带有时滞的捕食与被捕食系统的稳定性和分支

Stability and bifurcation of a delayed predator prey system

研究了一类带有时滞的捕食与被捕食系统.利用特征方程分析了系统平衡点的稳定性,得到了平衡点局部稳定的充分条件.通过选择适当的参数,当时滞取得一些数值时,系统将会产生Hopf分支.

A delayed predator-prey system was studied.The stability of the interior equilibrium was studied by analyzing the associated characteristic transcendental equation.A group of conditions to guarantee local stability were gived.By choosing the delay as a bifurcation parameter,we show that Hopf bifurcation can occur as the delay crosses some critical values.