Breathing pulses in an excitatory neural network
In this paper we show how an inhomogeneous input induces wave propagation
failure in an excitatory neural network due to the pinning of a
stationary pulse solution. A subsequent reduction of the input
inhomogeneity can then lead to a Hopf instability of the stationary
solution resulting in the formation of a breather. The breather can itself undergo a secondary instability leading to the periodic emission of traveling waves. In one
dimension such waves consist of pairs of counter--propagating pulses, whereas in two dimensions the waves are circular target patterns.
University of Utah
| Department of Mathematics
|
bressloff@math.utah.edu
Jan 2004.