Modelagem de população de neurônios via equações diferenciais parciais

• Autor(a) principal: Souza , Marcos Teixeira de
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/270
• topic: Neurociência computacional; Equações diferenciais parciais; Rede neural; Partial differential equations; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::EQUACOES DIFERENCIAIS PARCIAIS

Neuroscience aims to understand the mechanisms that regulate the nervous system, to fight existing maladier associated with brain functions, to extend the knowledge in human cognitive development, among others. In the present work we study the communication between neurons of a region of the brain with the purpose to construct a mathematical and computationally feasible model that accurately describes how the information is transmitted between neuronal cells. We approached the behavior of neurons through the FiztHugh-Nagumo equations, constructing a discrete model consistent with the continuous model through the strategy of increasing the number of neurons within the considered neural network. Consequently we obtain numerical results characterized by models of differential equations that describe a distribution of an action potential through non-linear equations of the reaction-diffusion-convection type and a convergence study of the discrete model.