Stability and Hopf bifurcation in a three-species system with feedback delays

Abstract

A kind of three-species system with Holling type II functional response and feedback delays is introduced. By analyzing the associated characteristic equation, its local stability and the existence of Hopf bifurcation are obtained. We derive explicit formulas to determine the direction of the Hopf bifurcation and the stability of periodic solution bifurcated out by using the normal-form method and center manifold theorem. Numerical simulations confirm our theoretical findings.

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