HOPF BIFURCATION IN THE DELAYED FRACTIONAL LESLIE-GOWER MODEL WITH HOLLING TYPE II FUNCTIONAL RESPONSE

Abstract

In this paper the fractional-order Leslie-Gower model with Holling type II functional response and a single time delay is firstly considered. The stability interval and bifurcation points of developed model are derived via analytic extrapolation by regarding time delay as a bifurcation parameter. Besides, a delayed feedback control is successfully designed to put off the onset of Hopf bifurcation, extend the stability domain, and then the system possesses the stability in a larger parameter range. Some numerical simulations are shown in order to check the availability of the theoretical results.