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  Bumps and oscillons in networks of spiking neurons

Schmidt, H., & Avitabile, D. (2020). Bumps and oscillons in networks of spiking neurons. Chaos, 30(3): 033133. doi:10.1063/1.5135579.

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 Creators:
Schmidt, Helmut1, Author              
Avitabile, Daniele2, Author
Affiliations:
1Methods and Development Group Brain Networks, MPI for Human Cognitive and Brain Sciences, Max Planck Society, ou_2205650              
2Department of Mathematics, Faculty of Sciences, VU University Amsterdam, the Netherlands, ou_persistent22              

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 Abstract: We study localized patterns in an exact mean-field description of a spatially extended network of quadratic integrate-and-fire neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps, and give an analytic estimate for the parameter range, where these solutions exist in parameter space, when one or more microscopic network parameters are varied. We develop Galerkin methods for the model equations, which enable numerical bifurcation analysis of stationary and time-periodic spatially extended solutions. We study the emergence of patterns composed of multiple bumps, which are arranged in a snake-and-ladder bifurcation structure if a homogeneous or heterogeneous synaptic kernel is suitably chosen. Furthermore, we examine time-periodic, spatially localized solutions (oscillons) in the presence of external forcing, and in autonomous, recurrently coupled excitatory and inhibitory networks. In both cases, we observe period-doubling cascades leading to chaotic oscillations.

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Language(s): eng - English
 Dates: 2020-032020-03-19
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1063/1.5135579
PMID: 32237760
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Title: Chaos
  Other : Chaos : an interdisciplinary journal of nonlinear science
Source Genre: Journal
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Publ. Info: Woodbury, NY : American Institute of Physics
Pages: - Volume / Issue: 30 (3) Sequence Number: 033133 Start / End Page: - Identifier: ISSN: 1054-1500
CoNE: https://pure.mpg.de/cone/journals/resource/954922836228