Abstract:

The complex dynamics of an intraguild predation (IGP) model is investigated in this paper, and the model incorporates the Holling-Ⅱ functional response functions. The sufficient conditions are obtained for the existence and local stability of boundary equilibria. Then, the numerical simulations are applied to the model under the given values of parameters. The numerical results show that the system may have an attracting invariant torus but no positive equilibrium. Furthermore, the Poincaré map and Fourier transform spectrum analysis are performed to study the complex dynamics of the system on the invariant torus. The results suggest that the dynamics on the invariant torus is almost periodic.

Key words: IGP model, Invariant torus, Numerical simulation, Poincaré map, Fourier spectrum analysis