Synchronization Patterns and Waves

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The dynamics of oscillator populations attracted a lot of interest across different fields of contemporary science, in particular, in physics, chemistry, engineering, biology, and neuroscience. The paradigmatic and universal model is the Kuramoto model of coupled phase oscillators. The effective method to analyze this model is the Ott-Antonsen approach, which allows formulating closed partial differential equations for a coarse-grained order parameter and to reduce the problem to that of evolution of a complex field. The latter situation can be treated as a pattern formation problem. The goal of the project is to analyze different static and moving synchronization patterns in one-dimensional oscillatory media. For different variants of coupling we will focus on chimera-like patterns and on wavy patterns in form of solitons, and their stability. Furthermore, we will study synchronization-desynchronization transitions in disordered lattices of coupled oscillators.