外来物种入侵的Logistic时滞模型的稳定性与Hopf分支分析

Stability and Hopf bifurcation analysis for Logistic model with the invasion of alien species

研究一类具有外来物种的单种鱼群时滞系统,考虑孕期时滞及外来物种的净化时滞效应,以提高系统描述的真实性.利用微分方程稳定性理论及Hopf分支理论,分析了系统边界平衡点的稳定性、正平衡点的局部渐近稳定性以及系统在正平衡点处出现Hopf分支的条件.最后,通过数值仿真验证了分析结论.

A single-species fish population model with alien species and delays is studied in this paper.Time delays,such as gestation delay,purification delay for alien species are considered in order to improve the authenticity of the system description.By applying qualitative theory and the stability theory of differential equation,the stability of the boundary equilibria and the local asymptotic stability at the positive equilibrium are exploited,respectively.Furthermore,the theory of Hopf bifurcation is used to obtain the appearance condition of Hopf bifurcation at the positive equilibrium.Finally,simulations are carried out to support the analytical conclusions.