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

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. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This research discusses bifurcation in a fractional order predator-prey system with two nonidentical delays. Critical delay values for Hopf bifurcation were calculated, and the effects of fractional order and additional delay on the bifurcation point were explored, showing that stability performance is greatly affected by these factors. The study suggests that the generation of Hopf bifurcation can be accelerated with an increase in fractional order and additional delay.