Front-bifurcations in an excitatory neural network
We show how a one--dimensional excitatory neural network can exhibit a symmetry breaking front bifurcation analogous to that found in reaction diffusion systems. This
occurs in a homogeneous network when a stationary front undergoes a pitchfork bifurcation leading to bi--directional wave propagation. We analyze the dynamics in a neighborhood of
the front bifurcation using perturbation methods, and establish that a weak input inhomogeneity can induce a Hopf instability of the
stationary front leading to the formation of a breather. Finally, we carry out a stability analysis of stationary fronts in an exactly
solvable model and use this to derive conditions for oscillatory waves beyond the weak input regime.
University of Utah
| Department of Mathematics
|
bressloff@math.utah.edu
Jan 2004.