Real and complex behavior for networks of coupled logistic maps
详细信息 查看全文
- 作者：Anca Rǎdulescu ; Ariel Pignatelli
- 关键词：Coupled complex maps ; Nonlinear network architecture ; Uni ; Julia set ; Equi ; Mandelbrot set ; Multi ; orbit ; Connectivity
- 刊名：Nonlinear Dynamics
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：87
- 期：2
- 页码：1295-1313
- 全文大小：
- 刊物类别：Engineering
- 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
- 出版者：Springer Netherlands
- ISSN：1573-269X
- 卷排序：87
文摘
Many natural systems are organized as networks, in which the nodes interact in a time-dependent fashion. The object of our study is to relate connectivity to the temporal behavior of a network in which the nodes are (real or complex) logistic maps, coupled according to a connectivity scheme that obeys certain constrains, but also incorporates random aspects. We investigate in particular the relationship between the system architecture and possible dynamics. In the current paper, we focus on establishing the framework, terminology and pertinent questions for low-dimensional networks. A subsequent paper will further address the relationship between hardwiring and dynamics in high-dimensional networks. For networks of both complex and real node maps, we define extensions of the Julia and Mandelbrot sets traditionally defined in the context of single-map iterations. For three different model networks, we use a combination of analytical and numerical tools to illustrate how the system behavior (measured via topological properties of the Julia set) changes when perturbing the underlying adjacency graph. We differentiate between the effects on dynamics of different perturbations that directly modulate network connectivity: increasing/decreasing edge weights, and altering edge configuration by adding, deleting or moving edges. We discuss the implications of extending Fatou–Julia theory from iterations of single maps, to iterations of ensembles of maps coupled as nodes in a network.