PMID: 16384107Dec 31, 2005

Breathers in two-dimensional neural media

Physical Review Letters
S E Folias, Paul C Bressloff

Abstract

In this Letter we show how nontrivial forms of spatially localized oscillations or breathers can occur in two-dimensional excitable neural media with short-range excitation and long-range inhibition. The basic dynamical mechanism involves a Hopf bifurcation of a stationary pulse solution in the presence of a spatially localized input. Such an input could arise from external stimuli or reflect changes in the excitability of local populations of neurons as a precursor for epileptiform activity. The resulting dynamical instability breaks the underlying radial symmetry of the stationary pulse, leading to the formation of a nonradially symmetric breather. The number of breathing lobes is consistent with the order of the dominant unstable Fourier mode associated with perturbations of the stationary pulse boundary.

Citations

Oct 30, 2009·Journal of Computational Neuroscience·Zachary P Kilpatrick, Paul C Bressloff
Dec 21, 2010·Journal of Computational Neuroscience·Jérémie LefebvreVictor G Leblanc
Jun 15, 2011·Journal of Computational Neuroscience·Zachary P Kilpatrick, G Bard Ermentrout
Mar 2, 2012·Journal of Biological Physics·Jérémie LefebvreVictor G Leblanc
Apr 22, 2011·The European Physical Journal. E, Soft Matter·Y-J Chen, Kenichi Yoshikawa
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Jun 1, 2011·PLoS Computational Biology·Volker PerniceStefan Rotter
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Feb 18, 2014·Cognitive Computation·Paul C Bressloff, Stephen Coombes
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Feb 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S V GurevichH-G Purwins
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Aug 17, 2019·Frontiers in Computational Neuroscience·Daniel Naoumenko, Pulin Gong
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zachary P Kilpatrick

Related Concepts

Insula of Reil
Fourier Transform
Neural Networks (Anatomic)
Neurons
Oscillometry

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