IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i14p2244-d1438209.html
   My bibliography  Save this article

A Novel Coupled Memristive Izhikevich Neuron Model and Its Complex Dynamics

Author

Listed:
  • Fengling Jia

    (School of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Peiyan He

    (College of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an 710021, China)

  • Lixin Yang

    (College of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an 710021, China)

Abstract

This paper proposes a novel, five-dimensional memristor synapse-coupled Izhikevich neuron model under electromagnetic induction. Firstly, we analyze the global exponential stability of the presented system by constructing an appropriate Lyapunov function. Furthermore, the Hamilton energy functions of the model and its corresponding error system are derived by using Helmholtz’s theorem. In addition, the influence of external current and system parameters on the dynamical behavior are investigated. The numerical simulation results indicate that the discharge pattern of excitatory and inhibitory neurons changes significantly when the amplitude and frequency of the external stimulus current are applied at different degrees. And the crucial dynamical behavior of the neuronal system is determined by the intensity of modulation of the induced current and the gain in the electromagnetic induction. Moreover, the amount of Hamilton energy released by the model could be evaluated during the conversion between the distinct dynamical behaviors.

Suggested Citation

  • Fengling Jia & Peiyan He & Lixin Yang, 2024. "A Novel Coupled Memristive Izhikevich Neuron Model and Its Complex Dynamics," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2244-:d:1438209
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/14/2244/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/14/2244/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kafraj, Mohadeseh Shafiei & Parastesh, Fatemeh & Jafari, Sajad, 2020. "Firing patterns of an improved Izhikevich neuron model under the effect of electromagnetic induction and noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. An, Xinlei & Qiao, Shuai, 2021. "The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 143(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. Xie, Ying & Huang, Weifang & Jia, Ya & Ye, Zhiqiu & Wu, Yong, 2024. "Collective behaviors of neural network regulated by the spatially distributed stimuli," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 651(C).
    2. Chen, Lianyu & Muthukumar, Deivasundari & Natiq, Hayder & Mehrabbeik, Mahtab & Lei, Tengfei & Jafari, Sajad, 2025. "Relay synchronization in a multiplex memristive neuronal network with electrical and field couplings," Chaos, Solitons & Fractals, Elsevier, vol. 190(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. 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).
    2. 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).
    3. Xu, Quan & Wang, Yiteng & Wu, Huagan & Chen, Mo & Chen, Bei, 2024. "Periodic and chaotic spiking behaviors in a simplified memristive Hodgkin-Huxley circuit," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    4. Xu, Quan & Wang, Kai & Feng, Chengtao & Fan, Weiwei & Wang, Ning, 2024. "Dynamical effects of low-frequency and high-frequency current stimuli in a memristive Morris–Lecar neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    5. Muni, Sishu Shankar & Rajagopal, Karthikeyan & Karthikeyan, Anitha & Arun, Sundaram, 2022. "Discrete hybrid Izhikevich neuron model: Nodal and network behaviours considering electromagnetic flux coupling," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. Shi, Qianqian & Qu, Shaocheng & An, Xinlei & Wei, Ziming & Zhang, Chen, 2024. "Three-dimensional m-HR neuron model and its application in medical image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    7. Chen, Yixuan & Guo, Qun & Zhang, Xiaofeng & Wang, Chunni, 2024. "Numerical approach and physical description for a two-capacitive neuron and its adaptive network dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    8. Guo, Yitong & Wang, Chunni & Ma, Jun, 2024. "Jointed pendulums driven by a neural circuit, electromechanical arm model approach," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    9. Njitacke, Zeric Tabekoueng & Ramakrishnan, Balamurali & Rajagopal, Karthikeyan & Fonzin Fozin, Théophile & Awrejcewicz, Jan, 2022. "Extremely rich dynamics of coupled heterogeneous neurons through a Josephson junction synapse," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Sharma, Sanjeev Kumar & Mondal, Arnab & Mondal, Argha & Aziz-Alaoui, M.A. & Upadhyay, Ranjit Kumar & Ma, Jun, 2022. "Emergence of Canard induced mixed mode oscillations in a slow–fast dynamics of a biophysical excitable model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. 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.
    12. 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).
    13. 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).
    14. Zhang, Jianlin & Bao, Han & Yu, Xihong & Chen, Bei, 2024. "Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    15. Wu, Huagan & Gu, Jinxiang & Wang, Ning & Chen, Mo & Xu, Quan, 2025. "Spiking and bursting activities in an NLAM-based CNN cell," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    16. Hu, Xueyan & Ding, Qianming & Wu, Yong & Huang, Weifang & Yang, Lijian & Jia, Ya, 2024. "Dynamical rewiring promotes synchronization in memristive FitzHugh-Nagumo neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    17. Slepukhina, Evdokiia & Bashkirtseva, Irina & Ryashko, Lev & Kügler, Philipp, 2022. "Stochastic mixed-mode oscillations in the canards region of a cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    18. Wang, Weiping & He, Chang & Wang, Zhen & Hramov, Alexander & Fan, Denggui & Yuan, Manman & Luo, Xiong & Kurths, Jürgen, 2021. "Dynamic analysis of synaptic loss and synaptic compensation in the process of associative memory ability decline in Alzheimer’s disease," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    19. Xu, Quan & Wang, Kai & Chen, Mo & Parastesh, Fatemeh & Wang, Ning, 2024. "Bursting and spiking activities in a Wilson neuron circuit with memristive sodium and potassium ion channels," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    20. Zhang, Jianlin & Bao, Han & Gu, Jinxiang & Chen, Mo & Bao, Bocheng, 2024. "Multistability and synchronicity of memristor coupled adaptive synaptic neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 185(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:gam:jmathe:v:12:y:2024:i:14:p:2244-:d:1438209. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.