The Role of Time Delay in the Fitzhugh-Nagumo Equations: The Impact of Alcohol on Neuron Firing
Repeated and frequent alcohol use can have serious repercussions on the nervous system, particularly the brain. Here, we focus on the nerve cell (neuron), the fundamental component of the brain. In 1952, Hodgkin and Huxley received the Nobel Prize in Physiology and Medicine for their research on neuron dynamics (firing) with the help of a mathematical model. Our research begins with the assumption that alcohol impairs neuron dynamics. Hence, we begin with the Hodgkin and Huxley model but its complexity moved us to the Fitzhugh-Nagumo equations, a caricature of the Hodgkin and Huxley model. The Fitzhugh-Nagumo equations include only two variables, the membrane potential and the restoring force. In our research, we assumed that alcohol delays the effect of the restoring force and changes the normal state of the system. We analyzed the dynamics of the Fitzhugh-Nagumo equations with and without delay using computer simulations, the qualitative theory of dynamical systems, and bifurcation theory. Alternative hypotheses are discussed in the conclusions.
Romel S. Franca, University of Florida
Ivy E. Prendergast, Queens College, CUNY
Eva-Shirley Sanchez, Rutgers University
Marco A. Sánchez, California State Polytechnic University, Pomona
Fiana Berezovsky, Georgia Institute of Technology
Stephen Wirkus, California State Polytechnic University, Pomona