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Dynamical behavior of a class of prey-predator system with impulsive state feedback control and Beddington–DeAngelis functional response

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Abstract

This paper studies systematically a Bedd-ington–DeAngelis prey–predator system with harvesting and impulsive state feedback control. Conditions for existence and stability of predator-free periodic solution are obtained. When the predator-free periodic solution loses its stability, the existence and stability of nontrivial period solution are also established. Furthermore, computer simulations show that this impulsive system displays a series of complex phenomena, including period-doubling bifurcation and cascade, period window, and chaotic bands. Through numerical simulation, it is also observed that capture capability can influence the amount of predator released and the interval of the stability for nontrivial period-1 solution. Moreover, the superiority of impulsive state feedback control strategy is also exhibited over the impulsive fixed-time control.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (60974004) and Liaoning Provincial Foundation of Science and Technology (20082023).

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Authors and Affiliations

  1. Institute of Systems Science, Northeastern University, Shenyang, 110819, P.R. China

    Yi Zhang, Qingling Zhang & Xue Zhang

  2. School of Science, Shenyang University of Technology, Shenyang, 110870, P.R. China

    Yi Zhang

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  1. Yi Zhang
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  2. Qingling Zhang
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  3. Xue Zhang
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Correspondence to Qingling Zhang.

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Zhang, Y., Zhang, Q. & Zhang, X. Dynamical behavior of a class of prey-predator system with impulsive state feedback control and Beddington–DeAngelis functional response. Nonlinear Dyn 70, 1511–1522 (2012). https://doi.org/10.1007/s11071-012-0551-7

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  • DOI: https://doi.org/10.1007/s11071-012-0551-7

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