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Noise-induced ecological shifts in a prey–predator model

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  • Belyaev, Alexander
  • Baiardi, Lorenzo Cerboni
  • Jungeilges, Jochen
  • Perevalova, Tatyana

Abstract

This work is devoted to the study of a map that describes the classical model of interaction between two populations of the “predator–prey” type in the presence of environmental noise. We carry out the analysis from several perspectives. First, deterministic bifurcation scenarios for attractors and their basins of attraction are studied. The critical line method is used to describe the occurrence of non-connected basins of attraction. Subsequently, we analyze the stochastic model using semi-analytical methods, namely the stochastic sensitivity function and the confidence domain method. A constructive parametric description of population extinction caused by random noise is given. An estimate of the critical noise intensity for the occurrence of the described phenomena is obtained. Finally, we provide a descriptive analysis of the extinction time series for prey and predator populations. By establishing the existence of a pronounced right-hand tail of the extinction-time density, we demonstrate that a species might avoid extinction over extended time periods.

Suggested Citation

  • Belyaev, Alexander & Baiardi, Lorenzo Cerboni & Jungeilges, Jochen & Perevalova, Tatyana, 2025. "Noise-induced ecological shifts in a prey–predator model," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006745
    DOI: 10.1016/j.chaos.2025.116661
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    References listed on IDEAS

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    1. Bashkirtseva, Irina & Perevalova, Tatyana & Ryashko, Lev, 2022. "Regular and chaotic variability caused by random disturbances in a predator–prey system with disease in predator," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Bashkirtseva, I. & Ryashko, L., 2019. "Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 78-84.
    3. Ralph H. Abraham & Laura Gardini & Christian Mira, 1997. "Chaos in Discrete Dynamical Systems," Springer Books, Springer, number 978-1-4612-1936-1, October.
    4. Jochen Jungeilges & Elena Maklakova & Tatyana Perevalova, 2022. "Stochastic sensitivity of bull and bear states," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 165-190, January.
    5. Kang, Li & Tang, Sanyi, 2016. "The reverse effects of random perturbation on discrete systems for single and multiple population models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 198-209.
    6. Bashkirtseva, I.A. & Ryashko, L.B., 2004. "Stochastic sensitivity of 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 55-67.
    7. Jungeilges, Jochen & Ryazanova, Tatyana, 2019. "Transitions in consumption behaviors in a peer-driven stochastic consumer network," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 144-154.
    8. Zhang, Limin & Wang, Tao, 2023. "Qualitative properties, bifurcations and chaos of a discrete predator–prey system with weak Allee effect on the predator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Alexander Kolinichenko & Irina Bashkirtseva & Lev Ryashko, 2023. "Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique," Mathematics, MDPI, vol. 11(2), pages 1-13, January.
    10. Bashkirtseva, Irina & Nasyrova, Venera & Ryashko, Lev, 2018. "Noise-induced bursting and chaos in the two-dimensional Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 76-81.
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    1. Mishra, Shivam Kumar & Abbas, Syed & Debbouche, Amar, 2026. "Ergodic stationary distribution and extinction of a stochastic eco-epidemiological model with disease in prey," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).

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