Stability of multiple attractors in the unidirectionally coupled circular networks of limit cycle oscillators

Abstract

The network structure plays a significant role in the system dynamics. In this work, we study the dynamic behaviors of a circular network of the coupled Landau–Stuart oscillators which interact unidirectionally with forward d nearest neighbors. Based on the method of linear stability analysis of existing attractor(s), we then theoretically and numerically investigate the stabilities of the stationary state together with different splay states, and in particular the global synchronization (or sync). Compared with the bidirectional topological approach, our analysis shows that d has a vital impact on the synchronous frequency and stability of global sync, i.e., dc∝N23, but the global sync is much harder to achieve. All the analytic findings are validated by numerical simulations.