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Regular and chaotic variability caused by random disturbances in a predator–prey system with disease in predator

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  • Bashkirtseva, Irina
  • Perevalova, Tatyana
  • Ryashko, Lev

Abstract

A “prey–predator” population model when the predator population is susceptible to disease is considered. We perform a deterministic bifurcation analysis in dependence on the infection rate parameter and specify multistability zones with coexistence of equilibrium and oscillatory modes. In this model, we study stochastic effects caused by random fluctuations in the predation rate and infection rate parameters. Noise-induced transitions between equilibrium and oscillatory modes are studied both numerically and analytically by the stochastic sensitivity approach. An opposite of consequences of random perturbations in two different parameters, namely noise-induced regularization or transition to chaos, is discovered and justified by Lyapunov exponents.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007457
    DOI: 10.1016/j.chaos.2022.112551
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    1. Garrett Jenkinson & John Goutsias, 2012. "Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.
    2. Bashkirtseva, Irina & Perevalova, Tatyana & Ryashko, Lev, 2020. "Noise-induced shifts in dynamics of multi-rhythmic population SIP-model," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.
    4. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2020. "Analysis of regular and chaotic dynamics in a stochastic eco-epidemiological model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    Cited by:

    1. Sk, Nazmul & Mondal, Bapin & Thirthar, Ashraf Adnan & Alqudah, Manar A. & Abdeljawad, Thabet, 2023. "Bistability and tristability in a deterministic prey–predator model: Transitions and emergent patterns in its stochastic counterpart," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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