Explosive Transition in Coupled Oscillators Through Mixed Attractive-Repulsive Interactions

Abstract

The emergence of many fascinating dynamic behaviors is affected by more than one interaction among the elements or cells in a network. In fact, the concurrence and competition of different types of effects among subsystems show a strong connection to the dynamic transition process between oscillation patterns. Here, a network of generic oscillators with mixed attractive-repulsive couplings is introduced to demonstrate the transition from oscillatory states to stationary equilibria, specifically for van der Pol oscillators and Lorenz oscillators. Through the observation of the normalized amplitude changing with the coupling strength, the sudden and irreversible transition appears in both systems, which has a close relation to the mutual repulsion on coupled oscillators. Whereas, for coupled van der Pol oscillators, three typical transition scenarios are found by varying the weight ratio of these two couplings, while the Lorenz system shows only one transition mode no matter how the weight ratio changes. Besides, in the cases of explosive transitions, the coexistence areas of oscillatory and death states also reveal a distinct manifestation for periodic and chaotic systems. The details of theoretical critical transition points on the first-order phase transition are also obtained. Our results pave a new way to control the explosive phenomenon, which is crucial to explain the sudden oscillation quenching and the coexistence of oscillatory and stationary states in biological as well as chemical systems.