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Bifurcation dynamics and FPGA implementation of coupled Fitzhugh-Nagumo neuronal system

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  • Shi, Wei
  • Min, Fuhong
  • Yang, Songtao

Abstract

This paper is devoted to studying the dynamical behaviors of the coupled FHN neural system by the discrete implicit mapping method, including bifurcation, coexistence, firing behaviors and synchronization. Two improved Fitzhugh-Nagumo (FHN) neurons are coupled through an asymmetric electrical synapse to investigate the effect of coupling strength on the firing behavior of neuronal networks, which is crucial to the progress of brain science. The types and stability of time-varying equilibrium points in the FHN neuron model are studied, and the corresponding discrete mapping model is established. The unstable periodic orbits hidden in chaos in the system are explored, and the mechanism of various bifurcations is explained through global eigenvalues. Simultaneously, the coexistence firing patterns are studied by basin of attraction, and the synchronization behavior of neural system is investigated through the normalized mean synchronization error (NMSE). Moreover, FPGA is employed for circuit implementation of the coupled neuronal system, and the correctness of theoretical results is verified. The results of this paper may help to better understand the firing and synchronization mechanisms of neural networks, which have important significance for the treatment of nervous system diseases and the development of neuroscience.

Suggested Citation

  • Shi, Wei & Min, Fuhong & Yang, Songtao, 2024. "Bifurcation dynamics and FPGA implementation of coupled Fitzhugh-Nagumo neuronal system," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
  • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010725
    DOI: 10.1016/j.chaos.2024.115520
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    References listed on IDEAS

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    1. Zhu, Jie & Min, Fuhong & Yang, Songtao & Shi, Wei, 2024. "Evolution of pitchfork bifurcation in a tabu learning neuron model and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Bao, Han & Rong, Kang & Chen, Mo & Zhang, Xi & Bao, Bocheng, 2023. "Multistability and synchronization of discrete maps via memristive coupling," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Lai, Qiang & Lai, Cong & Zhang, Hui & Li, Chunbiao, 2022. "Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Farshid Ashtiani & Alexander J. Geers & Firooz Aflatouni, 2022. "An on-chip photonic deep neural network for image classification," Nature, Nature, vol. 606(7914), pages 501-506, June.
    5. Kimberly C. Paul & Richard C. Krolewski & Edinson Lucumi Moreno & Jack Blank & Kristina M. Holton & Tim Ahfeldt & Melissa Furlong & Yu Yu & Myles Cockburn & Laura K. Thompson & Alexander Kreymerman & , 2023. "Publisher Correction: A pesticide and iPSC dopaminergic neuron screen identifies and classifies Parkinson-relevant pesticides," Nature Communications, Nature, vol. 14(1), pages 1-1, December.
    6. Kimberly C. Paul & Richard C. Krolewski & Edinson Lucumi Moreno & Jack Blank & Kristina M. Holton & Tim Ahfeldt & Melissa Furlong & Yu Yu & Myles Cockburn & Laura K. Thompson & Alexander Kreymerman & , 2023. "A pesticide and iPSC dopaminergic neuron screen identifies and classifies Parkinson-relevant pesticides," Nature Communications, Nature, vol. 14(1), pages 1-18, December.
    7. I.B., Tagne nkounga & F.M., Moukam kakmeni & R., Yamapi, 2022. "Birhythmic oscillations and global stability analysis of a conductance-based neuronal model under ion channel fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    8. Min, Fuhong & Zhu, Jie & Cheng, Yizi & Xu, Yeyin, 2024. "Dynamical analysis of a tabu learning neuron through the discrete implicit mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    9. Alharbi, Njud S. & Bekiros, Stelios & Jahanshahi, Hadi & Mou, Jun & Yao, Qijia, 2024. "Spatiotemporal wavelet-domain neuroimaging of chaotic EEG seizure signals in epilepsy diagnosis and prognosis with the use of graph convolutional LSTM networks," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    10. Parastesh, Fatemeh & Azarnoush, Hamed & Jafari, Sajad & Hatef, Boshra & Perc, Matjaž & Repnik, Robert, 2019. "Synchronizability of two neurons with switching in the coupling," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 217-223.
    11. Nkounga, I.B. Tagne & Xia, Yibo & Yanchuk, Serhiy & Yamapi, R. & Kurths, Jürgen, 2023. "Generalized FitzHugh–Nagumo model with tristable dynamics: Deterministic and stochastic bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    12. 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).
    Full references (including those not matched with items on IDEAS)

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