Self-organization and control in coupled networks and time-delayed systems (A03)

耦合网络和时滞系统中的自组织和控制（A03）

• 批准号: 193252782
• 金额: --
• 依托单位: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/193252782?language=en
• 关键词: Self; organization; control; coupled; networks

Self-organized dynamical phenomena and collective behavior can be found in large coupled systems from various fields of science, e.g neural networks or laser systems. We will analyze and control complex and high dimensional dynamics induced by complex network structures, large coupling delays, and adaptive coupling. This includes spatial localization in coupled excitable systems, as well as temporal localization in delay systems, describing phase solitons, or in coupled oscillator systems for mode locking. The main methods for large coupled systems will be symmetric bifurcation theory and continuum limits, while for adaptive coupling and large delays we will use multi-scale methods and singular perturbations.

自组织动力学现象和集体行为可以在各个科学领域的大型耦合系统中找到，例如神经网络或激光系统。我们将分析和控制由复杂网络结构，大耦合延迟和自适应耦合引起的复杂和高维动力学。这包括耦合可激发系统中的空间定位，以及延迟系统中描述相位孤立子或用于锁模的耦合振荡器系统中的时间定位。大耦合系统的主要方法是对称分叉理论和连续极限，而对于自适应耦合和大时滞，我们将使用多尺度方法和奇异摄动。