一类广义Logistic单种群时滞模型的Hopf分支

Hopf bifurcation of a general logistic equation with delay

研究了一类广义Logistic单种群时滞生态模型dx/dt=rx（t）（1-c1xa（t）-c2x^β（t-τ））/（1＋c3x^β（t-τ））的稳定性和Hopf分支问题．利用特征值理论和奇异摄动法，给出了系统唯一正平衡态的稳定性和Hopf分支存在条件，得到了分支周期解的近似解析表达式和周期解稳定性．通过若干实例的数值计算验证了定理条件和结论的可实现性．

The dynamics of a general delayed logistic equation dx/dt=rx（t）（1-c1xa（t）-c2x^β（t-τ））/（1＋c3x^β（t-τ））are investigated. The conditions under which a sequence of Hopf bifurcations occur at the positive equilibrium are obtained. The form of the approximate periodic solutions and the explicit algorithm for determining the stability of bifurcation periodic solutions are derived by using the singular perturbation method.