论文信息 - New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High r in the Lorenz Equations

New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High r in the Lorenz Equations

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.

Jianming Zhang | Jibin Li

[1] P. Olver. Applications of lie groups to differential equations , 1986 .

[2] P. Sachdev. Nonlinear Ordinary Differential Equations and Their Applications , 1990 .

[3] C. Sparrow. The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[4] K. Robbins,et al. Periodic solutions and bifurcation structure at high R in the Lorenz model , 1979 .

[5] K. Robbins. A moment equation description of magnetic reversals in the earth. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[6] Vladimir Igorevich Arnold,et al. Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[7] Philip Holmes,et al. Periodic orbits in slowly varying oscillators , 1987 .

[8] Steve Smale,et al. Dynamics retrospective: great problems, attempts that failed , 1991 .

[9] R. T. Sharp,et al. Invariants of real low dimension Lie algebras , 1976 .