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Stochastic generation and shifts of phantom attractors in the 2D Rulkov model

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  • Bashkirtseva, Irina
  • Ryashko, Lev

Abstract

In this paper, a new stochastic phenomenon of the noise-induced shift of random states of the stochastically forced system into the domain of the phase plane where the original unforced deterministic system does not have any attractors is studied. Previously, this phenomenon called a “phantom” attractor was observed only for continuous-time dynamical models. The present paper shows that “phantom” attractors can be generated in the discrete-time models too. To analyze location of “phantom” attractors in the map-based Rulkov model, the method of “freezing and averaging” is used. The critical intensities of noise that causes the onset of “phantom” attractors are estimated by the confidence domains method based on the stochastic sensitivity function technique.

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  • Bashkirtseva, Irina & Ryashko, Lev, 2022. "Stochastic generation and shifts of phantom attractors in the 2D Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003216
    DOI: 10.1016/j.chaos.2022.112111
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    8. 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.
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    Cited by:

    1. Bashkirtseva, Irina & Ryashko, Lev, 2023. "Transformations of spike and burst oscillations in the stochastic Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Li, Gaolei & Duan, Jicheng & Yue, Zhixuan & Li, Zhe & Li, Denghui, 2024. "Dynamical analysis of the Rulkov model with quasiperiodic forcing," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    3. Gao, Chenghua & Qiao, Shuai & An, Xinlei, 2022. "Global multistability and mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Ryashko, Lev & Bashkirtseva, Irina, 2025. "Noise-induced chaos and generation of phantom attractors in a birhythmic neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    5. Bashkirtseva, I. & Ryashko, L., 2024. "Dynamical variability, order-chaos transitions, and bursting Canards in the memristive Rulkov neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).

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