Amplitude death and phase-locked oscillations in delay-coupled oscillators with frequency mismatch and nonisochronism.

This paper presents an investigation of amplitude death and phase-locked oscillations in delay-coupled Stuart-Landau oscillators with frequency mismatch. These oscillators exhibit nonisochronism, in which the rotation velocities depend on amplitudes. We provide a simple procedure to numerically obtain the phase-locked periodic orbits and their stability for such oscillators. This procedure allows us to construct bifurcation diagrams for amplitudes and phase differences of the orbits, which include information on their stability. The bifurcation diagrams disclose the effects of frequency mismatch and nonisochronism on the global nonlinear dynamics of delay-coupled oscillators. We find that frequency mismatch can induce a stability region for amplitude death where the phase-flip phenomenon does not occur, and we reveal its mechanism. Furthermore, we show that explosive amplitude death can arise even in the presence of frequency mismatch.