Artigo
Switching-off in a minimal time a fitzhugh-nagumo system
Registro en:
International Journal of Applied Mathematics, v. 24, n. 1, p. 55-64, 2011.
1311-1728
9728054402919622
8544475466862991
3916521784535081
Autor
Damasceno, Berenice
Barbanti, Luciano
Chavanete, F. R.
Balthazar, José Manoel [UNESP]
Resumen
This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process. Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Estatística, Matemática Aplicada e Computacional, Instituto de Geociências e Ciências Exatas de Rio Claro, Rio Claro, Avenida 24A. 1515., Bela Vista, CEP 13506-700, SP, Brasil Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Estatística, Matemática Aplicada e Computacional, Instituto de Geociências e Ciências Exatas de Rio Claro, Rio Claro, Avenida 24A. 1515., Bela Vista, CEP 13506-700, SP, Brasil