中文摘要：

脉冲微分动力系统理论上综合了连续和离散系统的特征,但又超出了连续和离散系统的范围。以脉冲微分方程理论为基础,应用动力系统定性分析方法、离散动力系统的分岔理论,研究了一个具有两类脉冲的阶段结构模型的动力学性质,并且这两类脉冲是发生在不同时刻。通过建立一个具有两类脉冲的阶段结构模型,利用离散映射,讨论模型正周期解的存在性和稳定性。利用中心流形定理和分岔理论给出了跨临界分岔发生的条件。通过MATLAB软件,得出相图、周期解和分岔图等数值模拟结果,验证了理论分析结果。

英文摘要：

The impulsive differential dynamical system synthesizes the nature of continuity and discreteness but goes beyond its scope in theory.In this paper,in terms of the theory of impulsive differential equations,the dynamics of a stage structure model are studied by bifurcation theorem based on dynamic qualitative analysis and discrete dynamic systems,where two kinds of pulse act at different times.The stage structure model is constructed,the existence and stability of the positive period solution are debated.The condition of occurrence for transcritical bifurcation is derived.The numerical simulations results of the phase portraits,the periodic solutions and bifurcation graphs by MATLAB,which are illustrated by an example,are in good agreement with the theoretical analysis results.