Partial amplitude death in aging transition of coupled oscillators with amplitude heterogeneity

The collective behaviors of a large population of gobally coupled Stuart-Landau limit-cycle oscillators with uniform distribution of heterogeneous amplitude via the conjugate of the mean field are explored. Depending on the distribution parameters of the initial oscillators' amplitude and the coupling strength, the coupled oscillators transit from the oscillating state to partial amplitude death (PAD) and then to amplitude death (AD) or the oscillation death state with the competition between active and inactive oscillators. The transition process from the oscillating state to PAD may exhibit two types, namely, first-order and second-order transitions for the different distribution parameters given. Theoretical analysis indicates that the ratio of AD linearly increases with the increment of the coupling strength in the PAD region with its slope inversely proportional to the width of the uniform distribution. The width of the PAD region first increases linearly and then decreases with the increment of the mean of the uniform distribution. Moreover, the critical ratio of AD in the PAD region linearly decreases with different slopes as the mean-range ratio of the uniform distribution of the oscillators' initial amplitudes increases. This work advances the research on collective dynamics as well as the aging transition in globally coupled heterogeneous oscillator networks.