arXiv 2102.022722021-02nlin.CDmath.DSnlin.PS

耦合超图映射与混沌簇同步

Coupled Hypergraph Maps and Chaotic Cluster Synchronization

Tobias Böhle, Christian Kuehn, Raffaella Mulas, Jürgen Jost

备注：: 6 pages, 5 figures
发表信息：: EPL (2021)
DOI：: 10.1209/0295-5075/ac1a26

摘要：

耦合映射格是网络/图上的原型动力系统。它们表现出通过扩散/拉普拉斯耦合和非线性反应的相互作用产生的复杂模式，这些反应由每个节点处的单个迭代映射建模;这些映射通常被视为单峰，例如，后勤或帐篷地图。在这封信中，我们提出了一类涉及超图拉普拉斯算子的高阶耦合动力系统，我们称之为耦合超图映射（CHM）。通过结合同步状态的线性化（不）稳定性分析、超图谱理论和数值方法，我们发现了在不同耦合强度和单峰映射的主要分岔参数下，参数空间中发生的混沌簇同步的鲁棒区域.此外，我们发现拉普拉斯和超图拉普拉斯耦合之间的关键差异，并检测各种其他类的周期性和准周期性模式。结果表明，耦合图映射具有很高的复杂性，是理解经典图上动力学与超图上动力学异同的一个很好的通用模型类.

英文摘要：

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each node; the maps are often taken as unimodal, e.g., logistic or tent maps. In this letter, we propose a class of higher-order coupled dynamical systems involving the hypergraph Laplacian, which we call coupled hypergraph maps (CHMs). By combining linearized (in-)stability analysis of synchronized states, hypergraph spectral theory, and numerical methods, we detect robust regions of chaotic cluster synchronization occurring in parameter space upon varying coupling strength and the main bifurcation parameter of the unimodal map. Furthermore, we find key differences between Laplacian and hypergraph Laplacian coupling and detect various other classes of periodic and quasi-periodic patterns. The results show the high complexity of coupled graph maps and indicate that they might be an excellent universal model class to understand the similarities and differences between dynamics on classical graphs and dynamics on hypergraphs.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文