Synchronization of phase-coupled oscillators with plastic coupling strength

In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of a coupling strength between two oscillators is governed by the phase difference between these oscillators. We show that such systems are gradient and always achieve frequency synchronization. Moreover, for these systems 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 of stability for equilibria. Several examples are used to demonstrate variety of equilibria the system has, and to illustrate differences in behavior of systems with constant and plastic coupling strengths.