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

自组织动力现象和集体行为可以在各种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态。这包括耦合可激系统中的空间定位，以及延迟系统中的时间定位，描述相位孤子，或耦合振荡器系统中的模式锁定。对于大型耦合系统，我们将主要采用对称分岔理论和连续体极限方法，而对于自适应耦合和大时滞，我们将采用多尺度方法和奇异摄动方法。

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.