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

  • Received: 01 July 2009 Accepted: 29 June 2018 Published: 01 April 2010
  • MSC : 35B25, 35R10, 92B20, 92C20.

  • 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

    Related Papers:

  • 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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