Stimulus-locked traveling waves and breathers in an excitatory neural network
We analyze the existence and stability of stimulus-locked traveling
waves in a one-dimensional synaptically coupled excitatory neural
network. The network is
modeled in terms of a non-local integro-differential equation, in
which the integral kernel represents the spatial distribution of
synaptic weights and the
output firing rate of a neuron is taken to be a Heaviside function of
activity. Given an inhomogeneous moving input of amplitude $I_0$ and
velocity $v$, we
derive conditions for the existence of stimulus--locked waves by
working in the moving frame of the input. We use this to construct
existence tongues in $(v,I_0)$-parameter space whose tips at $I_0 =0$ correspond to the intrinsic
waves of the homogeneous network. We then determine the linear
stability of
stimulus-locked waves within the tongues by constructing the
associated Evans function and numerically calculating its zeros as a
function of network parameters.
We show that, as the input amplitude is reduced, a stimulus-locked wave
within the tongue of an unstable intrinsic wave can undergo a Hopf
bifurcation leading to
the emergence of either a traveling breather or a
traveling pulse emitter.
University of Utah
| Department of Mathematics
|
bressloff@math.utah.edu
Aug 2001.