Stability and Hopf bifurcation analysis of a biotic resource enrichment on a prey predator population in fractional-order system

Abstract

In this paper, we work on predator-prey Model of fractional order. The system of the model in [1] is extending in the sense of Caputo fractional derivatives. More specifically, the study discussed the fractional predator-prey model that rely on biotic resources existence. The idea of Caputo derivative was employed in defining the fractional ordinary differential equations. The fractional models’ stability analysis for the models equilibrium points were also presented. Adams-type predictor-corrector (ATPC) scheme is applied to compute an approximation to the solution of the model of fractional order. Furthermore, we investigated the Hopf bifurcation analysis. The result of the experiment show that, for certain values, the model undergo Hopf bifurcation, and further confirmed that the choice of an appropriate figure of the fractional α ∈ (0, 1] increase the region of the stability for the equilibrium points.