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Stochastic variability and transitions to chaos in a hierarchical three-species population model

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

Abstract

A variability of the dynamic behavior in stochastically forced multi-species population models is studied. We address how noise can generate complex oscillatory regimes with transitions between attractors and order-chaos transformations. For the parametric analysis of noise-induced transitions, we utilize a semi-analytical technique based on the stochastic sensitivity analysis of attractors and confidence domains method. This approach is used in the study of the fairly realistic three-species population model describing the interaction of prey, predator and top predator. We consider in detail the parametric zone where the system is monostable with excitable limit cycle, or bistable with coexisting limit cycle and chaotic attractor. These zones are separated by the crisis bifurcation point. Noise-induced transitions between regular and chaotic attractors in the bistability zone are analysed by the confidence ellipses method. In the monostability zone, a mechanism of the transition from regular periodic to multimodal chaotic oscillations is studied.

Suggested Citation

  • Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2019. "Stochastic variability and transitions to chaos in a hierarchical three-species population model," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 276-283.
    • Handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:276-283
    DOI: 10.1016/j.chaos.2018.12.035
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    References listed on IDEAS

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    1. Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
    2. Castellanos, Víctor & Chan-López, Ramón E., 2017. "Existence of limit cycles in a three level trophic chain with Lotka–Volterra and Holling type II functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 157-167.
    3. La Barbera, A & Spagnolo, B, 2002. "Spatio-temporal patterns in population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 120-124.
    4. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
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    1. 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.
    2. Wang, Yupin & Liu, Shutang & Li, Hui & Wang, Da, 2019. "On the spatial Julia set generated by fractional Lotka-Volterra system with noise," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 129-138.
    3. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

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