具有捕食者相互残杀项时滞系统的Hopf分支

Stability and Hopf Bifurcation Analysis on a Predator-prey Model with Delay Dependence and the Term of Predator Kill Each Other

研究了具有捕食者相互残杀项的时滞系统的Hopf分支,通过选择时滞作为一个分支参数,研究了正平衡点的稳定性和正周期解的Hopf分支.而且通过应用规范型和中心流形的理论,得出了确定分支方向的明确的算法.

Hopf bifurcation for two-species Lokta-Volterra predator-prey systems with delay dependence and the term of predator kill each other is investigated. By choosing the delay as a bifurcation parameter, we investigate the stability of positive equilibrium and Hopf bifurcation of positive periodic solutions. By using the normal form theory and center manifold argument, the explicit formulae which determine the direction of bifurcating periodic solutions are derived.