Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays

Abstract

In this paper, the subject of bifurcation for a fractional order predator–prey system involving two nonidentical delays is nicely discussed. The critical values of delays for Hopf bifurcation are exactly calculated for the proposed model by using two nonidentical delays as bifurcation parameter, respectively. In addition, the effects of fractional order and additional delay on the bifurcation point are delicately explored. It detects that the stability performance is extremely pulverized with the enhancement of fractional order and another delay. This hints that the generation of Hopf bifurcation can be advanced as fractional order and another delay increase. The final numerical simulations gauge the correctness of the developed theoretical analysis.