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Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments

Author

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  • Nirapada Santra

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

  • Sudeshna Mondal

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

  • Guruprasad Samanta

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India)

Abstract

Many ecological models have received much attention in the past few years. In particular, predator–prey interactions have been examined from many angles to capture and explain various environmental phenomena meaningfully. Although the consumption of prey directly by the predator is a well-known ecological phenomenon, theoretical biologists suggest that the impact of anti-predator behavior due to the fear of predators (felt by prey) can be even more crucial in shaping prey demography. In this article, we develop a predator–prey model that considers the effects of fear on prey reproduction and on environmental carrying capacity of prey species. We also include two delays: prey species birth delay influenced by fear of the predator and predator gestation delay. The global stability of each equilibrium point and its basic dynamical features have been investigated. Furthermore, the “paradox of enrichment” is shown to exist in our system. By analysing our system of nonlinear delay differential equations, we gain some insights into how fear and delays affect on population dynamics. To demonstrate our findings, we also perform some numerical computations and simulations. Finally, to evaluate the influence of a fluctuating environment, we compare our proposed system to a stochastic model with Gaussian white noise terms.

Suggested Citation

  • Nirapada Santra & Sudeshna Mondal & Guruprasad Samanta, 2022. "Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(20), pages 1-38, October.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3795-:d:942684
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    References listed on IDEAS

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    1. Fangyuan Hua & Kathryn E. Sieving & Robert J. Fletcher & Chloe A. Wright, 2014. "Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(3), pages 509-519.
    2. Dutta, Protyusha & Sahoo, Debgopal & Mondal, Sudeshna & Samanta, Guruprasad, 2022. "Dynamical complexity of a delay-induced eco-epidemic model with Beddington–DeAngelis incidence rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 45-90.
    3. 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.
    4. Das, Bijoy Kumar & Sahoo, Debgopal & Samanta, G.P., 2022. "Impact of fear in a delay-induced predator–prey system with intraspecific competition within predator species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 134-156.
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    Cited by:

    1. Sk Golam Mortoja & Prabir Panja & Shyamal Kumar Mondal, 2023. "Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    2. Santra, Nirapada & Saha, Sangeeta & Samanta, Guruprasad, 2023. "Role of multiple time delays on a stage-structured predator–prey system in a toxic environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 548-583.

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