Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA.
Department of Mathematics, Trinity College, Hartford, Connecticut 06106, USA.
Chaos. 2020 Jun;30(6):060401. doi: 10.1063/5.0016491.
Synchronization phenomena and collective behavior are commonplace in complex systems with applications ranging from biological processes such as coordinated neuron firings and cell cycles to the stability of alternating current power grids. A fundamental pursuit is the study of how various types of symmetry-e.g., as manifest in network structure or coupling dynamics-impact a system's collective behavior. Understanding the intricate relations between structural and dynamical symmetry/asymmetry also provides new paths to develop strategies that enhance or inhibit synchronization. Previous research has revealed symmetry as a key factor in identifying optimization mechanisms, but the particular ways that symmetry/asymmetry influence collective behavior can generally depend on the type of dynamics, networks, and form of synchronization (e.g., phase synchronization, group synchronization, and chimera states). Other factors, such as time delay, noise, time-varying structure, multilayer connections, basin stability, and transient dynamics, also play important roles, and many of these remain underexplored. This Focus Issue brings together a survey of theoretical and applied research articles that push forward this important line of questioning.
同步现象和集体行为在复杂系统中很常见，其应用范围从生物过程（如协调的神经元发射和细胞周期）到交流电网的稳定性。一个基本的研究方向是研究各种类型的对称（例如，在网络结构或耦合动力学中表现出来的对称）如何影响系统的集体行为。理解结构和动力对称/不对称之间的复杂关系也为开发增强或抑制同步的策略提供了新途径。先前的研究表明，对称是识别优化机制的关键因素，但对称/不对称对集体行为的影响方式通常取决于动力学、网络和同步形式（例如，相位同步、群同步和嵌合体状态）。其他因素，如时滞、噪声、时变结构、多层连接、盆地稳定性和瞬态动力学，也起着重要作用，其中许多仍有待探索。本期特刊汇集了一系列推动这一重要问题研究的理论和应用研究文章。
