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Updated: Jun 13, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
Wave fronts in neuronal fields with nonlocal post-synaptic axonal connections and delayed nonlocal feedback
Felicia Maria G Magpantay1, Xingfu Zou
1Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada. magpantay@math.mcgill.ca
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.
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