Wave trains, self-oscillations and synchronization in discrete media

TL;DR

This paper investigates wave propagation, wave trains, and synchronization phenomena in networks of coupled excitable and self-oscillatory cells, providing analytical predictions and phase evolution equations.

Contribution

It introduces an asymptotic construction for wave trains in excitable media and derives phase evolution equations for self-oscillatory media.

Findings

Predicts wave train shape, speed, and critical parameters for propagation failure.

Describes stable wave train generation through boundary firing.

Analyzes synchronization phenomena in self-oscillatory media.

Abstract

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated firing at a boundary. In self-oscillatory media, wave trains persist but synchronization phenomena arise. An equation describing the evolution of the oscillator phases is derived.