Nonlinear Dynamics

, Volume 94, Issue 4, pp 2527–2536 | Cite as

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

  • Umer Saeed
  • Irfan AliEmail author
  • Qamar Din
Original Paper


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.


Predator–prey system Local stability Neimark–Sacker bifurcation Chaos control 



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


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.

Compliance with ethical standards

Conflicts of interest

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.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.NUST Institute of Civil EngineeringNational University of Sciences and TechnologyIslamabadPakistan
  2. 2.School of Natural SciencesNational University of Sciences and Technology (NUST)IslamabadPakistan
  3. 3.Department of MathematicsThe University of Poonch RawalakotRawalakotPakistan

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