Abstract:

We employed the polynomial theorem to analyze the distribution of the roots of the associated characteristic equation for the linearized system at the coexisting equilibrium in a Gausetype food chain model. A group of conditions of existence of FoldHopf bifurcation were obtained at the coexisting equilibrium. The result indicates that there exists a FoldHopf bifurcation point p=p*, τ=τ₀ in the model. There are complex dynamic behavior such as quasiperiodic motion and bursting behavior on the parameter plane (p,τ).

Key words: Gausetype model, FoldHopf bifurcation, quasiperiodic, bursting behavior