Improved detection of bifurcations in large nonlinear systems via the continuation of invariant subspaces algorithm

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 8, 2001, Pages 2277-2285

  Friedman, M J ^a  

^a UNIVERSITY OF ALABAMA IN HUNTSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035537569     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401003255     Document Type: Article

References (12)

1. Beyn, W.-J., Kleß, W. & Thümmler, V. [2001] "Continuation of low-dimensional invariant subspaces in dynamical systems of large dimension," in Ergodic Theory Analysis, and Efficient Simulation of Dynamical Systems, ed. Fiedler, B. (Springer), pp. 47-72.
2. Böhmer, K. & Sassmannshausen, N. [1999] "Numerical Liapunov-Schmidt spectral method for k-determined problems," in Computational Methods and Bifurcation Theory with Applications, Computer Methods in Applied Mechanics and Engineering, Vol. 170, pp. 277-312.
3. Chow S.-N., Li, C. & Wang, D. [1994] Normal Forms and Bifurcations of Planar Vector Fields (Cambridge University Press).
4. Demmel, J. [1987] "Three methods for refining estimates of invariant subspaces," Computing 38, 43-57.
5. Demmel, J., Dieci, L. & Friedman, M. J. [2001] "Computing connecting orbits via an improved algorithm for continuing invariant subspaces," Preprint math DS/9812031, LANL E-PRINT: http://xxx.lanl.gov/abs/math. DS/9812031, SIAM J. Sci. Comp. 22, 81-94.
6. Dieci, L. & Friedman, M. J. [2001] "Continuation of invariant subspaces," Numer. Lin. Alg. Appl. 8, 317-327.
7. Doedel, E. J., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Yu. A., Sandstede, B. & Wang, X. J. [1997] AUTO97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont).
8. Fedoseyev, A. I., Friedman, M. J. & Kansa, E. J. [2000a] "Continuation for nonlinear elliptic partial differential equations discretized by the multiquadric method," Int. J. Bifurcation and Chaos 10(2), 481-492.
9. Fedoseyev, A. I., Friedman, M. J. & Kansa, E. J. [2000b] "An improved Multiquadric method for nonlinear elliptic partial differential equations via PDE collocation on the boundary," Comput. Math. Appl., to appear.
10. Govaerts, W. [2000] Numerical Methods for Bifurcations of Dynamical Equilibria (Siam Publications, Philadelphia).
11. Kuznetsov, Yu. A. & Levitin, V. V. [1997] "CONTENT, a multi-platform interactive environment for analyzing dynamical systems," Dynamical Systems Laboratory, CWI, Amsterdam (ftp.cwi.nl/pub/CONTENT).
12. Stewart, G. W. [1973] "Error and perturbation bounds for subspaces associated with certain eigenvalue problems," SIAM Rev. 15(4), 727-764.