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Neimark–Sacker bifurcation and chaos control in discrete-time predator–prey model with parasites

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Abstract

In this paper, we discuss the qualitative behavior of a four-dimensional discrete-time predator–prey model with parasites. We investigate existence and uniqueness of positive steady state and find parametric conditions for local asymptotic stability of positive equilibrium point of given system. It is also proved that the system undergoes Neimark–Sacker bifurcation (NSB) at positive equilibrium point with the help of an explicit criterion for NSB. The system shows chaotic dynamics at increasing values of bifurcation parameter. Chaos control is also discussed through implementation of hybrid control strategy, which is based on feedback control methodology and parameter perturbation. Finally, numerical simulations are conducted to illustrate theoretical results.

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Acknowledgements

The authors thank the anonymous referees for their valuable comments and suggestions leading to improvement of this paper.

Funding

Funding will be provided by School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan, for the publication of this paper.

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Authors and Affiliations

  1. NUST Institute of Civil Engineering, National University of Sciences and Technology, Islamabad, Pakistan

    Umer Saeed

  2. School of Natural Sciences, National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Irfan Ali

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

    Qamar Din

Authors
  1. Umer Saeed
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  2. Irfan Ali
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  3. Qamar Din
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Correspondence to Irfan Ali.

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The authors declare that they have no conflict of interest. They have no competing financial, professional, or personal interests that might have influenced the performance of the work described in this manuscript.

Additional information

This work is supported by Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan. The corresponding School will help financially for the publication of this article.

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Saeed, U., Ali, I. & Din, Q. Neimark–Sacker bifurcation and chaos control in discrete-time predator–prey model with parasites. Nonlinear Dyn 94, 2527–2536 (2018). https://doi.org/10.1007/s11071-018-4507-4

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  • DOI: https://doi.org/10.1007/s11071-018-4507-4

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