波动，还可能取决于初始条件的变化。然而，迄今为止，关于初始值影响的数学讨论相当少。本文关注二维逻辑耦合映射格子的模式形成，其中任何初始值都可以由相应的特征向量线性表示，并且模式形成可以通过选择相应的特征向量来确定。进行了一组模拟，其结果证明了这一事实。本文所采用的方法也可应用于其他离散系统。
