Systematic derivation of amplitude equations and normal forms for dynamical systems

Chaos

Volumn 8, Issue 4, 1998, Pages 834-852

  Ipsen, M ^a   Hynne, F ^b   Sorensen P G ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001221261     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166370     Document Type: Article

References (35)

1. M. Ipsen, Ph.D. thesis, University of Copenhagen, Department of Chemistry, 1997.
2. M. Ipsen, F. Hynne, and P. G. Sørensen, Int. J. Bifurcation Chaos 7, 1539 (1997).
3. A. C. Newell, Lect. Appl. Math 15, 157 (1974).
4. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
5. A. C. Newell and J. V. Moloney, Non-linear Optics (Addison-Wesley, California, 1992).
6. G. Nicolis, Introduction to Nonlinear Science (Cambridge University Press, Cambridge, England, 1995).
7. D. Bruno, Local Methods in Nonlinear Differential Equations, Springer Series in Soviet Mathematics (Springer Verlag, New York, 1989).
8. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory (Springer-Verlag, New York, 1995).
9. J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
10. P. H. Coullet and E. A. Spiegel, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 43, 776 (1983).
11. C. Elphick et al., Physica D 29, 95 (1987).
12. Golubitsky, I. Stewart, and P. G. Schaeffer, Singularities and Groups in Bifurcation Theory (Springer-Verlag, New York, 1988), Vol. 2.
13. J. D. Crawford, Rev. Mod. Phys. 63, 991 (1991).
14. G. Iooss and D. D. Joseph, Elementary Stability and Bifurcation Theory, 2nd ed. (Springer-Verlag, New York, 1990).
15. B. D. Hassard, N. D. Kazarinoff, and Y.-H. Wan, Theory and Applications of Hopf Bifurcation, No. 41 in London Mathematical Society Lecture Note Series (Cambridge University Press, Cambridge, England, 1981).
16. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer-Verlag, New York, 1983).
17. D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems (Cambridge University Press, Cambridge, 1990).
18. G. H. Golub and C. F. V. Loan, Matrix Computations (The Johns Hopkins University Press, Baltimore, 1996), 3rd ed.
19. L. D. Landau, C. R. Acad. Sci. URSS 44, 311 (1944).
20. J. T. Stuart, J. Fluid Mech. 9, 353 (1960).
21. T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, Belin, 1966).
22. F. Hynne, P. G. Sørensen, and K. Nielsen, J. Chem. Phys. 92, 1747 (1990).
23. F. Hynne and P. G. Sørensen, Phys. Rev. E 48, 4106 (1993).
24. S. Wolfram, The Mathematica Book (Cambridge University Press, Cambridge, UK, 1996), 3rd ed.
25. M. B. Monagan et al., Maple V Programming Guide (Springer-Verlag, New York, 1996).
26. I. Schreiber, CONT - A Program for Construction of Parameter Dependence of Stationary or Periodic Solutions of Ordinary Differential or Difference Equations (Department of Chemical Engineering, Prague Institute of Chemical Technology, 1995).
27. M. Marek and I. Schreiber, Chaotic Behavior of Deterministic Dissipative Systems (Academia, Prague, 1991).
28. E. J. Doedel et al., AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont) (1997).
29. M. Kubíček and M. Marek, Computational Methods in Bifurcation Theory and Dissipative Structures (Springer-Verlag, New York, 1983).
30. M. Holodniok and M. Kubíček, Math. Comp. Sim. 29, 33 (1987).
31. W.-J. Beyn, in Nonlinear Partial Differential Equations and Dynamical Systems, Vol. 1 of Advances in Numerical Analysis, edited by W. Light (Clarendon, Oxford, 1991), Chap. 5, pp. 175-236.
32. M. Ipsen, F. Hynne, and P. G. Sørensen, to be submitted (unpublished).
33. E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963).
34. P. Gray and S. K. Scott, J. Phys. Chem. 89, 22 (1985).
35. M. Hénon, Commun. Math. Phys. 50, 69 (1976).