Abstract:

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.

Key words:  Gausetype model, delay, stability, Hopf bifurcation