IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i2p547-560.html
   My bibliography  Save this article

Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay

Author

Listed:
  • Hutt, Axel
  • Atay, Fatihcan M.

Abstract

The spatiotemporal dynamics of neural activity are studied using an integro-differential model of spatially extended neuronal ensembles. The model includes both synaptic and axonal propagation delay while spatial synaptic connectivities are represented by gamma distributions. This family of connectivity kernels has been observed experimentally and covers the cases of divergent, finite, and negligible self-connections. We give conditions for stationary and non-stationary instabilities for gamma-distributed kernels, which can be formulated in terms of the mean spatial interaction ranges and the mean spatial interaction times. We present novel mechanisms for Turing patterns and traveling waves, which result from the special shape of the gamma-distributed interactions. We give a numerical study of the propagation of evoked spatiotemporal response activity caused by short local stimuli, and reveal maximum response activity after the mean interaction time. This maximum occurs at a distance from stimulus offset location, which is equal to the mean interaction range.

Suggested Citation

  • Hutt, Axel & Atay, Fatihcan M., 2007. "Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 547-560.
  • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:547-560
    DOI: 10.1016/j.chaos.2005.10.091
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905010817
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2005.10.091?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. Gushchin, Alexander A. & Küchler, Uwe, 2000. "On stationary solutions of delay differential equations driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 195-211, August.
    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. Zhang, Lei & Wang, Wenjuan & Xue, Yakui, 2009. "Spatiotemporal complexity of a predator–prey system with constant harvest rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 38-46.
    2. Ingo Bojak & David T J Liley, 2010. "Axonal Velocity Distributions in Neural Field Equations," PLOS Computational Biology, Public Library of Science, vol. 6(1), pages 1-25, January.

    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. Uwe Küchler & Michael Sørensen, 2010. "A simple estimator for discrete-time samples from affine stochastic delay differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 125-132, June.
    2. Li, Zhi & Long, Qinyi & Xu, Liping & Wen, Xueqi, 2022. "h-stability for stochastic Volterra–Levin equations," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Küchler, Uwe & Gapeev, Pavel V., 2003. "On Large Deviations in Testing Ornstein-Uhlenbeck Type Models with Delay," SFB 373 Discussion Papers 2003,45, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Uwe Küchler & Vyacheslav Vasiliev, 2005. "Sequential Identification of Linear Dynamic Systems with Memory," Statistical Inference for Stochastic Processes, Springer, vol. 8(1), pages 1-24, January.
    5. Li, Zhi & Zhang, Wei, 2017. "Stability in distribution of stochastic Volterra–Levin equations," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 20-27.
    6. Nielsen, Mikkel Slot, 2020. "On non-stationary solutions to MSDDEs: Representations and the cointegration space," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3154-3173.
    7. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan & Rohde, Victor, 2019. "Multivariate stochastic delay differential equations and CAR representations of CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4119-4143.
    8. Reiß, M. & Riedle, M. & van Gaans, O., 2006. "Delay differential equations driven by Lévy processes: Stationarity and Feller properties," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1409-1432, October.
    9. Fasen, Vicky, 2006. "Extremes of subexponential Lévy driven moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 116(7), pages 1066-1087, July.
    10. John Appleby & Markus Riedle & Catherine Swords, 2013. "Bubbles and crashes in a Black–Scholes model with delay," Finance and Stochastics, Springer, vol. 17(1), pages 1-30, January.

    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:32:y:2007:i:2:p:547-560. 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.