Amplitude death in globally coupled oscillators with time-scale diversity

We analyze amplitude death (AD) in large systems of globally coupled oscillators with randomly distributed time scales. We show that the distribution of characteristic eigenvalues of a large but finite system is well approximated by the continuous and discrete spectra of the system in the thermodynamic limit. The stability analysis from the continuous and discrete spectra of the infinite system provides a fairly accurate prediction for the onset of AD in the large finite system. We prove the argument by examining the stability of AD in a paradigmatic system of coupled Stuart-Landau limit cycles with mismatched time scales. The proposed technique is extended to systems of globally coupled nonlinear oscillators of a general form with time-scale diversity, which is verified in coupled chaotic Rossler oscillators. Our study provides analytical insight into the understanding of the emergence of AD in populations of globally coupled dynamical systems.