Explosive synchronization in phase oscillator populations with attractive and repulsive adaptive interactions

The attractive and repulsive adaptive coupling schemes among dynamical agents are ubiquitous in systems ranging from physics, biology to neuroscience, which have attracted increasing interest and ample attention during recent years. Here, we extend the classical Kuramoto model to the coupling with mixed signs by considering a particular adaptive scheme in a system of globally coupled phase oscillators. The time-varying coupling weight between each pair of oscillators is correlated with the local coherence that involves according to a nonlinear differential equation. The studied model is capable of capturing the essential properties of the explosive synchronization induced by the adaptive interactions. We carry out extensive simulations to explore the collective dynamics in different perspectives. Remarkably, we reveal that the occurrence of the abrupt transitions of the macroscopic overall weights, as well as the emergence of the correlations between the microscopic structure features (including degrees and frequency dissasortativity) and local dynamics trigger the explosive synchronization, which manifests the suppression rule for the formation of small synchronized clusters. Furthermore, we provide an analytical treatment for the reduced system that allows us to grasp the underlying mechanism of the observed phenomena. Our study can deepen the understanding of the explosive synchronization transitions and other related abrupt dynamic phenomena occurring in networked oscillators with generic adaptive schemes.

Automated summary

The attractive and repulsive adaptive coupling schemes among dynamical agents have attracted increasing interest in systems ranging from physics to neuroscience. By extending the classical Kuramoto model, we propose a particular adaptive scheme for globally coupled phase oscillators, which captures the explosive synchronization induced by adaptive interactions. Our simulations reveal the transitions of overall weights and correlations between microscopic structure features and local dynamics as triggers for explosive synchronization, providing insights into the formation of small synchronized clusters. We also provide an analytical treatment for the reduced system, enhancing the understanding of abrupt dynamic phenomena in networked oscillators with generic adaptive schemes.