Bifurcação de Hopf generalizada para um sistema planar suave por partes

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

In this work we use the qualitative theory of the di?erential equations to quickly study the Hopf bifurcation for a smooth planar dynamical system under the variation of the control parameter of the system, and a generalized Hopf bifurcation emanated from a corner for piecewise smooth planar dynamical system, about the generation of a branch of periodic orbits bifurcating, varying the control parameter. For this, we define the Liapunov number and the Poincare map. And, through the composition of the Poinacre maps, we build a Return map and we study its fixed points. We illustrate those bifurcation phenomena by a analysis of the smooth and piece- wise smooth models for a vocal fold oscillation in process of the voice production (phona- tion). The main part of this dissertation is based on [28, 30, 35, 37, 40].

ASSUNTO(S)

periodic solution aplicação de poincaré phonation model return map modelo da fonação solução periódica matematica aplicada hopf bifurcation poincare map bifurcação de hopf aplicação retorno

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