Email Alert    RSS

Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (10): 947-950.

• 论文 • 上一篇    下一篇

APPLICATIONS OF THE SIGNS OF MELNIKOV'S FUNCTION

沈家骐   

  1. Shanghai Normal University, Shanghai
  • 收稿日期:1991-10-25 出版日期:1992-10-18 发布日期:1992-10-18
  • 基金资助:

    The project is supported by the National Natural Science Foundation of China

APPLICATIONS OF THE SIGNS OF MELNIKOV'S FUNCTION

Shen Jia-qi   

  1. Shanghai Normal University, Shanghai
  • Received:1991-10-25 Online:1992-10-18 Published:1992-10-18
  • Supported by:

    The project is supported by the National Natural Science Foundation of China

PDF

339

摘要： The existence and stability ol periodic solutions for the two-dimensional system x'= f(x)+εg(x ,a), 0<ε<<1 ,a∈R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.

关键词: Melnikov's function, codimension two bifurcations of flows, bifurcation set

Abstract: The existence and stability ol periodic solutions for the two-dimensional system x'= f(x)+εg(x ,a), 0<ε<<1 ,a∈R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.

Key words: Melnikovs function, codimension two bifurcations of flows, bifurcation set

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals
Total visitors:
Copyright © Applied Mathematics and Mechanics (English Edition)
Address：P. O. Box 122, Shanghai University, 99 Shangda Road, Shanghai 200444, China
E-mail： amm@department.shu.edu.cn
Technical support: Beijing Magtech Co.ltd support@magtech.com.cn