NEW TREATMENT ON BIFURCATIONS OF PERIODIC-SOLUTIONS AND HOMOCLINIC ORBITS AT HIGH-R IN THE LORENZ EQUATIONS

被引：18

作者：

LI, JB ^{[1
]}

ZHANG, JM ^{[1
]}

机构：

[1] GEORGIA INST TECHNOL,CTR DYNAM SYST & NONLINEAR STUDIES,ATLANTA,GA 30332

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1993年 / 53卷 / 04期

关键词：

LORENZ EQUATIONS; SLOWLY VARYING PENDULUM EQUATIONS; MELNIKOV VECTOR; BIFURCATION OF PERIODIC SOLUTIONS; HOMOCLINIC ORBITS;

D O I：

10.1137/0153053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the existence of periodic solutions and homoclinic orbits in the Lorenz equations with high r is rigorously proved. The paper deals with the Lorenz model as a three-dimensional perturbed Hamiltonian system generated by the three-dimensional Lie algebra. By using the method of Melnikov vector, the explicit parametric conditions can be determined.

引用

页码：1059 / 1071

页数：13

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