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Article Dans Une Revue Qualitative Theory of Dynamical Systems Année : 2014

The Slow Invariant Manifold of the Lorenz–Krishnamurthy Model

Résumé

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.
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Dates et versions

hal-01856954 , version 1 (13-08-2018)

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Jean-Marc Ginoux. The Slow Invariant Manifold of the Lorenz–Krishnamurthy Model. Qualitative Theory of Dynamical Systems, 2014, 13 (1), pp.19 - 37. ⟨10.1007/s12346-013-0104-6⟩. ⟨hal-01856954⟩
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