Different Epileptiform Regimes in the Neural Population Modelled by the Generalized Telegraph Equation
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Keywords:
Neural Population, Epileptiform Behavior, Cattaneo Equation, Factorization Procedure, Traveling WavesAbstract
The field-type approach to the neural cortical activities serves as a good alternative to the
ANN-type models. It represents different states of the spiking and bursting neurons as a continuous field
with a certain initial spatial distribution. The evolution of the neural populations is described with the
generalized telegraph partial differential equations. In this paper, we use the Cattaneo generalization of
Fick’s model to describe the evolution of the epileptiform behavior in the small- and middle-scale neural
clusters. We study the factorization procedure for the generalized telegraph equation and investigate the
exact particular solutions to different dynamical regimes, which depend on the separation constant
playing the role of a control parameter in our model. Additionally, we derive the traveling wave solutions
and discuss briefly their properties.
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