Chaos and Time-Series Analysis
Chaos and Time-Series Analysis
Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay
Mathematics and Computers in Simulation
Mathematical and Computer Modelling: An International Journal
Mathematics and Computers in Simulation
Mathematics and Computers in Simulation
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In this paper, by using the theories and methods of ecology and ordinary differential equation, an ecological model consisting of two preys and one predator with impulsive control strategy 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 prey-eradication periodic solution. It is proved that the system is permanent. Further, influences of the impulsive perturbation 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, the computation of the largest Lyapunov exponent demonstrates the chaotic dynamic behavior of the model. At the same time, we investigate the qualitative nature of the strange attractor by using Fourier spectra. All these results may be useful for the study of the dynamic complexity of ecosystems.