Clustering and synchronization analysis of Networks of Bistable Systems
Optimization and Control
2024-08-09 v1 Systems and Control
Systems and Control
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.
Keywords
Cite
@article{arxiv.2408.04202,
title = {Clustering and synchronization analysis of Networks of Bistable Systems},
author = {Gianluca Villani and Luca Scardovi},
journal= {arXiv preprint arXiv:2408.04202},
year = {2024}
}