Cause型捕食模型的稳定性与分支分析

用多项式理论分析Gause型捕食模型特征方程特征根的分布规律, 给出了共存平衡点稳定及产生Hopf分支的条件. 结果表明, 该模型存在一个Hopf分支点τ=τ₀, 使得当0<τ<τ₀时, 平衡点是局部渐近稳定的; 当τ>τ₀时, 在平衡点附近出现一个稳定的周期解.

Stability and Bifurcation Analysis on Gause-Type Predator-Prey Model

We used the polynomial theorem to analyze the distribution of the roots of the associated characteristic equation for a Gause-type predator-prey model.A group of conditions of stability and the existence of Hopf bifurcation were obtained at the co-existing equilibrium.The result indicates that in the model,there exists a Hopf bifurcation point τ=τ0.The co-existing equilibrium is local asymptotically stable when 0<τ<τ0 and a stable periodic solution appears near the equilibrium point when τ>τ0.