Reconstructing the dynamics of coupled oscillators with cluster synchronization using parameter-aware reservoir computing

Abstract

Dynamics reconstruction of complex networks usually requires a large amount of resources; therefore, it is of great significance to find a fast and effective way to achieve this goal. In the study of synchronization dynamics in coupled oscillator networks, complex network structures may be simplified into a smaller-scale network called quotient networks through the external equitable partition. Reservoir computing has demonstrated the capability of rapidly reconstructing system dynamics. In this paper, we attempt to utilize the quotient system in parameter-aware reservoir computing to replace the original network system for training the computer’s neurons, in order to reconstruct the synchronization dynamics of the original network. The system reconstructed by the reservoir computing trained with the quotient network exhibits the same synchronization dynamics, bifurcation diagrams, and spatiotemporal structures as the original system, while the training time is also reduced. The results demonstrate the feasibility of using quotient networks to replace original large-scale networks when reconstructing synchronization dynamics with reservoir computing.