一类带有分段常数变量的蚊子种群模型动力学分析

The dynamic behavior analysis of mosquito model with piecewise constant arguments and stage-structured

研究一类带有分段常数变量和阶段结构的蚊子种群模型的稳定性和分支行为.首先通过计算将该模型转化为对应的差分模型,利用线性稳定性理论讨论零平衡态和正平衡点局部渐近稳定的充分条件.其次利用分支理论研究在平衡态处产生Saddle-Node分支和Flip分支的充分条件,并且使用规范形理论和中心流形定理构造判断分支解稳定性的阈值公式.最后数值模拟不仅验证了理论分析的正确性,而且展示了模型复杂的动力学行为.

Differential mosquito model with piecewise constant arguments and stage-structured is modeled. Firstly the discrete solutions of the model is achieved to obtain the local and bifurcation behaviors.Thus, the sufficient conditions for the local asymptotic stability about the zero and positive equilibrium are derived by using the linear stability theorem.Secondly it is shown that the mosquito model can undergo Saddle-Node bifurcation and Flip bifurcation nearby equilibrium when the bifurcation parameter exceeds a critical value. Furthermore, the formulas distinguishing the stability of bifurcation solutions are constructed by using the normal form; center mani- fold theorem and bifurcation theory.Finally numerical simulations are given to show the effectiveness of the theoretical analysis and exhibit the complex dynamic behavior.