IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921007293.html
   My bibliography  Save this article

Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons

Author

Listed:
  • Mondal, Argha
  • Hens, Chittaranjan
  • Mondal, Arnab
  • Antonopoulos, Chris G.

Abstract

Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity, especially in cortical areas. Here, we present an explicit mathematical analysis, corroborated by numerical results, to identify and investigate the spatiotemporal, non-uniform, patterns that emerge due to instability in an extended homogeneous 2D spatial domain, using the excitable Izhikevich neuron model. We examine diffusive instability and perform bifurcation and fixed-point analyses to characterize the patterns and their stability. Then, we derive analytically the amplitude equations that establish the activities of reaction-diffusion structures. We report on the emergence of diverse spatial structures including hexagonal and mixed-type patterns by providing a systematic mathematical approach, including variations in correlated oscillations, pattern variations and amplitude fluctuations. Our work shows that the emergence of spatiotemporal behavior, commonly found in excitable systems, has the potential to contribute significantly to the study of diffusively-coupled biophysical systems at large.

Suggested Citation

  • Mondal, Argha & Hens, Chittaranjan & Mondal, Arnab & Antonopoulos, Chris G., 2021. "Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007293
    DOI: 10.1016/j.chaos.2021.111375
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921007293
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111375?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. Iqbal, Naveed & Wu, Ranchao & Liu, Biao, 2017. "Pattern formation by super-diffusion in FitzHugh–Nagumo model," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 245-258.
    2. Rory G Townsend & Pulin Gong, 2018. "Detection and analysis of spatiotemporal patterns in brain activity," PLOS Computational Biology, Public Library of Science, vol. 14(12), pages 1-29, December.
    3. Yan, Shuixian & Jia, Dongxue & Zhang, Tonghua & Yuan, Sanling, 2020. "Pattern dynamics in a diffusive predator-prey model with hunting cooperations," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Gui-Quan Sun & Li Li & Zhen Jin & Zi-Ke Zhang & Tao Zhou, 2013. "Pattern Dynamics in a Spatial Predator-Prey System with Allee Effect," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, September.
    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. Mondal, Arnab & Upadhyay, Ranjit Kumar & Mondal, Argha & Sharma, Sanjeev Kumar, 2022. "Emergence of Turing patterns and dynamic visualization in excitable neuron model," Applied Mathematics and Computation, Elsevier, vol. 423(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. Fateev, I. & Polezhaev, A., 2024. "Chimera states in a lattice of superdiffusively coupled neurons," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Mondal, Arnab & Upadhyay, Ranjit Kumar & Mondal, Argha & Sharma, Sanjeev Kumar, 2022. "Emergence of Turing patterns and dynamic visualization in excitable neuron model," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    3. Shi, Yu & Luo, Xiao-Feng & Zhang, Yong-Xin & Sun, Gui-Quan, 2023. "An indicator of Crohn’s disease severity based on Turing patterns," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Hua Liu & Yong Ye & Yumei Wei & Weiyuan Ma & Ming Ma & Kai Zhang, 2019. "Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay," Complexity, Hindawi, vol. 2019, pages 1-14, November.
    5. Cristina Gutiérrez & Carmen Minuesa, 2020. "A Predator–Prey Two-Sex Branching Process," Mathematics, MDPI, vol. 8(9), pages 1-26, August.
    6. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    7. Yifan Gu & Yang Qi & Pulin Gong, 2019. "Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-34, April.
    8. Wang, Fatao & Yang, Ruizhi, 2023. "Spatial pattern formation driven by the cross-diffusion in a predator–prey model with Holling type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. Djilali, Salih & Cattani, Carlo, 2021. "Patterns of a superdiffusive consumer-resource model with hunting cooperation functional response," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    10. Song, Binbin & Zuo, Wenjie, 2023. "Spatiotemporal dynamics of a three-component chemotaxis model for Alopecia Areata," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Wang, Henan & Liu, Ping, 2023. "Pattern dynamics of a predator–prey system with cross-diffusion, Allee effect and generalized Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    12. Zheng, Qianqian & Shen, Jianwei, 2020. "Turing instability induced by random network in FitzHugh-Nagumo model," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    13. Boli Xie & Zhijun Wang & Yakui Xue & Zhenmin Zhang, 2015. "The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, October.
    14. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.
    15. Meng Zhu & Jing Li & Xinze Lian, 2022. "Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    16. Yang Qi & Pulin Gong, 2022. "Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits," Nature Communications, Nature, vol. 13(1), pages 1-19, December.
    17. Tah, Forwah Amstrong & Tabi, Conrad Bertrand & Kofane, Timoléon Crépin, 2021. "Pattern formation in the Fitzhugh–Nagumo neuron with diffusion relaxation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. Yanfei Du & Ben Niu & Junjie Wei, 2021. "Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect," Mathematics, MDPI, vol. 9(24), pages 1-40, December.
    19. Djilali, Salih, 2019. "Impact of prey herd shape on the predator-prey interaction," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 139-148.
    20. Yuqi Liang & Junhao Liang & Chenchen Song & Mianxin Liu & Thomas Knöpfel & Pulin Gong & Changsong Zhou, 2023. "Complexity of cortical wave patterns of the wake mouse cortex," Nature Communications, Nature, vol. 14(1), pages 1-13, December.

    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:152:y:2021:i:c:s0960077921007293. 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.