DFG-RSF: Complex dynamical networks: effects of heterogeneity, adaptivity, and delays

DFG-RSF：复杂动态网络：异质性、适应性和延迟的影响

基本信息

批准号：
308748074
负责人：
Professor Dr. Eckehard Schöll
金额：
--
依托单位：
Forschungsbereich Komplexitätsforschung
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/308748074?language=en
关键词：
DFG RSF Complex dynamical networks

项目摘要

Two types of network models have been mostly considered so far in the literature: static and dynamic networks. In static networks, only the structure of connections is of importance. In contrast, in dynamical networks the state of each unit depends on time, and its dynamics is influenced by the interaction with other units. In spite of the large number of interesting and significant results, the general theory of dynamical networks is only at the stage of early development, which is due to the extreme complexity and broadness of the subject. This project addresses a fundamental problem of the theory of complex nonlinear dynamical networks. More specifically, it considers the following aspects of complexity: inhomogeneous topological structure, adaptive connections, and the presence of coupling delays. The types of networks to be studied include but are not limited to neural and neuromorphic networks, wireless sensor networks, and networks of electronic oscillators. The main objectives include: I. Development of the definition of the term ''complexity'' for dynamical networks, as well as the qualitative criteria and quantitative measures for their complexity. This direction is very important since the term ''complex network'' has not been strictly defined so far, although its wide use in nonlinear dynamics has long been calling for elaboration of its definition.II. Development of neuromorphic network models with complex modular structure and analytic methods of study of such models. We will construct models reproducing structural properties of real neuronal networks, primarily their modularity, and study the link between the connectivity characteristics and their function. III. Study of the influence of coupling delays and adaptivity of connections on the dynamics of pulse-coupled networks of phase oscillators. The main objective is to study the suppression of the global synchronization and emergence of phase patterns and other complex dynamical regimes. We aim to understand how delayed coupling and plasticity affect the bifurcation mechanisms for the desynchronization in pulse-coupled systems. IV. Development and study of electronic prototypes of complex networks with coupling delays demonstrating nontrivial dynamical regimes. Particularly, we plan to implement a network of oscillators interacting via long chains of excitable units and demonstrating novel types of chimera-like behavior.

到目前为止，在文献中大多考虑了两种类型的网络模型：静态和动态网络。在静态网络中，仅连接结构很重要。相反，在动态网络中，每个单元的状态取决于时间，其动力学受到与其他单位的相互作用的影响。尽管有大量有趣和重要的结果，但动态网络的一般理论仅在早期发展阶段，这是由于受试者的极端复杂性和广泛性所致。该项目解决了复杂非线性动力网络理论的基本问题。更具体地说，它考虑了复杂性的以下方面：不均匀的拓扑结构，适应性连接以及耦合延迟的存在。要研究的网络类型包括但不限于神经和神经形态网络，无线传感器网络以及电子振荡器的网络。主要目标包括：I。为动态网络的“复杂性”一词的定义开发，以及其复杂性的定性标准和定量措施。这个方向非常重要，因为到目前为止，“复杂网络”一词尚未严格定义，尽管它在非线性动力学中的广泛使用一直在呼吁阐述其定义。具有复杂模块化结构和研究模型的分析方法的神经形态网络模型的开发。我们将构建模型，重现实际神经元网络的结构特性，主要是它们的模块化，并研究连接特性及其功能之间的联系。 iii。研究耦合延迟和连接适应性对相振荡器脉冲耦合网络动力学的影响。主要目的是研究抑制全局同步和相位模式和其他复杂动力学制度的出现。我们旨在了解延迟的耦合和可塑性如何影响脉冲耦合系统中对同步的分叉机理。 iv。耦合延迟的复杂网络的电子原型的开发和研究表明了非平凡的动力学制度。特别是，我们计划实施通过可激发单元的长链相互作用的振荡器网络，并展示新型类似嵌合体的行为。