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Zbl 1221.34039
Yu, Hengguo; Zhong, Shouming; Agarwal, Ravi P.; Sen, S.K.
Three-species food web model with impulsive control strategy and chaos. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 16, No. 2, 1002-1013 (2011). ISSN 1007-5704

Summary: A three-species ecological model with impulsive control strategy is developed using the theory and methods of ecology and ordinary differential equations. Conditions for extinction of the system are given based on the theory of impulsive equations and small amplitude perturbations. Using comparison involving multiple Lyapunov functions, the system is shown to be permanent. Further, the influence of the impulsive perturbation on the inherent oscillation is 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.

MSC 2000:: *34A37 Differential equations with impulses
92D25 Population dynamics

Keywords: chaotic behavior; Fourier spectra; globally asymptotically stability; impulsive control strategy; largest Lyapunov exponent; periodic solution

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