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Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Author

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  • Lev Ryashko

    (Department of Theoretical and Mathematical Physics, Institute of Mathematics and Computer Sciences, Ural Federal University, 620000 Ekaterinburg, Russia)

  • Dmitri V. Alexandrov

    (Department of Theoretical and Mathematical Physics, Institute of Mathematics and Computer Sciences, Ural Federal University, 620000 Ekaterinburg, Russia)

  • Irina Bashkirtseva

    (Department of Theoretical and Mathematical Physics, Institute of Mathematics and Computer Sciences, Ural Federal University, 620000 Ekaterinburg, Russia)

Abstract

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

Suggested Citation

  • Lev Ryashko & Dmitri V. Alexandrov & Irina Bashkirtseva, 2021. "Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model," Mathematics, MDPI, vol. 9(12), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1329-:d:571585
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    References listed on IDEAS

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    1. Bashkirtseva, Irina & Ryashko, Lev, 2017. "How environmental noise can contract and destroy a persistence zone in population models with Allee effect," Theoretical Population Biology, Elsevier, vol. 115(C), pages 61-68.
    2. Roberts, A.J., 2008. "Normal form transforms separate slow and fast modes in stochastic dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 12-38.
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    Cited by:

    1. Lev Ryashko & Irina Bashkirtseva, 2022. "Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction," Mathematics, MDPI, vol. 10(6), pages 1-11, March.
    2. Bashkirtseva, Irina & Ryashko, Lev, 2022. "Stochastic generation and shifts of phantom attractors in the 2D Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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