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NORMAL BIFURCATION [1 record]

Record 1 1993-06-02

English

Subject field(s)
  • Fluid Mechanics and Hydraulics (Physics)
CONT

The bifurcation to which [this] equation gives rise (...) is called supercritical or normal. The limit cycle is created with a zero amplitude and at the bifurcation point, the system is in a state of marginal stability. This results from the presence of the dissipative term ... whose effect ... counteracts that of the instability. Consequently, the solution does not undergo a sudden transformation at the bifurcation but changes gradually. This is generally the case whenever the nonlinear terms of lowest order are such as to counteract the instability.

French

Domaine(s)
  • Mécanique des fluides et hydraulique (Physique)
CONT

La bifurcation à laquelle donne lieu l'équation [...] est dite surcritique (ou supercritique) ou normale. Le cycle limite naît avec une amplitude nulle et, au point de bifurcation, le système se trouve dans un état de stabilité marginale. Ceci résulte de la présence du terme de dissipation [...] dont l'effet [...] est antagoniste de celui de l'instabilité. Par suite la solution ne subit pas de transformation brutale à la bifurcation, mais se modifie de manière progressive. De façon générale il en est ainsi chaque fois que les termes non-linéaires d'ordre le plus bas s'opposent à l'instabilité.

Spanish

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