Emergence of death islands in fractional-order oscillators via delayed coupling

The oscillating dynamics have been widely studied during the past several decades. However, the previous studies mainly focus on the oscillators which modeled by differential equations with integer-order derivative, few efforts have been contributed to studying the oscillating behaviors in oscillators containing the fractional-order derivative. In this paper, we study the effects of fractional-order derivative on delay-induced amplitude death (AD) in coupled oscillators. It is found that the interplay between the fractional-order derivative and the coupling delay causes the massive emergence of death islands. By decreasing the values of fractional-order derivative, the domains of death islands can be enlarged along directions of coupling delay and coupling strength. The threshold of the natural frequency, above which death island is possible, decreases along with the decreasing of fractional-order derivative. Therefore, our findings shed an improved light on the understanding of oscillating dynamics in delay-coupled fractional-order systems.