Stability of amplitude death in conjugate-coupled nonlinear oscillator networks

This paper is concerned with stability of amplitude death (AD) in conjugate-coupled Stuart-Landau (SL) limit-cycle oscillators. For two conjugate-coupled SL oscillators, the frequency mismatch is revealed to make no contribution to the stability of AD, which is solely determined by the mean frequency. For a mean-field system of N conjugate-coupled SL oscillators, analytic equations for the continuous and discrete spectra are derived, which govern the AD stability in the thermodynamic limit N -> infinity. Particularly, AD boundaries are explicitly calculated for the Lorentzian frequency distribution. For networked SL oscillators with conjugate coupling, AD is proved to be of topology-free. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the stability of amplitude death in conjugate-coupled Stuart-Landau oscillators. It is found that frequency mismatch has no impact on the stability, which is solely determined by the mean frequency. Analytic equations for the continuous and discrete spectra are derived for a mean-field system of conjugate-coupled oscillators, defining the stability of amplitude death in the thermodynamic limit. The explicit calculation of amplitude death boundaries is presented for the Lorentzian frequency distribution. It is proven that amplitude death in networked oscillators with conjugate coupling is topology-free.