Stability and Hopf Bifurcation Analysis for a Gause-Type Predator-Prey System with Multiple Delays

摘要

This paper is concerned with a Gause-type predator-prey system with two delays. Firstly,we study the stability and the existence of Hopf bifurcation at the coexistence equilibrium byanalyzing the distribution of the roots of the associated characteristic equation. A group ofsufficient conditions for the existence of Hopf bifurcation is obtained. Secondly, an explicitformula for determining the stability and the direction of periodic solutions that bifurcate fromHopf bifurcation is derived by using the normal form theory and center manifold argument. Finally, some numerical simulations are carried out to illustrate the main theoretical results.