Ionization waves: Hopf-Hopf bifurcations and nonlinear wave-wave interactions

Physics of Plasmas

Volumn 11, Issue 9, 2004, Pages 4446-4455

  Bruhn, B ^a  

^a Institut fur Physik   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; COUPLED CIRCUITS; GLOW DISCHARGES; HYDRODYNAMICS; IONIZATION; NEON; PARAMETER ESTIMATION; STABILITY; TURBULENCE; WAVES;

HOPF-HOPF BIFURCATION; IONIZATION WAVES; NEON GLOW DISCHARGE; WAVE-WAVE INTERACTION;

DYNAMICS;

EID: 5444273533     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1782551     Document Type: Article

References (38)

1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
2. K. Ohe and M. Hashimoto, J. Appl. Phys. 58, 2975 (1985).
3. C. Wilke, R. W. Leven, and H. Deutsch, Phys. Lett. A 136, 114 (1989).
4. J.-B. Du, C.-H. Chiang, and I. Lin, Phys. Rev. E 54, 1829 (1996).
5. T. Mausbach, T. Klinger, A. Piel, A. Atipo,.T. Pierre, and G. Bonhomme, Phys. Lett. A 228, 373 (1997).
6. M. Novak, Czech. J. Phys. 10, 954 (1960).
7. S. Pfau and A. Rutscher, Beitr. Plasmaphys. 4, 11 (1969).
8. A. Dinklage, B. Bruhn, H. Deutsch, P. Jonas, B.-P. Koch, and C. Wilke, Phys. Plasmas 5, 833 (1998).
9. A. Dinklage and C. Wilke, Phys. Lett. A 277, 331 (2000).
10. A. Atipo, G. Bonhomme, and T. Pierre, Eur. Phys. J. D 19, 79 (2002).
11. R. N. Franklin, Plasma Phenomena in Gas Discharges (Clarendon, Oxford, 1976).
12. P. S. Landa, N. A. Miskinova, and Yu. V. Ponemarev, Sov. Phys. Usp. 23, 813 (1980).
13. B. P. Koch, N. Goepp, and B. Bruhn, Phys. Rev. E 56, 2118 (1997); 62, 1455 (2000).
14. B. P. Koch, N. Goepp, and B. Bruhn, Phys. Rev. E 56, 2118 (1997); 62, 1455 (2000).
15. B. Bruhn, B.-P. Koch, and N. Goepp, Physica D 115, 353 (1998).
16. J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, New York, 1983).
17. H. van Saarloos and P. C. Hohenberg, Physica D 56, 303 (1992).
18. I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
19. N. Bekki, J. Phys. Soc. Jpn. 50, 659 (1981).
20. M. Rottmann and K. H. Spatschek, J. Plasma Phys. 60, 215 (1998).
21. B. Bruhn, B. P. Koch, and P. Jonas, Phys. Rev. E 58, 3793 (1998).
22. A. Garscadden, in Ionization Waves in Glow Discharges, Gaseous electronics Vol. I, edited by M. N. Hirsch and H. J. Oskam (Academic, New York, 1978).
23. Y. A. Kusnetsov, Elements of Applied Bifurcation Theory (Springer, Berlin, 1981).
24. B. Bruhn and B.-P. Koch, Phys. Rev. E 61, 3078 (2000).
25. S. Pfau, A. Rutscher, and K. Wojaczek, Beitr. Plasmaphys. 9, 333 (1969).
26. J. Carr, Applications of Centre Manifold Theory (Springer, Berlin, 1981).
27. G. Iooss and M. Adelmeyer, Topics in Bifurcation Theory (World Scientific, Singapore, 1992).
28. A. Dinklage, C. Wilke, G. Bonhomme, and A. Atipo, Phys. Rev. E 62, 7219 (2000).
29. C. Wilke and R. Kozakov (private communication). A paper on this matter is in preparation.
30. H. W. Müller, M. Tveitereid, and S. Trainoff, Phys. Rev. E 48, 263 (1993).
31. G. D. Granzow and H. Riecke, Phys. Rev. Lett. 77, 2451 (1996).
32. L. Oil, Phys. Rev. Lett. 70, 162 (1993).
33. M. San Miguel, Phys. Rev. Lett. 75, 425 (1995).
34. W. Eckhaus, Studies in Non-Linear Stability Theory (Springer, Berlin, 1965).
35. H. Chaté, in Spatio-Temporal Patterns in Nonequilibrium Complex Systems, edited by P. E. Cladis and P. Palffy-Muhoray (Reading, Addison-Wesley, 1995), p. 33.
36. H. Sakaguchi, Phys. Scr. T67, 148 (1996).
37. A. Amengual, E. Hernández-Garcia, R. Montagne, and M. San Miguel, Phys. Rev. Lett. 78, 4379 (1997).
38. L. A. Bunimovich, Physica D 131, 31 (1999).