IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v602y2022ics0378437122003351.html
   My bibliography  Save this article

The effects of symmetry breaking on the dynamics of an inertial neural system with a non-monotonic activation function: Theoretical study, asymmetric multistability and experimental investigation

Author

Listed:
  • Boui A Boya, Bertrand Frederick
  • Ramakrishnan, Balamurali
  • Effa, Joseph Yves
  • Kengne, Jacques
  • Rajagopal, Karthikeyan

Abstract

Multistability and symmetry breaking have been significantly investigated recently. In this paper, we study the effects of symmetry breaking on the behavior of a particular class of inertial neural systems with a non-monotonic activation function. By introducing a constant term in the nonlinearity of the model, we show that this system presents asymmetric type dynamics marked by the coexistence of chaotic bursting oscillations according to the different membranes of the neurons. We also report some interesting phenomena such as rising voltage peaks, the coexistence of several asymmetric attractors (six, five, four and three), the coexistence of asymmetric bubbles of bifurcation and transient chaos as well. We illustrate the influence of the symmetry breaking parameter by using 2D Lyapunov exponent, plotted for three different values of the symmetry control parameter. We prove that this model owns offset boosting and total amplitude control features. The experimental study is executed based on a microcontroller implementation and the results are in agreement with the numerical analysis.

Suggested Citation

  • Boui A Boya, Bertrand Frederick & Ramakrishnan, Balamurali & Effa, Joseph Yves & Kengne, Jacques & Rajagopal, Karthikeyan, 2022. "The effects of symmetry breaking on the dynamics of an inertial neural system with a non-monotonic activation function: Theoretical study, asymmetric multistability and experimental investigation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    • Handle: RePEc:eee:phsmap:v:602:y:2022:i:c:s0378437122003351
    DOI: 10.1016/j.physa.2022.127458
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122003351
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.127458?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. Megam Ngouonkadi, E.B. & Fotsin, H.B. & Louodop Fotso, P. & Kamdoum Tamba, V. & Cerdeira, Hilda A., 2016. "Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 151-163.
    2. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    3. Xu, Quan & Tan, Xiao & Zhu, Dong & Bao, Han & Hu, Yihua & Bao, Bocheng, 2020. "Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    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. Chen, Chengjie & Min, Fuhong & Zhang, Yunzhen & Bao, Han, 2023. "ReLU-type Hopfield neural network with analog hardware implementation," Chaos, Solitons & Fractals, Elsevier, vol. 167(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. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Xu, Quan & Wang, Yiteng & Chen, Bei & Li, Ze & Wang, Ning, 2023. "Firing pattern in a memristive Hodgkin–Huxley circuit: Numerical simulation and analog circuit validation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Yu, Xihong & Bao, Han & Chen, Mo & Bao, Bocheng, 2023. "Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Zuolei Wang & Lizhou Zhuang & Jianjiang Yu & Haibo Jiang & Wanjiang Xu & Xuerong Shi, 2023. "Hidden Dynamics of a New Jerk-like System with a Smooth Memristor and Applications in Image Encryption," Mathematics, MDPI, vol. 11(22), pages 1-18, November.
    5. Zhang, Sen & Zheng, Jiahao & Wang, Xiaoping & Zeng, Zhigang, 2021. "A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Njitacke, Zeric Tabekoueng & Takembo, Clovis Ntahkie & Awrejcewicz, Jan & Fouda, Henri Paul Ekobena & Kengne, Jacques, 2022. "Hamilton energy, complex dynamical analysis and information patterns of a new memristive FitzHugh-Nagumo neural network," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Noel Freddy Fotie Foka & Balamurali Ramakrishnan & André Rodrigue Tchamda & Sifeu Takougang Kingni & Karthikeyan Rajagopal & Victor Kamgang Kuetche, 2021. "Dynamical analysis of Josephson junction neuron model driven by a thermal signal and its digital implementation based on microcontroller," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(12), pages 1-7, December.
    8. Evgeniya V. Pankratova & Maria S. Sinitsina & Susanna Gordleeva & Victor B. Kazantsev, 2022. "Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration," Mathematics, MDPI, vol. 10(8), pages 1-20, April.
    9. Zhang, Zefeng & Huang, Lilian & Liu, Jin & Guo, Qiang & Du, Xiuli, 2022. "A new method of constructing cyclic symmetric conservative chaotic systems and improved offset boosting control," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    10. 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).
    11. Bao, Bocheng & Chen, Liuhui & Bao, Han & Chen, Mo & Xu, Quan, 2024. "Bifurcations to bursting oscillations in memristor-based FitzHugh-Nagumo circuit," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    12. Fossi, Jules Tagne & Njitacke, Zeric Tabekoueng & Tankeu, William Nguimeya & Mendimi, Joseph Marie & Awrejcewicz, Jan & Atangana, Jacques, 2023. "Phase synchronization and coexisting attractors in a model of three different neurons coupled via hybrid synapses," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    13. Noel Freddy Fotie Foka & Balamurali Ramakrishnan & André Cheage Chamgoué & Alain Francis Talla & Victor Kamgang Kuetche, 2022. "Neuronal circuit based on Josephson junction actuated by a photocurrent: dynamical analysis and microcontroller implementation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(6), pages 1-8, June.
    14. Njitacke, Zeric Tabekoueng & Doubla, Isaac Sami & Mabekou, Sandrine & Kengne, Jacques, 2020. "Hidden electrical activity of two neurons connected with an asymmetric electric coupling subject to electromagnetic induction: Coexistence of patterns and its analog implementation," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    15. Chen, Xiongjian & Wang, Ning & Wang, Yiteng & Wu, Huagan & Xu, Quan, 2023. "Memristor initial-offset boosting and its bifurcation mechanism in a memristive FitzHugh-Nagumo neuron model with hidden dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    16. Hu, Dongpo & Ma, Linyi & Song, Zigen & Zheng, Zhaowen & Cheng, Lifang & Liu, Ming, 2024. "Multiple bifurcations of a time-delayed coupled FitzHugh–Rinzel neuron system with chemical and electrical couplings," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    17. Tabekoueng Njitacke, Zeric & Tsafack, Nestor & Ramakrishnan, Balamurali & Rajagopal, Kartikeyan & Kengne, Jacques & Awrejcewicz, Jan, 2021. "Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: Application in images encryption," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    18. Ding, Shoukui & Wang, Ning & Bao, Han & Chen, Bei & Wu, Huagan & Xu, Quan, 2023. "Memristor synapse-coupled piecewise-linear simplified Hopfield neural network: Dynamics analysis and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    19. Wang, Ning & Cui, Mengkai & Yu, Xihong & Shan, Yufan & Xu, Quan, 2023. "Generating multi-folded hidden Chua’s attractors: Two-case study," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    20. Leutcho, Gervais Dolvis & Jafari, Sajad & Hamarash, Ibrahim Ismael & Kengne, Jacques & Tabekoueng Njitacke, Zeric & Hussain, Iqtadar, 2020. "A new megastable nonlinear oscillator with infinite attractors," Chaos, Solitons & Fractals, Elsevier, vol. 134(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:phsmap:v:602:y:2022:i:c:s0378437122003351. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.