We consider a neuronal network model with both axonal connections (in the form of
synaptic coupling) and delayed non-local feedback connections. The kernel in the
feedback channel is assumed to be a standard non-local one, while for
the kernel in the synaptic coupling, four types are considered.
The main concern is the existence of travelling wave front. By employing
the speed index function, we are able to obtain the existence of a travelling wave
front for each of these four types within certain range of model parameters.
We are also able to describe how the feedback coupling strength and
the magnitude of the delay affect the wave speed. Some particular kernel functions
for these four cases are chosen to numerically demonstrate the
theoretical results.
Citation: Felicia Maria G. Magpantay, Xingfu Zou. Wave fronts in neuronal fields with nonlocalpost-synaptic axonal connections and delayed nonlocal feedbackconnections[J]. Mathematical Biosciences and Engineering, 2010, 7(2): 421-442. doi: 10.3934/mbe.2010.7.421
Abstract
We consider a neuronal network model with both axonal connections (in the form of
synaptic coupling) and delayed non-local feedback connections. The kernel in the
feedback channel is assumed to be a standard non-local one, while for
the kernel in the synaptic coupling, four types are considered.
The main concern is the existence of travelling wave front. By employing
the speed index function, we are able to obtain the existence of a travelling wave
front for each of these four types within certain range of model parameters.
We are also able to describe how the feedback coupling strength and
the magnitude of the delay affect the wave speed. Some particular kernel functions
for these four cases are chosen to numerically demonstrate the
theoretical results.