DYNNET

Networks of coupled dynamical systems serve as a paradigm for a variety of applications. When modeling realistic systems, time delays naturally occur due to finite signal propagation between the components. Moreover, if the network is adaptive, i.e., its topology changes with time, the resulting systems become a challenging object for theoretical study. So far, the effects of time delays and adaptivity have mostly been studied either separately or using purely numerical approaches. The project aims at studying the effects of time delays, adaptivity, and other properties of realistic dynamical networks such as heterogeneity or multiscale dynamics. Among the topics of the project, the following problems will be considered: (i) universality classes in delay systems, temporal dissipative solitons; (ii) stability and emergent complex patterns in adaptive networks; (iii) synchronization in coupled systems with multiple types of adaptation rules and/or multiple delays; (iv) study of the dynamics of nonlinear active optical networks, and others. In cooperation with external partners, the project aims to explore new concepts in machine learning applications related to dynamical systems. In addition to the models arising in coupled optoelectronic systems, we consider power grid networks and especially their relationship to adaptive neural networks.