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

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., d(c) proportional to N-2/3 , but the global sync is much harder to achieve. All the analytic findings are validated by numerical simulations. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study investigates the effect of network structure on system dynamics by studying a circular network of coupled Landau-Stuart oscillators. The stability of stationary states and different splay states, as well as global synchronization, are analyzed using linear stability analysis. The analysis shows that the network connectivity has a significant impact on the synchronous frequency and stability of global synchronization.