Multistability Analysis of Diffusively Coupled Positive Loop Motifs

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 a function of the coupling gain. The theoretical results are illustrated with numerical simulations.