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Dynamics of a stochastic prey–predator system with prey refuge, predation fear and its carry-over effects

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  • Rao, Feng
  • Kang, Yun

Abstract

This paper proposes and studies the dynamics of a Holling-type II predator–prey interaction system that incorporates the following three components: (1) a prey refuge; (2) predation fear and its carry-over effects; and (3) environmental noise in both prey and predator populations. The impacts of those three components are studied through both rigorous analysis and numerical simulations. Analytical results show that the introduction of prey refuge, predation fear, and its carry-over effects can generate Hopf bifurcation. It is found that increasing prey refuge and predation fear effect in a reasonable region can stabilize the system, while excessive refuge strength would lead to the extinction of predators. The theoretical results of the corresponding system with environmental noise include (1) sufficient conditions for the existence of a unique ergodic stationary distribution of the SDE system by constructing appropriate stochastic Lyapunov functions; (2) the explicit probability density function of the distribution by solving the Fokker–Planck equation; and (3) the extinction conditions of prey and/or predator species at an exponential rate in the long run. Our work shows that the proposed model, incorporating prey refuge, predation fear, carry-over effect, and environmental noise, exhibits rich and complex dynamic behaviors. Moreover, our results indicate that small environmental noise can save the prey and predator from extinction, while large environmental noise can drive the species to extinction. These interesting findings provide more perspectives on the protection and control of species in complex communities.

Suggested Citation

  • Rao, Feng & Kang, Yun, 2023. "Dynamics of a stochastic prey–predator system with prey refuge, predation fear and its carry-over effects," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008366
    DOI: 10.1016/j.chaos.2023.113935
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    References listed on IDEAS

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    1. Maria Francesca Carfora & Isabella Torcicollo, 2020. "Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense," Mathematics, MDPI, vol. 8(8), pages 1-20, July.
    2. G. Bonanno & D. Valenti & B. Spagnolo, 2005. "Role of Noise in a Market Model with Stochastic Volatility," Papers cond-mat/0510154, arXiv.org, revised Oct 2006.
    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. Mikhaylov, A.N. & Guseinov, D.V. & Belov, A.I. & Korolev, D.S. & Shishmakova, V.A. & Koryazhkina, M.N. & Filatov, D.O. & Gorshkov, O.N. & Maldonado, D. & Alonso, F.J. & Roldán, J.B. & Krichigin, A.V. , 2021. "Stochastic resonance in a metal-oxide memristive device," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Han, Bingtao & Jiang, Daqing & Zhou, Baoquan & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Rao, Feng & Luo, Junling, 2021. "Stochastic effects on an HIV/AIDS infection model with incomplete diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Gerasimova, S.A. & Lebedeva, A.V. & Fedulina, A. & Koryazhkina, M. & Belov, A.I. & Mishchenko, M.A. & Matveeva, M. & Guseinov, D. & Mikhaylov, A.N. & Kazantsev, V.B. & Pisarchik, A.N., 2021. "A neurohybrid memristive system for adaptive stimulation of hippocampus," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. G. Bonanno & D. Valenti & B. Spagnolo, 2006. "Role of noise in a market model with stochastic volatility," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 405-409, October.
    10. Roy, Jyotirmoy & Alam, Shariful, 2020. "Fear factor in a prey–predator system in deterministic and stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
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