The Slow Invariant Manifold of the Lorenz–Krishnamurthy Model
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Jean-Marc Ginoux [1]
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[1] Universite De Toulon Et Du Var
Universite De Toulon Et Du Var
Arrondissement de Toulon, Francia
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 13, Nº 1, 2014, págs. 19-37
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
During this last decades, several attempts to construct slow invariant manifold of the Lorenz–Krishnamurthy five-mode model of slow–fast interactions in the atmosphere have been made by various authors. Unfortunately, as in the case of many two-time scales singularly perturbed dynamical systems the various asymptotic procedures involved for such a construction diverge. So, it seems that till now only the first-order and third-order approximations of this slow manifold have been analytically obtained. While using the Flow Curvature Method we show in this work that one can provide the eighteenth-order approximation of the slow manifold of the generalized Lorenz–Krishnamurthy model and the thirteenth-order approximation of the “conservative” Lorenz–Krishnamurthy model. The invariance of each slow manifold is then established according to Darboux invariance theorem.
