Transients versus network interactions give rise to multistability through trapping mechanism

Abstract

In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients that give rise to multistability from such interplay remain poorly understood. In a network of coupled excitable units, we show that this interplay generating multistability occurs through a competition between the units' transient dynamics and their coupling. Specifically, the diffusive coupling between the units manages to reinject them in the excitability region of their individual state space and effectively trap them there. We show that this trapping mechanism leads to the coexistence of multiple types of oscillations: periodic, quasiperiodic, and even chaotic, although the units separately do not oscillate. Interestingly, we show that the attractors emerge through different types of bifurcations - in particular, the periodic attractors emerge through either saddle-node of limit cycles bifurcations or homoclinic bifurcations - but in all cases the reinjection mechanism is present.