Real and complex behavior for networks of coupled logistic maps
Real and complex behavior for networks of coupled logistic maps
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DOI：
10.1007/s11071-016-3115-4
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发表时间：
2016-04
影响因子：
5.6
通讯作者：
A. Rădulescu;A. Pignatelli
中科院分区：
文献类型：
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作者：
A. Rădulescu;A. Pignatelli
许多自然系统被组织成网络，其中节点以时间依赖的方式相互作用。我们研究的目的是将连通性与网络的时间行为联系起来，其中节点是（真实的或复杂的）逻辑映射，根据服从某些约束的连通性方案耦合，但也包含随机方面。我们特别调查的系统架构和可能的动态之间的关系。在这篇论文中，我们主要讨论低维网络的框架、术语和相关问题。随后的论文将进一步解决高维网络中的硬连线和动态之间的关系。对于复杂和真实的节点映射的网络，我们定义了传统上定义在单映射迭代的上下文中的Julia和Mandelbrot集的扩展。对于三种不同的模型网络，我们使用分析和数值工具的组合来说明系统行为（通过theJulia集的拓扑性质测量）如何改变时，扰动底层邻接图。我们区分不同的扰动，直接调制网络的连接动态的影响：增加/减少边的权重，并通过添加，删除或移动边缘改变边缘配置。我们讨论了扩展Fatou-Julia理论的影响，从单个映射的迭代，到作为网络节点耦合的映射集合的迭代。
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 theJulia 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.