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Analysis of regular and chaotic dynamics in a stochastic eco-epidemiological model

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  • Bashkirtseva, Irina
  • Ryashko, Lev
  • Ryazanova, Tatyana

Abstract

An eco-epidemiological system with disease in the prey species is studied. We consider 3D dynamical SIP-model of interacting populations of susceptible (S) prey, infected (I) prey, and predator (P). A variability of regimes, both regular and chaotic, is described via bifurcation analysis in dependence on the rate of the infection spread. It is shown how parametric stochastic disturbances can drastically change a behavior system and cause both total extinction of all populations and the recovery of prey. For the parametric analysis of stochastic phenomena, we use the mathematical approach based on the stochastic sensitivity function technique and method of principal directions. Results of the application of this approach are compared with data of the direct numerical simulation. A phenomenon of the noise-induced chaos in this eco-epidemiological SIP-model is discussed.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919305065
    DOI: 10.1016/j.chaos.2019.109549
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    3. 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).
    4. Bashkirtseva, Irina & Zaitseva, Svetlana, 2021. "Variability, transients and excitement in a stochastic model of enzyme kinetics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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