Geometry of Basins of Attraction and Heteroclinic Connections in Coupled Bistable Systems

The fundamental principle of bistability is widely used across various disciplines, including biology, chemistry, mechanics, physics, electronics and materials science. As the need for more powerful, efficient and sensitive complex-engineered systems grow, networks of coupled bistable systems have gained significant attention in recent years. Modeling and analysis of such higherdimensional systems is usually focused on finding conditions for the existence and stability of typical invariant sets, i.e. steady states, periodic solutions and chaotic sets. High-dimensionality leads to complex patterns of collective behavior. Which type of behavior is exhibited by a network depends greatly on the initial conditions. Thus, it is also important to study the geometric structure and evolution of the basins of attraction of such patterns. In this manuscript, a complete study of the basins of attraction of a ring of bistable systems, coupled unidirectionally, is presented. 3D visualizations are included to aid the discussion of the changes in the basins of attraction as the coupling parameter varies. The results are broad enough that they can be applied to a wide range of systems with similar coupling topologies.