IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v165y2022ip1s0960077922009183.html
   My bibliography  Save this article

Route to chaos in a branching model of neural network dynamics

Author

Listed:
  • Williams-García, Rashid V.
  • Nicolis, Stam

Abstract

Simplified models are a necessary steppingstone for understanding collective neural network dynamics, in particular the transitions between different kinds of behavior, whose universality can be captured by such models, without prejudice. One such model, the cortical branching model (CBM), has previously been used to characterize part of the universal behavior of neural network dynamics and also led to the discovery of a second, chaotic transition which has not yet been fully characterized. Here, we study the properties of this chaotic transition, that occurs in the mean-field approximation to the kin=1 CBM by focusing on the constraints the model imposes on initial conditions, parameters, and the imprint thereof on the Lyapunov spectrum. Although the model seems similar to the Hénon map, we find that the Hénon map cannot be recovered using orthogonal transformations to decouple the dynamics. Fundamental differences between the two, namely that the CBM is defined on a compact space and features a non-constant Jacobian, indicate that the CBM maps, more generally, represent a class of generalized Hénon maps which has yet to be fully understood.

Suggested Citation

  • Williams-García, Rashid V. & Nicolis, Stam, 2022. "Route to chaos in a branching model of neural network dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009183
    DOI: 10.1016/j.chaos.2022.112739
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922009183
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112739?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. Meixiang Cai, 2015. "Complex Dynamics in Generalized Hénon Map," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-18, March.
    2. Erik Mosekilde & Zhanybai T. Zhusubaliyev & Vadim N. Rudakov & Evgeniy A. Soukhterin, 2000. "Bifurcation analysis of the Henon map," Discrete Dynamics in Nature and Society, Hindawi, vol. 5, pages 1-19, January.
    3. Sinisa Pajevic & Dietmar Plenz, 2009. "Efficient Network Reconstruction from Dynamical Cascades Identifies Small-World Topology of Neuronal Avalanches," PLOS Computational Biology, Public Library of Science, vol. 5(1), pages 1-20, January.
    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. Chen, Chengjie & Min, Fuhong & Zhang, Yunzhen & Bao, Han, 2023. "ReLU-type Hopfield neural network with analog hardware implementation," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Deng, Jie & Li, Hong-Li & Cao, Jinde & Hu, Cheng & Jiang, Haijun, 2023. "State estimation for discrete-time fractional-order neural networks with time-varying delays and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(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. Mikail Rubinov & Olaf Sporns & Jean-Philippe Thivierge & Michael Breakspear, 2011. "Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons," PLOS Computational Biology, Public Library of Science, vol. 7(6), pages 1-14, June.
    2. Wu Zhu & Jian-an Fang & Yang Tang & Wenbing Zhang & Wei Du, 2012. "Digital IIR Filters Design Using Differential Evolution Algorithm with a Controllable Probabilistic Population Size," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    3. Suchin S Gururangan & Alexander J Sadovsky & Jason N MacLean, 2014. "Analysis of Graph Invariants in Functional Neocortical Circuitry Reveals Generalized Features Common to Three Areas of Sensory Cortex," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-12, July.

    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:165:y:2022:i:p1:s0960077922009183. 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.