Akademik Veri Yönetim Sistemi
International Journal of Advanced Natural Sciences and Engineering Researches, sa.8, ss.394-398, 2024 (Hakemli Dergi)
Abstract – 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.
Keywords – Neural Population, Epileptiform Behavior, Cattaneo Equation, Factorization Procedure, Traveling Waves.
This work was supported by the Abdullah Gül University Foundation, Project “Feedback control of epileptiform behavior in the mathematical models of neuron clusters”.