Frequency-amplitude correlation inducing first-order phase transition in coupled oscillators

Abstract

The first-order phase transitions in coupled oscillators have been widely studied because of their discontinuity and irreversibility. In previous research, the designed coupling mechanisms between each pair of oscillators can cause the first-order phase transitions occur stably. In the present study, we propose a new mechanism which requires the existence of an inversely proportional relationship between the natural frequencies and the intrinsic amplitudes in the homogeneously coupled oscillators. Based on two classical oscillator models, i.e., the Poincaré model and the Stuart-Landau model, the emergence of explosive oscillation death is independent of the frequency distribution. Our findings indicate that the first-order phase transitions can be induced by the frequency-amplitude correlation for the first time . Therefore, it provides a novel perspective to understand explosive phenomena in coupled oscillators.

Stasis in heterogeneous networks of coupled oscillators: discontinuous transition with hysteresis

“…In contrast to the continuous transitions to stasis that have typically been observed so far [1], this is also different from the related phenomenon of explosive death that occurs in a homogeneous ensemble of coupled oscillators. Such an abrupt transition, from collective oscillations to a global fixed point, has been seen in networks of Stuart-Landau oscillators for a specific coupling and network topology [14,15], as well as in ensembles of identical limit-cycle and chaotic oscillators coupled via mean-field diffusion [16,17]. While the eventual dynamics is similar, the underlying mechanism appears to be different.…”