Stability and bifurcation for time delay fractional predator prey system by incorporating the dispersal of prey

摘要

In this paper, we consider a fractional delayed predator-prey model with Holling type II functional response which incorporates prey refuge and diffusion. The conditions of the Hopf bifurcation existence are obtained by analyzing the associated characteristic equation. The influence of fractional order and time delay to control the system is considered. By applying analytic and numerical method, in order to locate all unstable poles and determine the locus crosses the imaginary axis, we then derive the conditions under which the positive equilibrium becomes asymptotically stable. Furthermore the impulsive perturbation of the fractional system is introduced and dynamics of this system is revealed using a numerical scheme. Numerical simulation of the fractional system indicates that the system experiences the process of cycles, period-doubling bifurcation, period-halving bifurcation. Finally, it concludes that the fractional system exhibits periodic solution with shorter period comparing to that of the classical case and the stability domain can be extended under the fractional order. (C) 2019 Elsevier Inc. All rights reserved.