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

被引：0

作者：

Carvalho, Tiago ^{[1
]}

Llibre, Jaume ^{[2
]}

机构：

[1] UNESP, Dept Matemat, Fac Ciencias, Av Eng Luiz Edmundo Carrijo Coube 14-01, BR-17033360 Bauru, SP, Brazil

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 06期

基金：

巴西圣保罗研究基金会;

关键词：

Lorenz system; periodic solution; averaging theory; SLOW MANIFOLD; SYSTEM;

D O I：

10.1142/S0218127417500900

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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)).

引用

页数：6

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