Reentrance-like vibrational resonance in a fractional-order birhythmic biological system. (February 2022) - Fu, Peng; Wang, Can-Jun; Yang, Ke-Li; Li, Xu-Bo; Yu, Biao
Abstract: The occurrence of vibrational resonance in an enzymatic substrate reaction described by a fractional-order birhythmic biological model driven by a low-frequency and a high-frequency signal is investigated. A novel reentrance-like vibrational resonance phenomenon is found, i.e., a switch from "single peak → double peaks → single peak" with the order of the fractional time-derivatives q, the parameters α, and β varying. However, the nonlinearity parameter μ induces only a switch from "single peak → double peaks". The mechanics is demonstrated based on the best phase synchronization between the input and the output signal. Meanwhile, the theoretical analysis is carried out by means of the method of the separation of fast and slow variables. The theoretical results show the same phenomenon as the numerical results.