IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921010031.html
   My bibliography  Save this article

Reentrance-like vibrational resonance in a fractional-order birhythmic biological system

Author

Listed:
  • Fu, Peng
  • Wang, Can-Jun
  • Yang, Ke-Li
  • Li, Xu-Bo
  • Yu, Biao

Abstract

The occurrence of vibrational resonance in an enzymatic substrate reaction described by a fractional-order birhythmic biological model driven by a low-frequency and a high-frequency signal is investigated. A novel reentrance-like vibrational resonance phenomenon is found, i.e., a switch from “single peak→ double peaks → single peak” with the order of the fractional time-derivatives q, the parameters α, and β varying. However, the nonlinearity parameter μ induces only a switch from “single peak→ double peaks”. The mechanics is demonstrated based on the best phase synchronization between the input and the output signal. Meanwhile, the theoretical analysis is carried out by means of the method of the separation of fast and slow variables. The theoretical results show the same phenomenon as the numerical results.

Suggested Citation

  • Fu, Peng & Wang, Can-Jun & Yang, Ke-Li & Li, Xu-Bo & Yu, Biao, 2022. "Reentrance-like vibrational resonance in a fractional-order birhythmic biological system," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010031
    DOI: 10.1016/j.chaos.2021.111649
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921010031
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111649?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. Haiping Ye & Yongsheng Ding, 2009. "Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-12, June.
    2. Christophe Tricaud & YangQuan Chen, 2010. "Time-Optimal Control of Systems with Fractional Dynamics," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-16, February.
    3. Yu, Dong & Lu, Lulu & Wang, Guowei & Yang, Lijian & Jia, Ya, 2021. "Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Wang, Guowei & Yu, Dong & Ding, Qianming & Li, Tianyu & Jia, Ya, 2021. "Effects of electric field on multiple vibrational resonances in Hindmarsh-Rose neuronal systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. René Yamapi & André Chéagé Chamgoué & Giovanni Filatrella & Paul Woafo, 2017. "Coherence and stochastic resonance in a birhythmic van der Pol system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(8), pages 1-16, August.
    6. Chéagé Chamgoué, A. & Ngueuteu, G.S.M. & Yamapi, R. & Woafo, P., 2018. "Memory effect in a self-sustained birhythmic biological system," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 160-169.
    7. Ge, Mengyan & Lu, Lulu & Xu, Ying & Mamatimin, Rozihajim & Pei, Qiming & Jia, Ya, 2020. "Vibrational mono-/bi-resonance and wave propagation in FitzHugh–Nagumo neural systems under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    8. Kadji, H.G. Enjieu & Orou, J.B. Chabi & Yamapi, R. & Woafo, P., 2007. "Nonlinear dynamics and strange attractors in the biological system," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 862-882.
    9. Yan, Ye & Kou, Chunhai, 2012. "Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1572-1585.
    10. Guo, Qin & Sun, Zhongkui & Xu, Wei, 2019. "Delay-induced transitions in the birhythmic biological model under joint noise sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 337-348.
    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. Taiwo O. Roy-Layinde & Kehinde A. Omoteso & Babatunde A. Oyero & John A. Laoye & Uchechukwu E. Vincent, 2022. "Vibrational resonance of ammonia molecule with doubly singular position-dependent mass," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(5), pages 1-11, May.
    2. Qiao, Zijian & He, Yuanbiao & Liao, Changrong & Zhu, Ronghua, 2023. "Noise-boosted weak signal detection in fractional nonlinear systems enhanced by increasing potential-well width and its application to mechanical fault diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Zhou, Zhao-Xiang & Yang, Ke-Li & Wang, Can-Jun & Yu, Biao & Li, Xu-Bo & Su, Yue-Wen, 2023. "Theory and numerics of vibrational resonance in a three-level atomic optical bistable system," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Nganso, E. Njinkeu & Mbouna, S.G. Ngueuteu & Yamapi, R. & Filatrella, G. & Kurths, J., 2023. "Two-attractor chimera and solitary states in a network of nonlocally coupled birhythmic van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Roy-Layinde, T.O. & Omoteso, K.A. & Diala, U.H. & Runsewe, J.A. & Laoye, J.A., 2024. "Analysis of vibrational resonance in an oscillator with exponential mass variation," Chaos, Solitons & Fractals, Elsevier, vol. 178(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. Mbakob Yonkeu, R. & David, Afungchui, 2022. "Coherence and stochastic resonance in the fractional-birhythmic self-sustained system subjected to fractional time-delay feedback and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Wang, Guowei & Wu, Yong & Xiao, Fangli & Ye, Zhiqiu & Jia, Ya, 2022. "Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    3. Li, Tianyu & Wu, Yong & Yang, Lijian & Zhan, Xuan & Jia, Ya, 2022. "Spike-timing-dependent plasticity enhances chaotic resonance in small-world network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    4. Ding, Qianming & Wu, Yong & Li, Tianyu & Yu, Dong & Jia, Ya, 2023. "Metabolic energy consumption and information transmission of a two-compartment neuron model and its cortical network," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Xiao, Fangli & Fu, Ziying & Jia, Ya & Yang, Lijian, 2023. "Resonance effects in neuronal-astrocyte model with ion channel blockage," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    6. Yu, Dong & Wang, Guowei & Ding, Qianming & Li, Tianyu & Jia, Ya, 2022. "Effects of bounded noise and time delay on signal transmission in excitable neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Kaijun Wu & Jiawei Li, 2023. "Effects of high–low-frequency electromagnetic radiation on vibrational resonance in FitzHugh–Nagumo neuronal systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(9), pages 1-19, September.
    8. Shadizadeh, S. Mohadeseh & Nazarimehr, Fahimeh & Jafari, Sajad & Rajagopal, Karthikeyan, 2022. "Investigating different synaptic connections of the Chay neuron model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    9. Yu, Dong & Wu, Yong & Yang, Lijian & Zhao, Yunjie & Jia, Ya, 2023. "Effect of topology on delay-induced multiple resonances in locally driven systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    10. Zhang, Xu & Min, Fuhong & Dou, Yiping & Xu, Yeyin, 2023. "Bifurcation analysis of a modified FitzHugh-Nagumo neuron with electric field," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    11. Wang, Guowei & Yu, Dong & Ding, Qianming & Li, Tianyu & Jia, Ya, 2021. "Effects of electric field on multiple vibrational resonances in Hindmarsh-Rose neuronal systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    12. Li, Tianyu & Wu, Yong & Yang, Lijian & Fu, Ziying & Jia, Ya, 2023. "Neuronal morphology and network properties modulate signal propagation in multi-layer feedforward network," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    13. Zhou, Zhao-Xiang & Yang, Ke-Li & Wang, Can-Jun & Yu, Biao & Li, Xu-Bo & Su, Yue-Wen, 2023. "Theory and numerics of vibrational resonance in a three-level atomic optical bistable system," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    14. Nganso, E. Njinkeu & Mbouna, S.G. Ngueuteu & Yamapi, R. & Filatrella, G. & Kurths, J., 2023. "Two-attractor chimera and solitary states in a network of nonlocally coupled birhythmic van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    15. Yao, Chenggui & Yao, Yuangen & Qian, Yu & Xu, Xufan, 2022. "Temperature-controlled propagation of spikes in neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    16. Jing Bai & Guoguang Wen & Ahmed Rahmani & Yongguang Yu, 2015. "Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(13), pages 2380-2392, October.
    17. Jing Bai & Guoguang Wen & Ahmed Rahmani & Xing Chu & Yongguang Yu, 2016. "Consensus with a reference state for fractional-order multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(1), pages 222-234, January.
    18. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    19. Hao, Zhaopeng & Fan, Kai & Cao, Wanrong & Sun, Zhizhong, 2016. "A finite difference scheme for semilinear space-fractional diffusion equations with time delay," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 238-254.
    20. Taiwo O. Roy-Layinde & Kehinde A. Omoteso & Babatunde A. Oyero & John A. Laoye & Uchechukwu E. Vincent, 2022. "Vibrational resonance of ammonia molecule with doubly singular position-dependent mass," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(5), pages 1-11, May.

    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:155:y:2022:i:c:s0960077921010031. 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.