Lotka–Volterra Like Dynamics in Phase Oscillator Networks

Abstract

Many neural processes, including higher order cognitive functions, are characterized by metastable rather than attractor dynamics. Generalized Lotka–Volterra equations provide a suitable model that can give rise to switching dynamics between metastable equilibria and we review some results how such models can predict bounds on neural processing capacity. In this context generalized Lotka–Volterra system describes the interaction of macroscopic quantities rather than individual neural oscillators. We indicate a connection between generalized Lotka–Volterra equations and the mean field dynamics of networks of multiple identical populations of phase oscillators. This relationship not only gives insight into the global dynamics of phase oscillator populations but also hints at how spatiotemporal dynamics of synchronization can arise in phase oscillator networks.