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The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Author

Listed:
  • Jialin Chen

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

  • Xiaqing He

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

  • Fengde Chen

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

Abstract

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

Suggested Citation

  • Jialin Chen & Xiaqing He & Fengde Chen, 2021. "The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:865-:d:536332
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    References listed on IDEAS

    as
    1. Yalong Xue & Xiangdong Xie & Fengde Chen & Rongyu Han, 2015. "Almost Periodic Solution of a Discrete Commensalism System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-11, October.
    2. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    3. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    4. P. K. Santra & G. S. Mahapatra & G. R. Phaijoo, 2020. "Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-18, January.
    5. Runxin Wu & Lin Li, 2009. "Permanence and Global Attractivity of Discrete Predator-Prey System with Hassell-Varley Type Functional Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-17, June.
    6. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.
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