IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v159y2022ics0960077922003216.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922003216
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112111?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andreev, Andrey V. & Makarov, Vladimir V. & Runnova, Anastasija E. & Pisarchik, Alexander N. & Hramov, Alexander E., 2018. "Coherence resonance in stimulated neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 80-85.
    2. 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).
    3. Xu, Pengfei & Jin, Yanfei, 2020. "Coherence and stochastic resonance in a second-order asymmetric tri-stable system with memory effects," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. D. Valenti & G. Augello & B. Spagnolo, 2008. "Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 443-451, October.
    5. Jaimes-Reátegui, R. & García-López, J.H. & Gallegos, A. & Huerta Cuellar, G. & Chholak, P. & Pisarchik, A.N., 2021. "Deterministic coherence and anti-coherence resonances in networks of chaotic oscillators with frequency mismatch," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. 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.
    7. Qian, Jiamin & Chen, Lincong, 2021. "Stochastic P-bifurcation analysis of a novel type of unilateral vibro-impact vibration system," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. Bashkirtseva, Irina & Ryashko, Lev, 2023. "Transformations of spike and burst oscillations in the stochastic Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jin, Yanfei & Wang, Haotian & Xu, Pengfei, 2023. "Noise-induced enhancement of stability and resonance in a tri-stable system with time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Slepukhina, Evdokia & Bashkirtseva, Irina & Ryashko, Lev, 2020. "Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. 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.
    4. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Zhang, Jingyu & Li, Xuefeng & Li, Renfu & Dai, Lu & Wang, Wei & Yang, Kai, 2021. "Internal resonance of a two-degree-of-freedom tuned bistable electromagnetic actuator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Xu, Pengfei & Gong, Xulu & Wang, Haotian & Li, Yiwei & Liu, Di, 2023. "A study of stochastic resonance in tri-stable generalized Langevin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    7. de la Cruz, H. & Jimenez, J. C, 2020. "Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    8. Ai, Hao & Yang, GuiJiang & Liu, Wei & Wang, Qiubao, 2023. "A fast search method for optimal parameters of stochastic resonance based on stochastic bifurcation and its application in fault diagnosis of rolling bearings," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    9. Guo, Shengli & Xu, Ying & Wang, Chunni & Jin, Wuyin & Hobiny, Aatef & Ma, Jun, 2017. "Collective response, synapse coupling and field coupling in neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 120-127.
    10. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    11. Bashkirtseva, Irina A. & Ryashko, Lev B. & Pisarchik, Alexander N., 2020. "Ring of map-based neural oscillators: From order to chaos and back," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    12. Lin, Lifeng & Lin, Tianzhen & Zhang, Ruoqi & Wang, Huiqi, 2023. "Generalized stochastic resonance in a time-delay fractional oscillator with damping fluctuation and signal-modulated noise," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    13. Aguilar-Velázquez, D. & Guzmán-Vargas, L., 2017. "Synchronization and 1/f signals in interacting small-world networks," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 418-425.
    14. Dai, Shiqi & Lu, Lulu & Wei, Zhouchao & Zhu, Yuan & Yi, Ming, 2022. "Influence of temperature and noise on the propagation of subthreshold signal in feedforward neural network," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    15. Makouo, L. & Woafo, P., 2017. "Experimental observation of bursting patterns in Van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 95-101.
    16. Bunder, J.E. & Roberts, A.J., 2017. "Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 164-179.
    17. Mondal, Argha & Mistri, Kshitish Ch. & Aziz-Alaoui, M.A. & Upadhyay, Ranjit Kumar, 2021. "An analytical scheme on complete integrability of 2D biophysical excitable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    18. Zhang, Dongjian & Ma, Qihua & Dong, Hailiang & Liao, He & Liu, Xiangyu & Zha, Yibin & Zhang, Xiaoxiao & Qian, Xiaomin & Liu, Jin & Gan, Xuehui, 2023. "Time-delayed feedback bistable stochastic resonance system and its application in the estimation of the Polyester Filament Yarn tension in the spinning process," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    19. Chen, Ruyin & Xiong, Yue & Zhuge, Shengying & Li, Zekun & Chen, Qitie & He, Zhifen & Wu, Dingqiang & Hou, Fang & Zhou, Jiawei, 2023. "Regulation and prediction of multistable perception alternation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    20. Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003216. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.