Clustering and synchronization analysis of Networks of Bistable Systems

TL;DR

This paper analyzes the global behavior and synchronization of networks of bistable systems, providing conditions for convergence and stability, supported by theoretical analysis and numerical simulations.

Contribution

It offers new conditions for convergence and synchronization in bistable networks without requiring smooth vector fields.

Findings

Solutions converge globally to equilibria

Conditions for global state synchronization are established

Existence and stability of equilibria depend on coupling gain

Abstract

This paper studies the dynamics of a network of diffusively-coupled bistable systems. Under mild conditions and without requiring smoothness of the vector field, we analyze the network dynamics and show that the solutions converge globally to the set of equilibria for generic monotone (but not necessarily strictly monotone) regulatory functions. Sufficient conditions for global state synchronization are provided. Finally, by adopting a piecewise linear approximation of the vector field, we determine the existence, location and stability of the equilibria as function of the coupling gain. The theoretical results are illustrated with numerical simulations.