On non-linear dynamics and a periodic control design applied to the potential of membrane action
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Data
2006-01-01
Autores
Chavarette, F. R.
Peruzzi, N. J.
Balthazar, José Manoel [UNESP]
Hermini, H. A.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Trans Tech Publications Ltd
Resumo
The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).
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Palavras-chave
action potential, non-linear dynamics, Fitzhugh-Nagumo model, L-F transformation
Como citar
Modern Practice In Stress and Vibration Analysis Vi, Proceedings. Stafa-zurich: Trans Tech Publications Ltd, v. 5-6, p. 47-54, 2006.