On the Periodic Solutions of the Five-Dimensional Lorenz Equation Modeling Coupled Rosby Waves and Gravity Waves

Autor(es)

Carvalho, Tiago ; Llibre, Jaume

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 27, n. 6 JUN 15 2017.
• Citações Web of Science: 0

Resumo

Lorenz studied the coupled Rosby waves and gravity waves using the differential system (U) over dot = -VW + bVZ, (V) over dot = UW -bUZ, (W) over dot = -UV, (X) over dot = -Z, Z over dot = bUV + X. This system has the two first integrals H-1 = U-2 + V-2, H-2 = V-2 + W-2 + X-2 + Z(2). Our main result shows that in each invariant set [H-1 = h(1) > 0] boolean AND [H-2 = h(2) > 0] there are at least four (resp., 2) periodic solutions of the differential system with b not equal 0 and h(2) > h(1) (resp., h(2) < h(1)). (AU)

• Processo FAPESP: 14/02134-7 - Teoria qualitativa e bifurcações de campos de vetores suaves por partes
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular