Breathers in Two-Dimensional Neural Media
In this Letter we show how nontrivial forms of spatially localized oscillations or {\em 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.
University of Utah
| Department of Mathematics
|
bressloff@math.utah.edu
Aug 2001.