Drift bifurcations of relative equilibria and transitions of spiral waves

Nonlinearity

Volumn 12, Issue 4, 1999, Pages 741-755

  Ashwin, Peter ^a   Melbourne, Ian ^b   Nicol, Matthew ^c  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b University of Houston   (United States)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033164115     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/4/301     Document Type: Article

References (18)

1. Arnold V I 1971 On matrices depending on parameters Russ. Math. Surv. 26 29-43 Arnold V I 1971 Usp. Mat. Nauk 26 101-14
2. Arnold V I 1971 On matrices depending on parameters Russ. Math. Surv. 26 29-43 Arnold V I 1971 Usp. Mat. Nauk 26 101-14
3. Ashwin P and Melbourne I 1997 Noncompact drift for relative equilibria and relative periodic orbits Nonlinearity 10 595-616
4. Barkley D and Kevrekidis I G 1994 A dynamical systems approach to spiral wave dynamics Chaos 4 1-8
5. Fiedler B, Sandstede B, Scheel A and Wulff C 1996 Bifurcation from relative equilibria of noncompact group actions: skew products, meanders and drifts Doc. Math. 1 479-505
6. Field M J 1980 Equivariant dynamical systems Trans. Am. Math. Soc. 259 185-205
7. Field M J 1991 Local structure for equivariant dynamics Singularity theory and its applications (Lecture Notes in Math. vol 1463) part II ed M Roberts and I Stewart (Berlin: Springer) pp 142-66
8. Galin D M 1982 Versal deformations of linear Hamiltonian systems AMS Transl. 118 1-12 Galin D M 1975 Tr. Sem. Petrovsk. 1 63-74
9. Galin D M 1982 Versal deformations of linear Hamiltonian systems AMS Transl. 118 1-12 Galin D M 1975 Tr. Sem. Petrovsk. 1 63-74
10. Golubitsky M, LeBlanc V G and Melbourne I 1997 Meandering of the spiral tip, an alternative approach J. Nonlin. Sci. 7 557-86
11. Jahnke W and Winfree A T 1991 A survey of spiral-wave behaviors in the Oregonator model Int. J. Bifurcation Chaos 1 45-466
12. Krupa M 1990 Bifurcations of relative equilibria SIAM J. Math. Anal. 21 1453-86
13. Melbourne I 1993 Versal unfoldings of equivariant linear Hamiltonian vector fields Math. Proc. Camb. Phil. Soc. 114 559-73
14. Mikhailov A S and Zykov V S 1991 Kinematical theory of spiral waves in excitable media: comparison with numerical simulations Physica D 52 379-97
15. Patera J, Rousseau C and Schlomiuk D 1982 Versal deformations of elements of real classical Lie algebras J. Phys. A: Math. Gen. 15 1063-86
16. Sandstede B, Scheel A and Wulff C 1997 Dynamics of spiral waves in unbounded domains using center-manifold reductions J. Diff. Eqns 141 122-49
17. Sandstede B, Scheel A and Wulff C 1999 Bifurcation and dynamics of spiral waves J. Nonlin. Sci. 9 to appear
18. Wulff C 1996 Theory of meandering and drifting spiral waves in reaction-diffusion systems Thesis Freie Universität, Berlin