Pethel Shawn D, Corron Ned J, Bollt Erik
U.S. Army Aviation and Missile Command, AMSRD-AMR-WS-ST, Redstone Arsenal, Alabama 35898, USA.
Phys Rev Lett. 2006 Jan 27;96(3):034105. doi: 10.1103/PhysRevLett.96.034105.
We present a method to reduce the [FORMULA: SEE TEXT] dynamics of coupled map lattices (CMLs) of N invertibly coupled unimodal maps to a sequence of N-bit symbols. We claim that the symbolic description is complete and provides for the identification of all fixed points, periodic orbits, and dense orbits as well as an efficient representation for studying pattern formation in CMLs. We give our results for CMLs in terms of symbolic dynamical concepts well known for one-dimensional chaotic maps, including generating partitions, Gray orderings, and kneading sequences. An example utilizing coupled quadratic maps is given.
我们提出了一种方法，可将由N个可逆耦合单峰映射构成的耦合映射格（CML）的[公式：见文本]动力学简化为一系列N位符号。我们声称，这种符号描述是完整的，能够识别所有不动点、周期轨道和稠密轨道，并且为研究CML中的模式形成提供了一种有效的表示方法。我们根据一维混沌映射中熟知的符号动力学概念给出了CML的结果，包括生成划分、格雷排序和揉序列。给出了一个利用耦合二次映射的示例。
