Complex Dynamics in a Ratio-dependent Food-chain Model with Beddington-DeAngelis Functional Response

In this paper, a ratio-dependent food-chain model is studied, and the local stability of the positive equilibrium point of the system is analyzed. By means of computer simulation, rich system dynamics are revealed: chaos, period-doubling bifurcations, and others. From the bifurcation diagram with different bifurcation parameters, the strong influence of intra-species competition can be observed. Finally, Poincaré sections and power spectra are used to demonstrate chaotic dynamics.