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2010, 7(2): 421-442. doi: 10.3934/mbe.2010.7.421

Wave fronts in neuronal fields with nonlocal post-synaptic axonal connections and delayed nonlocal feedback connections

Felicia Maria G. Magpantay 1, and  Xingfu Zou 2,

1. 

Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada
2. 

Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7

Received  July 2009 Revised  January 2010 Published  April 2010

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.
Keywords: speed index function, Neuronal networks, integro-differential equation, spatially non-local, travelling wave front., delay, feedback.
Mathematics Subject Classification: 35B25, 35R10, 92B20, 92C2.
Citation: Felicia Maria G. Magpantay, Xingfu Zou. Wave fronts in neuronal fields with nonlocal post-synaptic axonal connections and delayed nonlocal feedback connections. Mathematical Biosciences & Engineering, 2010, 7 (2) : 421-442. doi: 10.3934/mbe.2010.7.421
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