Scaling of Lyapunov exponents of coupled chaotic systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 1, 2000, Pages 332-341

  Zillmer, Rüdiger ^a   Ahlers, Volker ^a   Pikovsky, Arkady ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

ANALYTICAL RESULTS; COUPLED CHAOTIC SYSTEM; COUPLING SENSITIVITY; LARGEST LYAPUNOV EXPONENT; LOGARITHMIC SINGULARITY; LYAPUNOV EXPONENT; SCALING RELATIONS; STATISTICAL THEORY;

CONTINUOUS TIME SYSTEMS;

EID: 4243263219     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.332     Document Type: Article

References (29)

1. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983).
2. T. Yamada and H. Fujisaka, Prog. Theor. Phys. 70, 1240 (1983).
3. A.S. Pikovsky, Z. Phys. B: Condens. Matter 55, 149 (1984).
4. H. Daido, Prog. Theor. Phys. 72, 853 (1984).
5. H. Daido, Prog. Theor. Phys. Suppl. 79, 75 (1984).
6. H. Daido, Phys. Lett. 110A, 5 (1985).
7. H. Daido, Phys. Lett. A 121, 60 (1987).
8. R. Livi, A. Politi, and S. Ruffo, J. Phys. A 25, 4813 (1992).
9. A. Torcini, R. Livi, A. Politi, and S. Ruffo, Phys. Rev. Lett. 78, 1391 (1997).
10. F. Cecconi and A. Politi, e-print chao-dyn/9901014.
11. H. Fujisaka, H. Ishii, M. Inoue, and T. Yamada, Prog. Theor. Phys. 76, 1198 (1986).
12. H. Z. Risken, The Fokker–Planck Equation (Springer, Berlin, 1989).
13. A. Crisanti, G. Paladin, and A. Vulpiani, Products of Random Matrices in Statistical Physics (Springer, Berlin, 1993).
14. L.A. Bunimovich and Y.G. Sinai, Nonlinearity 1, 491 (1988).
15. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, (GPO, Washington, D.C., 1964).
16. K. Furutsu, J. Res. Natl. Bur. Stand., Sect. D 67, 303 (1963).
17. E. A. Novikov, Zh. Éksp. Teor. Fiz. 47, 1919 (1964) [Sov. Phys. JETP 20, 1290 (1965)].
18. A. Becker and L. Kramer, Phys. Rev. Lett. 73, 955 (1994).
19. C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1996).
20. K. Kaneko, Physica D 41, 137 (1990).
21. A. Crisanti, M. Falcioni, and A. Vulpiani, Phys. Rev. Lett. 76, 612 (1996).
22. R. Graham and T. Tel, Phys. Rev. A 31, 1109 (1985).
23. R. Zillmer, Diploma thesis, University of Potsdam, 1999.
24. K. Geist, U. Parlitz, and W. Lauterborn, Prog. Theor. Phys. 83, 875 (1991).
25. A. Björck, Linear Algebr. Appl. 197/198, 297 (1994).
26. A. Pikovsky and U. Feudel, Chaos 5, 253 (1995).
27. C. Grebogi, E. Ott, S. Pelikan, and J. A. Yorke, Physica D 13, 261 (1984).
28. G. Keller, Fundam. Math. 151, 139 (1996).
29. K. Ikeda and K. Matsumoto, Physica D 29, 223 (1987).