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.