Natural Frequency Adaptation as a Mechanism for Phase Synchronization in Neural Systems

Abstract We consider the problem of adaptive phase synchronization in a system of coupled phase oscillators. The system is limited to a pair of phase oscillators of which the natural frequencies are uncertain, yet they can be tuned. Coupling between the oscillators is allowed to depend on the natural frequencies nonlinearly. Three different mechanisms for the natural frequency self-tuning leading to the emergence of synchronous states are presented and analyzed. The problem is relevant for explaining and modelling phase synchronization and purposeful frequency adaptation in neuronal networks.