Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay

In this paper, by using the theories and methods of ecology and ordinary differential equation, an ecological model with impulsive control strategy and distributed time delay is established. By using the theories of impulsive equation, small amplitude perturbation skills and comparison technique, we get the condition which guarantees the global asymptotical stability of the lowest level prey and top predator eradication periodic solution. Further, influences of the impulsive perturbation and the parameter a on the inherent oscillation are studied numerically, which shows rich dynamics, such as period-doubling bifurcation, period-halving bifurcation, chaotic band, narrow or wide periodic window, chaotic crises, etc. Moreover, computation of the largest Lyapunov exponent demonstrates the chaotic dynamic behavior of the model. Meanwhile. we investigate the qualitative nature of strange attractor by using Fourier spectra. All these results may be useful for study of the dynamic complexity of ecosystems.