Collective dynamics of random Janus oscillator networks

• Published in: Physical review research Vol. 2; no. 1; p. 013255
• Main Authors: Peron, Thomas, Eroglu, Deniz, Rodrigues, Francisco A., Moreno, Yamir
• Format: Journal Article
• Language: English
• Published: American Physical Society 04.03.2020
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.2.013255

Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits nontrivial dynamical patterns—such as chimeras, explosive transitions, and asymmetry-induced synchronization—that were once observed only in specifically tailored models. Here we study ensembles of Janus oscillators coupled on large homogeneous and heterogeneous networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich dynamics of Janus oscillators persists in the thermodynamic limit of random regular, Erdős-Rényi, and scale-free random networks. We uncover for all these networks the coexistence between partially synchronized states and a multitude of solutions of a collective state we denominate as a breathing standing wave, which displays global oscillations. Furthermore, abrupt transitions of the global and local order parameters are observed for all topologies considered. Interestingly, only for scale-free networks, it is found that states displaying global oscillations vanish in the thermodynamic limit.