Breathing Pulses in an Excitatory Neural Network

Abstract

In this paper we show how a local inhomogeneous input can stabilize a stationary-pulse solution in an excitatory neural network. A subsequent reduction of the input amplitude can then induce 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 counterpropagating pulses, whereas in two dimensions the waves are circular target patterns.