IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip2s0960077921009656.html
   My bibliography  Save this article

Bifurcations underlying different excitability transitions modulated by excitatory and inhibitory memristor and chemical autapses

Author

Listed:
  • Wu, Fuqiang
  • Gu, Huaguang
  • Jia, Yanbing

Abstract

Memristor is an emerging modulation factor to mimic neuronal synapse, and the switch or transition between neuronal excitability classes is an important topic in nonlinear dynamics and neurophysiology. In the present investigation on the Morris-Lecar model, the memristive autapse is identified to induce excitability transitions different from those of the chemical one. The inhibitory and excitatory chemical autapses induce excitability switch from class I to II and from class II to I, respectively. However, the inhibitory and excitatory memristive autapses induce the transition from class II to I and from class I to II, respectively. Furthermore, comprehensive bifurcation mechanisms underlying the transitions are acquired. The class I excitability corresponds to saddle-node bifurcation on an invariant cycle (SNIC), and class II excitability to the saddle-node (SN) bifurcation and Hopf bifurcation. Type I spiking corresponds to the SNIC or big homoclinic (BHom) orbit bifurcations, and type II spiking to the Fold Limit Cycle (FLC) bifurcation or supercritical Hopf bifurcation. Among various codimension-2 bifurcations, the saddle-node homoclinic orbit bifurcation, which is related to the SNIC, BHom, and SN bifurcations, is responsible for the excitability transition. A nameless degenerate bifurcation associated with the BHom and FLC bifurcations, is responsible for the spiking transition. In addition, the nullcline shapes present the geometric mechanism for the transitions. The obtained results present different roles of memristive and chemical autapses on modulating neuronal electrical activities and the underlying dynamical mechanisms, which are helpful for the design and development of novel memristive synapses with excitatory or inhibitory effects.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921009656
    DOI: 10.1016/j.chaos.2021.111611
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009656
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111611?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. Uzun, Rukiye, 2017. "Influences of autapse and channel blockage on multiple coherence resonance in a single neuron," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 203-210.
    2. Wu, Fuqiang & Wang, Chunni & Jin, Wuyin & Ma, Jun, 2017. "Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 81-88.
    3. Ma, Jun & Mi, Lv & Zhou, Ping & Xu, Ying & Hayat, Tasawar, 2017. "Phase synchronization between two neurons induced by coupling of electromagnetic field," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 321-328.
    4. Ge, Mengyan & Jia, Ya & Xu, Ying & Lu, Lulu & Wang, Huiwen & Zhao, Yunjie, 2019. "Wave propagation and synchronization induced by chemical autapse in chain Hindmarsh–Rose neural network," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 136-145.
    5. Lin, Hairong & Wang, Chunhua, 2020. "Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network," Applied Mathematics and Computation, Elsevier, vol. 369(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. Lee, Geun Ho & Kim, Tae-Hyeon & Youn, Sangwook & Park, Jinwoo & Kim, Sungjoon & Kim, Hyungjin, 2023. "Low-fluctuation nonlinear model using incremental step pulse programming with memristive devices," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. 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).
    3. 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).
    4. Lin, Hairong & Wang, Chunhua & Sun, Jingru & Zhang, Xin & Sun, Yichuang & Iu, Herbert H.C., 2023. "Memristor-coupled asymmetric neural networks: Bionic modeling, chaotic dynamics analysis and encryption application," Chaos, Solitons & Fractals, Elsevier, vol. 166(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. 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).
    2. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    4. Paul Asir, M., 2023. "Chimeras in complex networks: A gear by nonlinear mean-field," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. 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).
    6. Wu, Fuqiang & Zhou, Ping & Alsaedi, Ahmed & Hayat, Tasawar & Ma, Jun, 2018. "Synchronization dependence on initial setting of chaotic systems without equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 124-132.
    7. Li, Fan, 2020. "Effect of field coupling on the wave propagation in the neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. Bao, Han & Yu, Xihong & Zhang, Yunzhen & Liu, Xiaofeng & Chen, Mo, 2023. "Initial condition-offset regulating synchronous dynamics and energy diversity in a memristor-coupled network of memristive HR neurons," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    9. Ni Zhang & Dongxi Li & Yanya Xing, 2021. "Autapse-induced multiple inverse stochastic resonance in a neural system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-11, January.
    10. Qin, Huixin & Wang, Chunni & Cai, Ning & An, Xinlei & Alzahrani, Faris, 2018. "Field coupling-induced pattern formation in two-layer neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 141-152.
    11. Liu, Zhilong & Ma, Jun & Zhang, Ge & Zhang, Yin, 2019. "Synchronization control between two Chua′s circuits via capacitive coupling," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 94-106.
    12. Yuangen Yao & Wei Cao & Qiming Pei & Chengzhang Ma & Ming Yi, 2018. "Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons," Complexity, Hindawi, vol. 2018, pages 1-10, April.
    13. Lin, Hairong & Wang, Chunhua, 2020. "Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    14. Zhang, Ge & Wang, Chunni & Alzahrani, Faris & Wu, Fuqiang & An, Xinlei, 2018. "Investigation of dynamical behaviors of neurons driven by memristive synapse," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 15-24.
    15. Xiaoyu Hu & Chongxin Liu, 2019. "Bursting and Synchronization of Coupled Neurons under Electromagnetic Radiation," Complexity, Hindawi, vol. 2019, pages 1-10, December.
    16. Ke Ding & Zahra Rostami & Sajad Jafari & Boshra Hatef, 2018. "Investigation of Cortical Signal Propagation and the Resulting Spatiotemporal Patterns in Memristor-Based Neuronal Network," Complexity, Hindawi, vol. 2018, pages 1-20, June.
    17. 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).
    18. Zhang, Ge & Ma, Jun & Alsaedi, Ahmed & Ahmad, Bashir & Alzahrani, Faris, 2018. "Dynamical behavior and application in Josephson Junction coupled by memristor," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 290-299.
    19. Guo, Shengli & Xu, Ying & Wang, Chunni & Jin, Wuyin & Hobiny, Aatef & Ma, Jun, 2017. "Collective response, synapse coupling and field coupling in neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 120-127.
    20. Ma, Jun & Mi, Lv & Zhou, Ping & Xu, Ying & Hayat, Tasawar, 2017. "Phase synchronization between two neurons induced by coupling of electromagnetic field," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 321-328.

    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:153:y:2021:i:p2:s0960077921009656. 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.