TY - JOUR
T1 - Aging transition in mixed active and inactive fractional-order oscillators
AU - Sun, Zhongkui
AU - Liu, Yuanyuan
AU - Liu, Ke
AU - Yang, Xiaoli
AU - Xu, Wei
N1 - Publisher Copyright:
© 2019 Author(s).
PY - 2019/10/1
Y1 - 2019/10/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85074415052&partnerID=8YFLogxK
U2 - 10.1063/1.5114998
DO - 10.1063/1.5114998
M3 - 文章
C2 - 31675845
AN - SCOPUS:85074415052
SN - 1054-1500
VL - 29
JO - Chaos
JF - Chaos
IS - 10
M1 - 103150
ER -