Three-species food web model with impulsive control strategy and chaos

Abstract

A three-species ecological model with impulsive control strategy is developed using the theory and methods of ecology and ordinary differential equation. Conditions for extinction of the system are given based on the theory of impulsive equation and small amplitude perturbation. Using comparison involving multiple Lyapunov functions, the system is shown to be permanent. Further, the influence of the impulsive perturbation on the inherent oscillation are studied numerically and is found to depict rich dynamics, such as the period-doubling bifurcation, the period-halving bifurcation, a chaotic band, a narrow or wide periodic window, and chaotic crises. In addition, the largest Lyapunov exponent is computed. This computation demonstrates the chaotic dynamic behavior of the model. The qualitative nature of concerned strange attractors is also investigated through their computed Fourier spectra. The foregoing results have the potential to be useful for the study of the dynamic complexity of ecosystems.