Dynamical networks with time delays and adaptation: theory and applications

• Applicant: Professor Dr. Jürgen Kurths, since 8/2023
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 411803875

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 realistic properties on dynamical networks.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.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.

• DFG Programme: Research Grants
• International Connection: United Kingdom
• Cooperation Partner: Dr. Antonio Politi
• Ehemaliger Antragsteller: Privatdozent Dr. Serhiy Yanchuk, until 7/2023