NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II) BIFURCATION IN INFINITE DIMENSIONS

被引:203
作者
Doedel, Eusebius [1 ]
Keller, Herbert B. [2 ]
Kernevez, Jean Pierre [3 ]
机构
[1] Concordia Univ, Dept Comp Sci, 1455 Blvd Maisonneuve O, Montreal, PQ H3G 1M8, Canada
[2] CALTECH, Pasadena, CA 91125 USA
[3] Univ Technol Compiegne, Math Appl, F-60206 Compiegne, France
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1991年 / 1卷 / 04期
关键词
D O I
10.1142/S0218127491000555
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A number of basic algorithms for the numerical analysis and control of bifurcation phenomena are described. The emphasis is on algorithms based on pseudoarclength continuation for ordinary differential equations. Several illustrative examples computed with the AUTO software package are included. This is Part II of the paper that appeared in the preceding issue [Doedel et al., 1991] and that mainly dealt with algebraic problems.
引用
收藏
页码:745 / 772
页数:28
相关论文
共 19 条
  • [1] Aronson D. G., 1980, DYNAMICS MODELLING R, V44, P161, DOI [DOI 10.1016/13978-0-12-669550-2.50010-5, 10.1016/B978, DOI 10.1016/B978, 10.1016/13978-0-12-669550-2.50010-5]
  • [2] ASCHER U, 1981, ACM T MATH SOFTWARE, V7, P209, DOI 10.1145/355945.355950
  • [3] REFORMULATION OF BOUNDARY-VALUE-PROBLEMS INTO STANDARD FORM
    ASCHER, U
    RUSSELL, RD
    [J]. SIAM REVIEW, 1981, 23 (02) : 238 - 254
  • [4] Beyn W.-J., 1989, NATO ASI SERIES
  • [5] STABILITY AND MULTIPLICITY OF SOLUTIONS TO DISCRETIZATIONS OF NON-LINEAR ORDINARY DIFFERENTIAL-EQUATIONS
    BEYN, WJ
    DOEDEL, E
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1981, 2 (01): : 107 - 120
  • [6] DEBOOR C, 1980, MATH COMPUT, V35, P679, DOI 10.1090/S0025-5718-1980-0572849-1
  • [7] COLLOCATION AT GAUSSIAN POINTS
    DEBOOR, C
    SWARTZ, B
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1973, 10 (04) : 582 - 606
  • [8] Doedel E., 1986, AUTO SOFTWARE CONTIN
  • [9] Doedel E. J., 1981, CONGRESSUS NUMERANTI, V30, P265
  • [10] Doedel E. J., 1980, BIT, V20, P58