IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v183y2024ics0960077924005198.html
   My bibliography  Save this article

Dynamics and stability of neural systems with indirect interactions involved energy levels

Author

Listed:
  • Shao, Yan
  • Wu, Fuqiang
  • Wang, Qingyun

Abstract

Dynamical modelling for neural systems with direct and indirect connections is to understand how these connections contribute to neural dynamics. Despite recent findings suggesting the existence of indirect connections in neural systems, their dynamical characteristics remain poorly understood. In this paper, we propose a simplified circuit model with indirect interactions inspired by the indirect connection between two neurons, from an energy perspective. Through bifurcation and dynamics analysis, we find that the presented model has a striking resemblance with the classical Hodgkin-Huxley neuronal model. Moreover, stability in a neural network coupled with energy is demonstrated by combining stability analysis and numerical simulation. Our analysis sheds light on the excitability dynamics and multi-stability that can emerge in biophysical systems with nonlinear interactions inspired by the neural systems and highlights the role of energy in propagating electrical activities.

Suggested Citation

  • Shao, Yan & Wu, Fuqiang & Wang, Qingyun, 2024. "Dynamics and stability of neural systems with indirect interactions involved energy levels," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924005198
    DOI: 10.1016/j.chaos.2024.114967
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924005198
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114967?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. Wu, Huagan & Bian, Yixuan & Zhang, Yunzhen & Guo, Yixuan & Xu, Quan & Chen, Mo, 2023. "Multi-stable states and synchronicity of a cellular neural network with memristive activation function," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Wu, Fuqiang & Kang, Ting & Shao, Yan & Wang, Qingyun, 2023. "Stability of Hopfield neural network with resistive and magnetic coupling," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Tianda Fu & Xiaomeng Liu & Hongyan Gao & Joy E. Ward & Xiaorong Liu & Bing Yin & Zhongrui Wang & Ye Zhuo & David J. F. Walker & J. Joshua Yang & Jianhan Chen & Derek R. Lovley & Jun Yao, 2020. "Bioinspired bio-voltage memristors," Nature Communications, Nature, vol. 11(1), pages 1-10, December.
    4. Wei Yi & Kenneth K. Tsang & Stephen K. Lam & Xiwei Bai & Jack A. Crowell & Elias A. Flores, 2018. "Biological plausibility and stochasticity in scalable VO2 active memristor neurons," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
    5. Corinne Teeter & Ramakrishnan Iyer & Vilas Menon & Nathan Gouwens & David Feng & Jim Berg & Aaron Szafer & Nicholas Cain & Hongkui Zeng & Michael Hawrylycz & Christof Koch & Stefan Mihalas, 2018. "Generalized leaky integrate-and-fire models classify multiple neuron types," Nature Communications, Nature, vol. 9(1), pages 1-15, December.
    6. Wu, Fuqiang & Gu, Huaguang & Jia, Yanbing, 2021. "Bifurcations underlying different excitability transitions modulated by excitatory and inhibitory memristor and chemical autapses," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    7. Xin Li & Qunxi Zhu & Chengli Zhao & Xiaojun Duan & Bolin Zhao & Xue Zhang & Huanfei Ma & Jie Sun & Wei Lin, 2024. "Higher-order Granger reservoir computing: simultaneously achieving scalable complex structures inference and accurate dynamics prediction," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    8. Francesco Randi & Anuj K. Sharma & Sophie Dvali & Andrew M. Leifer, 2023. "Neural signal propagation atlas of Caenorhabditis elegans," Nature, Nature, vol. 623(7986), pages 406-414, November.
    9. Zhongrui Wang & Mingyi Rao & Jin-Woo Han & Jiaming Zhang & Peng Lin & Yunning Li & Can Li & Wenhao Song & Shiva Asapu & Rivu Midya & Ye Zhuo & Hao Jiang & Jung Ho Yoon & Navnidhi Kumar Upadhyay & Saum, 2018. "Capacitive neural network with neuro-transistors," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
    10. Ma, Jun, 2024. "Energy function for some maps and nonlinear oscillators," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    11. Wu, Fuqiang & Hu, Xikui & Ma, Jun, 2022. "Estimation of the effect of magnetic field on a memristive neuron," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    12. Wu, Fuqiang & Guo, Yitong & Ma, Jun & Jin, Wuyin, 2023. "Synchronization of bursting memristive Josephson junctions via resistive and magnetic coupling," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    13. Luping Yin & Rui Zheng & Wei Ke & Quansheng He & Yi Zhang & Junlong Li & Bo Wang & Zhen Mi & Yue-sheng Long & Malte J. Rasch & Tianfu Li & Guoming Luan & Yousheng Shu, 2018. "Autapses enhance bursting and coincidence detection in neocortical pyramidal cells," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
    14. Chesebro, Anthony G. & Mujica-Parodi, Lilianne R. & Weistuch, Corey, 2023. "Ion gradient-driven bifurcations of a multi-scale neuronal model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    15. 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)

    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. Hu, Jingting & Bao, Han & Xu, Quan & Chen, Mo & Bao, Bocheng, 2024. "Synchronization generations and transitions in two map-based neurons coupled with locally active memristor," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. 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).
    3. Zhiyuan Li & Zhongshao Li & Wei Tang & Jiaping Yao & Zhipeng Dou & Junjie Gong & Yongfei Li & Beining Zhang & Yunxiao Dong & Jian Xia & Lin Sun & Peng Jiang & Xun Cao & Rui Yang & Xiangshui Miao & Ron, 2024. "Crossmodal sensory neurons based on high-performance flexible memristors for human-machine in-sensor computing system," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    4. 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).
    5. Sang Hyun Sung & Tae Jin Kim & Hyera Shin & Tae Hong Im & Keon Jae Lee, 2022. "Simultaneous emulation of synaptic and intrinsic plasticity using a memristive synapse," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    6. Jia, Junen & Wang, Chunni & Zhang, Xiaofeng & Zhu, Zhigang, 2024. "Energy and self-adaption in a memristive map neuron," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    7. Cristina Rueda & Itziar Fernández & Yolanda Larriba & Alejandro Rodríguez-Collado, 2021. "The FMM Approach to Analyze Biomedical Signals: Theory, Software, Applications and Future," Mathematics, MDPI, vol. 9(10), pages 1-13, May.
    8. 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).
    9. Yuan-Hang Zhang & Chesson Sipling & Erbin Qiu & Ivan K. Schuller & Massimiliano Di Ventra, 2024. "Collective dynamics and long-range order in thermal neuristor networks," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    10. 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).
    11. Peng, Lu & Tang, Jun & Ma, Jun & Luo, Jinming, 2022. "The influence of autapse on synchronous firing in small-world neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    12. Ushakov, Yury & Balanov, Alexander & Savel’ev, Sergey, 2021. "Role of noise in spiking dynamics of diffusive memristor driven by heating-cooling cycles," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    13. Ui Yeon Won & Quoc An Vu & Sung Bum Park & Mi Hyang Park & Van Dam Do & Hyun Jun Park & Heejun Yang & Young Hee Lee & Woo Jong Yu, 2023. "Multi-neuron connection using multi-terminal floating–gate memristor for unsupervised learning," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    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. Njitacke, Zeric Tabekoueng & Ramadoss, Janarthanan & Takembo, Clovis Ntahkie & Rajagopal, Karthikeyan & Awrejcewicz, Jan, 2023. "An enhanced FitzHugh–Nagumo neuron circuit, microcontroller-based hardware implementation: Light illumination and magnetic field effects on information patterns," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    16. Yan Wang & Yue Gong & Shenming Huang & Xuechao Xing & Ziyu Lv & Junjie Wang & Jia-Qin Yang & Guohua Zhang & Ye Zhou & Su-Ting Han, 2021. "Memristor-based biomimetic compound eye for real-time collision detection," Nature Communications, Nature, vol. 12(1), pages 1-12, December.
    17. Zhou, Wei & Jin, Peipei & Dong, Yujiao & Liang, Yan & Wang, Guangyi, 2023. "Memristor neurons and their coupling networks based on Edge of Chaos Kernel," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    18. Shi, Shuyu & Liang, Yan & Li, Yiqing & Lu, Zhenzhou & Dong, Yujiao, 2024. "A neuron circuit based on memristor and negative capacitor: Dynamics analysis and hardware implementation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    19. Dong Gue Roe & Dong Hae Ho & Yoon Young Choi & Young Jin Choi & Seongchan Kim & Sae Byeok Jo & Moon Sung Kang & Jong-Hyun Ahn & Jeong Ho Cho, 2023. "Humanlike spontaneous motion coordination of robotic fingers through spatial multi-input spike signal multiplexing," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    20. Wu, Huagan & Gu, Jinxiang & Guo, Yixuan & Chen, Mo & Xu, Quan, 2024. "Biphasic action potentials in an individual cellular neural network cell," Chaos, Solitons & Fractals, Elsevier, vol. 182(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:183:y:2024:i:c:s0960077924005198. 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.