具有非线性出生率的时滞Lasota-Wazewska模型的稳定性分岔

Stability Bifurcations of Lasota-Wazewska-type Model with Maturation Delay and Nonlinear Birth Rate

研究了一类Lasota-Wazewska单种群人口模型x′(t)=-μx(t)+pe-dτe-γx(t-τ).其中的出生率是时滞τ的非线性函数pe-dτ而不是常数p.应用选择性的方法或中心流形定理,确定了分岔周期解的稳定性及Hopf分岔的方向.应用计算机软件和数值方法,也得到了一些相图和轨线的时间历程图.

A Lasota-Wazewska-type single species population model x′(t)=-μx(t)+pe^(-dτ)e^(-γx(t-τ)) is investigated. We think its birth rate as pe^(-dτ) which is nonlinear about the delay τ instead of constant p. By exploring an alternative approach, which is also called as Center Manifold, we determine the stability of bifurcating periodic solutions and the direction of Hopf bifurcation. Some phase portraits, waveform diagrams are also given by computer simulation.