Global analysis of networks of piecewise affine bistable switches

In this paper we investigate the dynamics of a network of N diffusively-coupled compartments, each modelling a bistable switch. The dynamics of each compartment is described by a piecewise linear differential equation. We prove that all the solutions converge to the set of equilibria and that this is a structural property, as it does not depend on the system parameters and the interconnection topology. The theoretical results are supplemented with numerical results which suggest new directions for future research.