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arXiv · 1907.12065

Collective dynamics of random Janus oscillator networks

Thomas Peron·Deniz Eroglu·Francisco A. Rodrigues·Yamir Moreno
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Abstract

Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits non-trivial dynamical patterns -- such as chimeras, explosive transitions, and asymmetry-induced synchronization -- that once were only observed 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 state and a multitude of states displaying 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.

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Thomas Peron, Deniz Eroglu, Francisco A. Rodrigues, Yamir Moreno. 2019-07-28. Collective dynamics of random Janus oscillator networks. https://doi.org/10.1103/physrevresearch.2.013255

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