Aging transition in mixed active and inactive fractional-order oscillators.

Recently, a large number of studies have concentrated on aging transition, but they have so far been restricted to coupled integer-order oscillators. Here, we report the first study of aging transition in mixed active and inactive fractional-order oscillators. It has been demonstrated that while the heterogeneity is caused by the distance parameter, both the coupling strength and the fractional-order derivative can modulate the critical ratio at which aging transition occurs. In addition, a small fractional-order derivative may ruin the ability of oscillation and, thus, reduce the critical ratio in globally coupled fractional-order Stuart-Landau oscillators. Remarkably, the larger the natural frequency is the more easily the aging transition occurs in coupled fractional-order oscillators. Further studies have shown that, being diverse from an integer-order Stuart-Landau oscillator, the natural frequency may induce a Hopf bifurcation in a fractional-order Stuart-Landau oscillator, accordingly, introducing a new heterogeneity in the coupled fractional-order Stuart-Landau oscillators. Therein, a counterintuitive phenomenon has been found that the critical ratio depends unmonotonously on the coupling strength, which implies that the coupled fractional-order Stuart-Landau oscillators possess the weakest robustness of oscillation at a certain level of coupling strength.