具有放养率的时滞捕食模型的分岔行为

Bifurcation Behavior of the Breeding Rate-based Predator-prey Model with Time Delays

考虑一类具有常数放养率的时滞捕食种群模型,研究了种群稳定性和分岔行为。通过对特征方程的研究,得到种群稳定及发生分岔行为的充分条件;利用MATLAB软件进行数值模拟,给出相空间的轨迹,得到时滞与放养率是影响种群稳定的两个重要因素,验证了理论分析所得结果的正确性。

This paper considers a class of predator-prey species model with time delay which has the constant breeding rate and studies the stability and bifurcation of the species. Suffic：ient condition for stability and bifurcation is obtained by studying the characteristic equation. The numerical simulation is carried out by using Matlab software and the trace of phase space is obtained. It comes to a conclusion that time delay and stocking rate are the two factors effecting stability of species, which verifies the correctness of the theoretical analysis result.