Mathematical modeling of neurons: Hodgkin-Huxley and FitzHugh-Nagumo models

• Grant number: 12/10426-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2012
• End date: July 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Roberto Venegeroles Nascimento
• Grantee: Fernando Henrique Gomes Zucatelli
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

The purpose of this project is to study the main mathematical models that describe the transmission of signals between neurons. We will start by studying the models pioneered by Hodgkin-Huxley (Nobel Prize in Medicine, 1963) and Fitzhugh-Nagumo. We will study their physiological reasons and also compare their main characteristics. These models will be studied by performing extensive numerical simulations and qualitative analyzes using techniques from dynamical systems theory.(AU)