IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v69y2014icp233-245.html
   My bibliography  Save this article

Stable chaos in fluctuation driven neural circuits

Author

Listed:
  • Angulo-Garcia, David
  • Torcini, Alessandro

Abstract

We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare mean versus fluctuations driven networks, the former (latter) is realized by considering purely excitatory (inhibitory) sparse neural circuits. In the excitatory case the instabilities of the system can be completely captured by an usual linear stability (Lyapunov) analysis, whereas the inhibitory networks can display the coexistence of linear and nonlinear instabilities. The nonlinear effects are associated to finite amplitude instabilities, which have been characterized in terms of suitable indicators. For inhibitory coupling one observes a transition from chaotic to non chaotic dynamics by decreasing the pulse-width. For sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of stable chaos.

Suggested Citation

  • Angulo-Garcia, David & Torcini, Alessandro, 2014. "Stable chaos in fluctuation driven neural circuits," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 233-245.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:233-245
    DOI: 10.1016/j.chaos.2014.10.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077914001805
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2014.10.009?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. Michael London & Arnd Roth & Lisa Beeren & Michael Häusser & Peter E. Latham, 2010. "Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex," Nature, Nature, vol. 466(7302), pages 123-127, July.
    2. Gina G. Turrigiano & Kenneth R. Leslie & Niraj S. Desai & Lana C. Rutherford & Sacha B. Nelson, 1998. "Activity-dependent scaling of quantal amplitude in neocortical neurons," Nature, Nature, vol. 391(6670), pages 892-896, February.
    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. Mizusaki, Beatriz E.P. & Agnes, Everton J. & Erichsen, Rubem & Brunnet, Leonardo G., 2017. "Learning and retrieval behavior in recurrent neural networks with pre-synaptic dependent homeostatic plasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 279-286.
    2. Omri Harish & David Hansel, 2015. "Asynchronous Rate Chaos in Spiking Neuronal Circuits," PLOS Computational Biology, Public Library of Science, vol. 11(7), pages 1-38, July.
    3. Matteo Saponati & Martin Vinck, 2023. "Sequence anticipation and spike-timing-dependent plasticity emerge from a predictive learning rule," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    4. Niranjan Chakravarthy & Shivkumar Sabesan & Kostas Tsakalis & Leon Iasemidis, 2009. "Controlling epileptic seizures in a neural mass model," Journal of Combinatorial Optimization, Springer, vol. 17(1), pages 98-116, January.
    5. Volker Pernice & Benjamin Staude & Stefano Cardanobile & Stefan Rotter, 2011. "How Structure Determines Correlations in Neuronal Networks," PLOS Computational Biology, Public Library of Science, vol. 7(5), pages 1-14, May.
    6. Sacha Jennifer van Albada & Moritz Helias & Markus Diesmann, 2015. "Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-37, September.
    7. Aseel Shomar & Lukas Geyrhofer & Noam E Ziv & Naama Brenner, 2017. "Cooperative stochastic binding and unbinding explain synaptic size dynamics and statistics," PLOS Computational Biology, Public Library of Science, vol. 13(7), pages 1-24, July.
    8. Matthias Schultze-Kraft & Markus Diesmann & Sonja Grün & Moritz Helias, 2013. "Noise Suppression and Surplus Synchrony by Coincidence Detection," PLOS Computational Biology, Public Library of Science, vol. 9(4), pages 1-15, April.
    9. Juan Prada & Manju Sasi & Corinna Martin & Sibylle Jablonka & Thomas Dandekar & Robert Blum, 2018. "An open source tool for automatic spatiotemporal assessment of calcium transients and local ‘signal-close-to-noise’ activity in calcium imaging data," PLOS Computational Biology, Public Library of Science, vol. 14(3), pages 1-34, March.
    10. Kendra S Burbank, 2015. "Mirrored STDP Implements Autoencoder Learning in a Network of Spiking Neurons," PLOS Computational Biology, Public Library of Science, vol. 11(12), pages 1-25, December.
    11. Evan S Schaffer & Srdjan Ostojic & L F Abbott, 2013. "A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks," PLOS Computational Biology, Public Library of Science, vol. 9(10), pages 1-11, October.
    12. Christian Meisel & Andreas Klaus & Christian Kuehn & Dietmar Plenz, 2015. "Critical Slowing Down Governs the Transition to Neuron Spiking," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-20, February.
    13. Damien M O’Halloran, 2020. "Simulation model of CA1 pyramidal neurons reveal opposing roles for the Na+/Ca2+ exchange current and Ca2+-activated K+ current during spike-timing dependent synaptic plasticity," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-12, March.
    14. Ravi Pancholi & Lauren Ryan & Simon Peron, 2023. "Learning in a sensory cortical microstimulation task is associated with elevated representational stability," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    15. Emiliano Torre & Carlos Canova & Michael Denker & George Gerstein & Moritz Helias & Sonja Grün, 2016. "ASSET: Analysis of Sequences of Synchronous Events in Massively Parallel Spike Trains," PLOS Computational Biology, Public Library of Science, vol. 12(7), pages 1-34, July.
    16. Christian Keck & Cristina Savin & Jörg Lücke, 2012. "Feedforward Inhibition and Synaptic Scaling – Two Sides of the Same Coin?," PLOS Computational Biology, Public Library of Science, vol. 8(3), pages 1-15, March.
    17. Iris Reuveni & Sourav Ghosh & Edi Barkai, 2017. "Real Time Multiplicative Memory Amplification Mediated by Whole-Cell Scaling of Synaptic Response in Key Neurons," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-31, January.
    18. Giorgia Dellaferrera & Stanisław Woźniak & Giacomo Indiveri & Angeliki Pantazi & Evangelos Eleftheriou, 2022. "Introducing principles of synaptic integration in the optimization of deep neural networks," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    19. Vladimir Ilin & Ian H Stevenson & Maxim Volgushev, 2014. "Injection of Fully-Defined Signal Mixtures: A Novel High-Throughput Tool to Study Neuronal Encoding and Computations," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-10, October.
    20. John Palmer & Adam Keane & Pulin Gong, 2017. "Learning and executing goal-directed choices by internally generated sequences in spiking neural circuits," PLOS Computational Biology, Public Library of Science, vol. 13(7), pages 1-23, July.

    More about this item

    Statistics

    Access and download statistics

    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:69:y:2014:i:c:p:233-245. 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.