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Mathematics and dynamic analysis of an apparent competition community model with impulsive effect. (English) Zbl 1201.34018
Summary: 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.

MSC:
34A37 Ordinary differential equations with impulses
92D40 Ecology
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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