Synchronization Patterns and Waves

振子种群的动力学在当代科学的不同领域引起了人们的极大兴趣，特别是在物理、化学、工程、生物学和神经科学领域。耦合相位振荡器的范式和通用模型是Kuramoto模型。对该模型进行分析的有效方法是Ott-Antonsen方法，该方法允许对粗粒度阶参数建立封闭的偏微分方程，并将问题简化为复杂场的演化问题。后一种情况可以被视为模式形成问题。该项目的目标是分析一维振荡介质中不同的静态和移动同步模式。对于耦合的不同变体，我们将重点关注类似嵌合体的模式和孤子形式的波浪模式，以及它们的稳定性。此外，我们将研究耦合振荡器无序晶格中的同步-非同步跃迁。

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.