Dinamica e controle não lineares de um sistema neuronal ideal e nã-ideal / No-linear dynamics and control of an ideal and non-ideal neural system

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

In this work it is studied the plasmatic membrane behavior through an electric circuit. The electric model was developed by Hodgkin and Huxley at 1952 and it treats of the variation of the amount of time related with the potassium and sodium conductance s in the squid axon, this model has served as an archetype for mannering mathematical model of eletrophysiology of biological membranes. Hodgkin and Huxley developed differential equations for the propagation of electric signals, and later they had been modified to describe the behavior of neurons in other animals and for other excitable types of as pancreatic cells, cardio paths and staple fibres of Purkinje. Thus the dynamics of the Hodgkin-Huxley model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods that can be applied to more complex models. Recently, a chaotic irregular movement of the potential of action of the membrane was observes through several techniques of control with the objective to stabilize the variation of this potential. This Phd dissertation deals with an analysis of the nonlinear dynamics in the Hodgkin-Huxley mathematical model, namely, the existence of quasi-periodic solutions in the model with its original parameters, and still we present modifications in the system to demonstrate the non-ideal dynamics behavior, that is when one consider the interaction between the energy source and the dynamical system and we developed an optimal linear control design for the action potential of membrane. They had been disclosed the conditions that allow using a controllinear feedback for non-linear system

ASSUNTO(S)

modelos matematicos dynamics mathematical models dinamica eletrofisiologia electrophysiology

ACESSO AO ARTIGO

Documentos Relacionados