标题： 具有塑性耦合的相位耦合振子：同步与稳定性 显示英文标题

标题： Phase-coupled Oscillators with Plastic Coupling: Synchronization and Stability

摘要： 在本文中，我们研究具有可塑耦合强度和任意基础拓扑结构的同质相位耦合振子系统的同步问题。两个振子之间的耦合强度的动力学由这两个振子之间的相位差决定。我们证明，在温和假设下，此类系统是梯度系统，并且总是实现频率同步。此外，我们提供了基于代数图论结果的稳定性与不稳定性的充分条件。对于基础拓扑结构为树的特殊情况，我们提出了平衡点稳定性的准则（必要且充分条件）。对于树结构和任意拓扑结构，我们提供了相位锁定的充分条件，即几乎必然收敛到稳定平衡点。我们还发现了当系统具有唯一稳定平衡点时的条件，因此几乎全局稳定性随之而来。多个示例用于展示系统具有的多种平衡点，它们对系统参数的依赖性，并说明具有恒定和可塑耦合强度的系统行为之间的差异。 显示英文摘要

摘要： In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that, under mild assumptions, such systems are gradient systems, and always achieve frequency synchronization. Furthermore, we provide sufficient stability and instability conditions that are based on results from algebraic graph theory. For a special case when underlying topology is a tree, we formulate a criterion (necessary and sufficient condition) of stability of equilibria. For both, tree and arbitrary topologies, we provide sufficient conditions for phase-locking, i.e. convergence to a stable equilibrium almost surely. We additionally find conditions when the system possesses a unique stable equilibrium, and thus, almost global stability follows. Several examples are used to demonstrate variety of equilibria the system has, their dependence on system's parameters, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.