Breathers in two-dimensional neural media.
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.
Folias
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Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA.
Bressloff
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D000465:Algorithms; D002540:Cerebral Cortex / Q000502:physiology; D005583:Fourier Analysis; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D009991:Oscillometry