Amplitude death islands in globally delay-coupled fractional-order oscillators

In this paper, amplitude death (AD) is investigated theoretically and numerically in N globally delay-coupled fractional-order oscillators. Due to the presence of fractional-order derivative and coupling delay, Laplace transform method has been utilized to obtain the characteristic equations. Then, based on Lyapunov stability, we theoretically get the boundaries and number of death islands. It has been found that with the introduction of the fractional-order derivative, many more death islands emerge, and the oscillation quenching dynamics are facilitated. We find AD only occurs between two critical fractional-order derivatives c- (lower-bounded value) and c+ (upper-bounded value) which are affected by natural frequency and system size. With the increment of system size, the oscillation quenching dynamics are weakened. The number of death islands is closely geared to the fractional-order derivative and the system size. Furthermore, the results from numerical simulations best confirm the theoretical analyses.