Dynamics reconstruction in the presence of bistability by using reservoir computer

Abstract

Coupled chaotic oscillators usually display rich dynamics and undergo complicated bifurcations when the coupling strength changes. Dynamics reconstruction of the coupled system without relying on a model is a difficult problem in the field of nonlinear dynamics, especially in the presence of bistability. Following previous works (PRE 104 (2021) 014205 and 024205), we design a reservoir computer with parameter input channel consisting of the coupling strength and an indicator parameter. The indicator parameter is used to distinguish the possible coexisting dynamical states. Using a ring of coupled Rössler oscillators, we demonstrate the power of the reservoir computer in dynamics reconstruction and predicting the transitions between different dynamical states. We find that a single one reservoir computer is enough to reconstruct the complete bifurcation diagrams of the original coupled system.