具有时滞的广义Logistic模型的Hopf分支

Hopf bifurcation of a generalized Logistic model with delay

研究了广义Logistic单种群时滞生态模型的Hopf分支问题.利用特征值理论和奇异摄动方法,给出了系统惟一正平衡态的稳定性和Hopf分支存在的充分条件,得到了分支周期解的近似解析表达式和判断周期解稳定性的计算公式,通过若干实例验证了理论分析和数值计算的一致性.

Hopf bifurcation of a general delayed Logistic model are investigated. By using the theory of eigenvalues and singular perturbation, some sufficient 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. Some examples are also given.