带有疾病、分段常数变量的捕食-被捕食系统的稳定性和分支行为

The Stability and Bifurcation Behavior of a Prey-predator Model with Epidemic and Piecewise Constant Arguments

本文研究一类带有疾病和分段常数变量的捕食-被捕食模型的稳定性和分支行为.首先通过计算得到捕食-被捕食模型对应的差分模型,利用线性稳定性理论讨论边界和正平衡点局部渐近稳定的充分条件.其次将食饵种群的出生率作为分支参数,使用分支理论研究差分模型在边界和正平衡点处产生鞍结点分支、翻转分支、Neimark-Sacker分支、Neimark-Sacker分支、鞍结点-Neimark-Sacker分支、鞍结点-翻转分支和翻转-Neimark-Sacker分支的充分条件.最后数值模拟验证理论分析的正确性,并展示模型复杂的动力学性态.

In this paper, the stability and bifurcation behavior of a prey-predator with epidemic and piecewise constant arguments are researched. Firstly, through calculation the discrete solution of the model is achieved, which has the same dynamical behavior. Next, applying the linearized stability theorem, some sufficient conditions for the local asymptotic stability of equilibrium are achieved. Secondly, by choosing the intrinsic rate of increase as the bifurcation parameter, it is shown that the discrete model can undergo Fold bifurcation, Flip bifurcation and Neimark-Sacker bifurcation through using the bifurcation theory.Finally, the illustration of the analytic results and the complex dynamical behaviors of the model are shown from numerical simulations.