Resumo

CORTES GARCIA, Christian Camilo. Identification of a Hopf bifurcation with or without parameters. rev. cienc. [online]. 2017, vol.21, n.2, pp.59-82. ISSN 0121-1935.  https://doi.org/10.25100/rc.v21i2.6699.

In this paper, we present the theoretical guidelines that identify the presence of a generic Hopf bifurcation, with or without parameters, through a point or a line of equilibrium points for a continuous dynamic system. With these defined guidelines, the Hopf bifurcation without parameters is analyzed through the study of viscous contours for a system of partial differential equations conformed by a reaction-diffusion term; with initial condition constant to pieces and a line of equilibrium points that presents a pair of complex eigenvalues conjugated with null real part in its linearization as it approaches the origin. Under appropriate conditions, two cases are distinguished for this type of generic Hopf bifurcation without parameters: hyperbolic and elliptical, generic in the sense that it is a controlled bifurcation in a line of equilibrium points.

Palavras-chave : viscous profiles; hyperbolic system of conservation laws; Riemann problem; equilibrium line.

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