Nonstationary coherence-incoherence patterns in networks of coupled oscillators

• Applicant: Dr. Oleh Omelchenko
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Mathematics
• Term: since 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 408252383

Synchronization is one of the main mechanisms responsible for the emergence of a collective order in nonequilibrium statistical physics. In large networks of coupled oscillatory or excitable elements, it often leads to the appearance of coherence-incoherence patterns where some elements are synchronized, while others remain asynchronous. Our objective is to investigate nonstationary types of such patterns, including moving patterns and patterns with time-varying collective dynamics. We plan to develop efficient analytical and numerical methods to investigate the existence and stability of these patterns, and demonstrate the practical value of the proposed methods in various applied mathematical problems. In particular, we study a number of dynamic networks, motivated by applications in biological physics and neuroscience, which consist of phase oscillators, quadratic integrate-and-fire neurons and more complex dynamic elements.

• DFG Programme: Research Grants
• International Connection: New Zealand, USA
• Cooperation Partners: Professor Dr. Edgar Knobloch; Professor Dr. Carlo Laing