Stability of oscillation quenching in coupled oscillator populations with heterogeneous coupling

Coupled oscillator models are of fundamental importance for understanding the collective dynamics that underlie many realistic applications ranging from physics and biology to human society. Here, we investigate the dynamics of oscillation quenching in a system of globally coupled Stuart-Landau limit-cycle oscillators incorporating the random heterogeneous interactions. We aim to provide a generic approach to systematically comprehending stability properties, as well as to appreciating the underlying emergent mechanism, of the quenching dynamics under the impression of inhomogeneous couplings. Importantly, we uncover that the peculiar symmetry of the linearized system profoundly facilitates the analysis of the algebraic structures of the eigenspectrum, thereby reformulating the characteristic equations deciding the eigenvalues in the simple forms for both finite and infinite sizes of the coupled system. In particular, the critical conditions manifesting the onset of oscillation quenching can be analytically characterized in terms of the matrix theory with finite-rank perturbation. Our work, thus, is capable of providing insights for controlling and regulating the oscillatory dynamics in complex systems consisting of interacting agents with large degrees of freedom.