Fractal dimension for poincaré recurrences as an indicator of synchronized chaotic regimes

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 10, 2000, Pages 2323-2337

  Afraimovich, Valentin S ^a   Lin, Wen Wei ^b   Rulkov, Nikolai F ^c  

^a UNIVERSIDAD AUTÓNOMA DE SAN LUIS POTOSÍ   (Mexico)

^b NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034560159     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400001456     Document Type: Article

References (21)

1. Afraimovich, V. S., Verichev, N. N. & Rabinovich, M. I. [1986] "Stochastic synchronization of oscillations in dissipative systems," Izv. Vys. Uch. Zav. Radiofizika 29, 1050-1060; Radio Phys. Quant. Electron. 29, 747-751.
2. Afraimovich, V. S., Verichev, N. N. & Rabinovich, M. I. [1986] "Stochastic synchronization of oscillations in dissipative systems," Izv. Vys. Uch. Zav. Radiofizika 29, 1050-1060; Radio Phys. Quant. Electron. 29, 747-751.
3. Afraimovich, V. S. & Zaslavsky, G. M. [1995] "Fractal and multifractal properties of exit times and Poincaré recurrences," Phys. Rev. E55, 5418-5426.
4. Afraimovich, V. S. [1997] "Pesin's dimension for Poincaré recurrences," Chaos 1, 12-20.
5. Afraimovich, V. S. & Zaslavsky, G. M. [1998] "Sticky orbits of chaotic Hamiltonian dynamics," Lecture Notes in Physics 511, pp. 59-78.
6. Afraimovich, V. S. [1999] "Poincaré recurrences of coupled subsystems in synchronized regimes," Taiwanese J. Math. 3(2), 139-161.
7. Arnold, V. I, Afraimovich, V. S., Il'yashenko, Yu. S. & Shil'nikov, L. P. [1994] Encyclopedia of Mathemacical Science, NS, Dynamical Systems, Vol. V (Springer Verlag, Berlin, Heidelberg, NY).
8. Bronshteyn, I. U. [1997] "Synchronization of identical dynamical systems," preprint.
9. Fenichel, N. [1971] "Persistence and smoothness of invariant manifolds of flows," Indiana Univ. Math. J. 21, 193-226.
10. Fujisaka, H. & Yamada, T. [1983] "Stability theory of synchronized motion in coupled-oscillator systems," Progress of Theor. Phys. 69, 32-47.
11. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, NY-Heidelberg-Berlin).
12. Hale, J. K. [1997] "Diffusive coupling, dissipation and synchronization," J. Dyn. Diff. Eq. 9, 1-52.
13. Katok, A. & Hasselblatt, B. [1995] "Introduction to the modern theory of dynamical systems," Encyclopedia of Mathematics and its Applications Vol. 54 (Cambridge University Press, London-NY), 802pp.
14. Kocarev, L. & Parlitz, U. [1996] "Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems," Phys. Rev. Lett. 76, 1816-1819.
15. Pecora, L. M. & Carroll, T. L. [1990] "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824.
16. Pecora, L. M., Carrol, T. L., Johnson, G. A., Mar, D. J. & Heagy, J. F. [1997] "Fundamentals of synchronization in chaotic systems, concepts and applications," Chaos 7(4), 520-543.
17. Penne, V., Saussol, B. & Vaienti, S. [1997] "Fractal and statistical characteristics of recurrence times," preprint.
18. Pesin, Ya. B. [1997] Dimension Theory in Dynamical Systems: Contemporary Views and Application (The University of Chicago Press, Chicago and London), 304pp.
19. Pikovsky, A. S., Rosenblum, M. G., Osipov, G. V. & Kurths, J. [1997] "Phase synchronization of chaotic oscillators by external driving," Physica D104, 219-238.
20. Rulkov, N. F., Sushchik, M. M., Tsimring, L. S. & Abarbanel, H. D. I. [1996] "Generalized synchronization of chaos in directionally coupled chaotic systems," Phys. Rev. E51, p. 980.
21. Wu, C. W. & Chua, L. O. [1994] "A unified framework for synchronization and control of dynamical systems," Int. J. Bifurcation and Chaos 2, 979-988.