Symmetry Breaking Hopf Bifurcations in Equations with O(2) Symmetry with Application to the Kuramoto-Sivashinsky Equation

Journal of Computational Physics

Volumn 131, Issue 1, 1997, Pages 181-192

  Amdjadi, F ^a,b   Aston, P J ^a   Plechac P ^c  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b UNIVERSITY OF ZANJAN   (Iran)

^c HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; JACOBIAN MATRICES; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

COMPLEX EIGENVALUES; EIGEN-VALUE; IMAGINARY AXIS; KURAMOTO-SIVASHINSKY EQUATIONS; PHASE CONDITIONS; SPATIO-TEMPORAL; STEADY STATE SOLUTION; SYMMETRY BREAKINGS; TEMPORAL SYMMETRY; TRAVELING WAVE SOLUTION;

HOPF BIFURCATION;

EID: 0000877826     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.5599     Document Type: Article

References (30)

1. F. Amdjadi, 1994, Ph.D thesis, University of Surrey.
2. F. Amdjadi, P. J. Aston, Numerical methods for steady state/Hopf mode interactions, Int. J. Bif. Chaos.
3. Ashwin P., Böhmer K., Mei Z. Math. Comput. 64:1994;649.
4. Aston P. J. Scaling laws and bifurcation. Singularity Theory and Its Applications, Warwick 1989, Part II. 1991;Springer-Verlag, Heidelberg. p. 1-.
5. Aston P. J. SIAM J. Math. Anal. 22:1991;181.
6. Aston P. J., Spence A., Wu W. SIAM J. Appl. Math. 52:1992;792.
7. Aston P. J., Spence A., Wu W. An investigation of the bifurcation from travelling waves to modulated travelling waves. Allgower E., Böhmer K., Golubitsky M. Bifurcation and Symmetry. 1992;35 Birkhäuser, Basel.
8. Bluman G. W., Kumei S. Symmetries and Differential Equations. 1989;Springer-Verlag, New York.
9. Dellnitz M. IMA J. Numer. Anal. 12:1991;429.
10. Dellnitz M., Werner B. J. Comput. Appl. Math. 26:1989;97.
11. Doedel E. J. Congr. Numer. 30:1981;265.
12. Golubitsky M., Stewart I., Schaeffer D. G. Singularities and Groups in Bifurcation Theory, Vol. II. Appl. Math. Sci., 69:1988.
13. Hyman J. M., Nicolaenko B., Zaleski S. Physica D. 23:1986;265.
14. Janovský V., Plecháč P. Numerical applications of equivariant reduction techniques. Allgower E., Böhmer K., Golubitsky M. Bifurcation and Symmetry. 1992;203 (Birkhäuser, Basel.
15. Janovský V., Plecháč P. Local numerical analysis of Hopf bifurcation. SIAM J. Num. Anal. 33:1996;1150.
16. Jepson A. D., Spence A. SIAM J. Math. Anal. 20:1989;39.
17. Kevrekidis I. G., Nicolaenko B., Scovel J. C. SIAM J. Appl. Math. 50:1989;760.
18. Kuramoto Y. Prog. Theor. Phys. Suppl. 64:1978;346.
19. Kuramoto Y. Chemical Oscillations, Waves and Turbulence. 1984;Springer-Verlag, New York.
20. Kuramoto Y. Prog. Theor. Phys. Suppl. 71:1984;1182.
21. Krupa M. SIAM J. Math. Anal. 21:1990;1453.
22. Landsberg A. S., Knobloch E. Phys. Lett. A. 159:1991;17.
23. Landsberg A. S., Knobloch E. Phys. Lett. A. 179:1993;316.
24. Proctor M. R. E., Weiss N. O. Geophys. Astrophys. Fluid Dyn. 70:1992;137.
25. Matthews P. C., Proctor M. R. E., Rucklidge A. M., Weiss N. O. Phys. Lett. A. 183:1993;69.
26. Shlang T., Sivashinsky G. I. J. Phys. 43:1982;459.
27. Sivashinsky G. I. Acta Astronaut. 4:1977;1177.
28. Sivashinsky G. I. Ann. Rev. Fluid Mech. 15:1983;179.
29. Sivashinsky G. I., Michelson D. M. Prog. Theor. Phys. 63:1980;2112.
30. Werner B., Spence A. SIAM J. Numer. Anal. 21:1984;388.