On non-linear dynamics and a periodic control design applied to the potential of membrane action

• Autor(a) principal: Chavarette, F. R.
• Data de Publicação: 2006
• Outros Autores: Peruzzi, N. J., Balthazar, José Manoel [UNESP], Hermini, H. A.
• Tipo de documento: Artigo de conferência
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.4028/www.scientific.net/AMM.5-6.47; http://hdl.handle.net/11449/36249
• topic: action potential; non-linear dynamics; Fitzhugh-Nagumo model; L-F transformation

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).