一类具有时滞和Holling Ⅲ类功能性反应的捕食系统的稳定性与Hopf分支

Stability and Hopf Bifurcation of a Class Predator System with Time Delay and Holling Type Ⅲ Functional Response

研究一类具有时滞和Holling Ⅲ类功能性反应的捕食系统,通过分析系统的特征方程,研究了正平衡点的局部稳定性,得到了系统出现Hopf分支的条件,利用中心流形定理和规范型理论,得到了确定Hopf分支方向和分支周期解稳定性的计算公式.

A predator-prey system with time delay and Holling type III functional response is investigated. By analyzing the associated characteristic equations of the system, the local stability of the positive equilibrium and the existence of Hopf bifurcations are established. Based on the normal form theory and center manifold reduction, explicit formulae are derived to determine the stability and direction of Hopf bifurcation periodic solutions.