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Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps

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  • Bashkirtseva, I.
  • Ryashko, L.

Abstract

A response of chaotic discrete-time dynamical systems on parametric random disturbances is considered. For two-dimensional stochastic systems with non-invertible maps, a dispersion of random states near chaotic attractors is studied. To analyse the dispersion near the border of the chaotic attractor, we elaborate an asymptotic approach based on the stochastic sensitivity technique. In this analysis, critical curves defining parts of this border are used. An application of this theory to the study of the dispersion of random states near borders of chaotic attractors is given on the example of the Sprott model. Constructive abilities of the elaborated approach for the analysis of noise-induced escape from the basin of the chaotic attractor are demonstrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:78-84
    DOI: 10.1016/j.chaos.2019.05.032
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    References listed on IDEAS

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    1. Chen, Zhen & Liu, X.B., 2015. "Effect of bounded noise on chaotic motions of stochastically perturbed slowly varying oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 72-81.
    2. 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.
    3. Gan, Chunbiao, 2006. "Noise-induced chaos in a quadratically nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 920-929.
    4. Xu, Chaoqun & Yuan, Sanling & Zhang, Tonghua, 2018. "Sensitivity analysis and feedback control of noise-induced extinction for competition chemostat model with mutualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 891-902.
    5. 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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    Cited by:

    1. Irina Bashkirtseva, 2024. "Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems," Mathematics, MDPI, vol. 12(14), pages 1-12, July.
    2. Jungeilges, Jochen & Pavletsov, Makar & Perevalova, Tatyana, 2022. "Noise-induced behavioral change driven by transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Belyaev, Alexander & Bashkirtseva, Irina & Ryashko, Lev, 2021. "Stochastic variability of regular and chaotic dynamics in 2D metapopulation model," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. 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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