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Zbl 1221.34130
Yu, Hengguo; Zhong, Shouming; Agarwal, Ravi P.; Sen, Syamal K.
Effect of seasonality on the dynamical behavior of an ecological system with impulsive control strategy. (English)
[J] J. Franklin Inst. 348, No. 4, 652-670 (2011). ISSN 0016-0032; ISSN 1879-2693/e

Summary: On the basis of the theories and methods of ecology and ordinary differential equations, an ecological model consisting of two preys and one predator with impulsive control strategy and seasonal effects is established. Conditions which guarantee the global asymptotical stability of the prey-eradication periodic solution are obtained using the theory of impulsive equations, small amplitude perturbation skills, and comparison techniques. Further, the influences of the impulsive perturbation and seasonal effects on the inherent oscillation are studied numerically. These show to be consistent with the theoretical analysis and rich complex population dynamics, such as species extinction and permanence. Moreover, the dynamical behavior of the model is demonstrated by the computed largest Lyapunov exponent. By investigating the strange attractors through their computed Fourier spectra, we know that seasonality has a profound effect on the population dynamical behavior. All these results are expected to be of use in the study of dynamic complexity of ecosystems.

MSC 2000:: *34C60 Applications of qualitative theory of ODE
34A37 Differential equations with impulses
34D05 Asymptotic stability of ODE
92D25 Population dynamics
92D40 Ecology
34D08 Lyapunov exponents
34C28 Other types of "recurrent" solutions of ODE

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Zentralblatt MATH Berlin [Germany]