食饵具有庇护的时滞捕食系统稳定性和Hopf分支(英文)

Stabilityand Hopf bifurcation analysis for a competitive predator-preysystem with delayand preyrefuge

研究了一类具有2个食饵、1个捕食者,且食饵具有庇护所的Holling-II类时滞竞争捕食系统.结果表明,当时滞的值足够小时,系统的正平衡点是局部渐近稳定的.一旦时滞的值超过临界值,系统将失去稳定性并产生周期解.并利用规范型方法和中心流形定理确定了Hopf分支的方向和周期解的稳定性.最后,给出数值仿真验证了理论结果的正确性.

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.