Oscillation quenching of coupled limit-cycle oscillators with shear diversity

Abstract Coupled oscillator systems often exhibit collective dynamics as a consequence of their mutual heterogeneous interactions. Recent studies have highlighted the importance of shear diversity, an inhomogeneous pattern, in influencing the collective behavior of complex systems. Here, we investigate the quenching dynamics occurring within a network of limit-cycle oscillators that are globally coupled by taking into account both the shear diversity and the heterogeneous natural frequencies that are assumed to be statistically independent. Beyond the phase-only model considered in previous studies, we propose a general approach for identifying the critical criteria, demonstrating the instability of the incoherent state, by retaining the responses of both amplitudes and phases. This study advances the understanding of the role of heterogeneous couplings in interacting dynamical agents, offering valuable insights into the quenching phenomena observed in complex systems.