Lorenz bifurcation: Instabilities in quasireversible systems

Physical Review Letters

Volumn 83, Issue 19, 1999, Pages 3820-3823

  Clerc, M ^a   Coullet, P ^a,c   Tirapegui, E ^b  

^a INSTITUT NON LINÉAIRE DE NICE   (France)

^b DEPARTAMENTO DE FÍSICA   (Chile)

^c INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000929965     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.83.3820     Document Type: Article

References (20)

1. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
2. M. Cross and P. Hohenberg, Rev. Mod. Phys., 65, 851 (1993).
3. R. Devaney, Trans. Am. Math. Soc., 218, 89 (1976).
4. V. Arnold, Chapitres Supplémentaires de la Théorie des Équations Différentielles Ordinaires (MIR, Moscow, 1984).
5. Y. Rocard, L'instabilité en Mécanique (Masson, Paris, 1954).
6. A. Newell and J. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, CA, 1992).
7. C. Sparow, The Lorenz Equations: Bifurcation, Chaos, and Strange Attractor (Springer, New York, 1982).
8. M. Clerc, P. Coullet, J. M. Gilli, E. Tirapegui, and N. Vandenberghe, Des Phénomènes Critiques au Chaos P. Manneville (CEA., Direction des Sciences de la Matiere, Saclay,1998).
9. E. Lorenz, J. Atmos. Sci., 20, 130 (1963).
10. C. Elphick, E. Tirapegui, M. Brachet, P. Coullet, and G. Iooss, Physica (Amsterdam), 29D, 95 (1987).
11. G. Iooss and M. C. Peroueme, J. Differ. Equ., 102, 62 (1993).
12. J. D. Gibbon and M. McGuinness, Phys. Lett., 77A, 295 (1980).
13. J. D. Gibbon, M. McGuinness Proc. R. Soc. London A, 377, 185 (1981).
14. J. D. Gibbon, M. McGuinness Physica (Amsterdam), 7D, 126 (1983).
15. A. C. Fowler, J. D. Gibbon, and M. McGuinness, Physica (Amsterdam), 4D, 139 (1982).
16. H. Haken, Phys. Lett., 53A, 77 (1969).
17. J. Pedlosky, J. Atmos. Sci., 28, 587 (1971).
18. J. Atmos. Sci.J. Pedlosky 29, 680 (1972).
19. B. Malomed and A. Nepomnyashchy, Phys. Rev. A, 42, 6238 (1990).
20. M. Zaks, B. Malomed, and A. Nepomnyashchy, Phys. Scr., 76, 143 (1996).