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Controlling chaos in a discrete-time prey-predator model with Allee effects

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Abstract

In this paper, a discrete-time prey-predator model with Allee effect is proposed. The parametric conditions for local asymptotic stability of steady-states are investigated. Moreover, we discuss the existence and directions of period-doubling and Neimark-Sacker bifurcations with the of help center manifold theorem and bifurcation theory. In order to control chaos due to emergence of Neimar-Sacker bifurcation, we apply OGY feedback control method and the hybrid control methodology is also implemented. Numerical simulations are provided to illustrate theoretical discussion.

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Authors and Affiliations

  1. Department of Mathematics, The University of Poonch Rawalakot, Rawalakot, Pakistan

    Qamar Din

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  1. Qamar Din
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Correspondence to Qamar Din.

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Din, Q. Controlling chaos in a discrete-time prey-predator model with Allee effects. Int. J. Dynam. Control 6, 858–872 (2018). https://doi.org/10.1007/s40435-017-0347-1

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  • DOI: https://doi.org/10.1007/s40435-017-0347-1

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