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Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control

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  • Yangyang Su

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
    These authors contributed equally to this work.)

  • Tongqian Zhang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
    These authors contributed equally to this work.)

Abstract

In this paper, a predator–prey model with fear effect and impulsive state control is proposed and analyzed. By constructing an appropriate Poincaré map, the dynamic properties of the system, including the existence, nonexistence, and stability of periodic solutions are studied. More specifically, based on the biological meaning, the pulse and the phase set are firstly defined in different regions as well as the corresponding Poincaré map. Subsequently, the properties of the Poincaré map are analyzed, and the existence of a periodic solution for the system is investigated according to the properties of the Poincaré map. We found that the existence of the periodic solution for the system completely depends on the property of the Poincaré map. Finally, several examples containing numerical simulations verify the obtained theoretical result.

Suggested Citation

  • Yangyang Su & Tongqian Zhang, 2022. "Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control," Mathematics, MDPI, vol. 10(8), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1229-:d:789729
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    References listed on IDEAS

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    1. Y. Tian & H. M. Li & Toshikazu Kuniya, 2022. "The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy," Complexity, Hindawi, vol. 2022, pages 1-19, January.
    2. Evan L Preisser & Daniel I Bolnick, 2008. "The Many Faces of Fear: Comparing the Pathways and Impacts of Nonconsumptive Predator Effects on Prey Populations," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-8, June.
    3. Tian, Yuan & Sun, Kaibiao & Chen, Lansun, 2011. "Modelling and qualitative analysis of a predator–prey system with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 318-331.
    4. Steven M. Sait & Wei-Chung Liu & David J. Thompson & H. Charles J. Godfray & Michael Begon, 2000. "Invasion sequence affects predator–prey dynamics in a multi-species interaction," Nature, Nature, vol. 405(6785), pages 448-450, May.
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