食饵具有庇护的时滞捕食系统稳定性和Hopf分支(Stability and Hopf bifurcation analysis for a competitive predator-prey system with delay and prey refuge) - ZHANGZizhen(张子振); WANGKai(汪凯) (Zhejiang Daxue xuebao. Lixue ban, 2014)
This paper is concerned with a three-component model consisting of two prey and one predator with time delay and the inclusion of Holling type-Ⅱ response function incorporating a constant proportion of prey refuge. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Changes of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a critical value. Particularly, the direction of Hopf bifurcation and the stability of the periodic solutions are determined by using the normal form method and center manifold theorem. Finally, the numerical simulations are carried out to verify our theoretical findings.