Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

Chaos

Volumn 13, Issue 1, 2003, Pages 309-318

  Pazó, Diego ^a   Zaks, Michael A ^b   Kurths, Jürgen ^c  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b HUMBOLDT UNIVERSITY   (Germany)

^c UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037357458     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1518430     Document Type: Article

References (24)

1. Ch. Huygens (Hugenii), Horologium Oscillatorium (Apud. F. Muguet, Parisiis, France, 1673); English translation: The Pendulum Clock (Iowa State University Press, Ames, 1986).
2. Ch. Huygens (Hugenii), Horologium Oscillatorium (Apud. F. Muguet, Parisiis, France, 1673); English translation: The Pendulum Clock (Iowa State University Press, Ames, 1986).
3. I. I. Blekhman, Synchronization in Science and Technology (Nauka, Moscow, 1981) (in Russian); (English translation: ASME, New York, 1988).
4. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
5. H. Fujisaka and T. Yamada, "Stability theory of synchronized motion in coupled-oscillator systems," Prog. Theor. Phys. 69, 32-47 (1983).
6. A. S. Pikovsky, "On the interaction of strange attractors," Z. Phys. B: Condens. Matter 55, 149-155 (1984).
7. L. M. Pecora and T. L. Caroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
8. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, "Generalized synchronization of chaos in directionally coupled chaotic systems," Phys. Rev. E 51, 980-994 (1995).
9. L. Kocarev and U. Parlitz,. "Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems," Phys. Rev. Lett. 76, 1816-1819 (1996).
10. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "Phase synchronization of chaotic oscillators," Phys. Rev. Lett. 76, 1804-1807 (1996).
11. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196 (1997).
12. A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, "Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization," Phys. Rev. Lett. 79, 47-50 (1997).
13. A. Pikovsky, M. Zaks, M. Rosenblum, G. Osipov. and J. Kurths, "Phase synchronization of chaotic oscillators in terms of periodic orbits," Chaos 7, 680-687 (1997).
14. K. J. Lee, Y. Kwak, and T. K. Lim, "Phase jumps near a phase synchronization transition in systems of two coupled chaotic oscillators," Phys. Rev. Lett. 81, 321-324 (1998).
15. S. Boccaletti and D. L. Valladares, "Characterization of intermittent lag synchronization," Phys. Rev. E 62, 7497-7500 (2000).
16. M. Zhan, G. W. Wei, and C.-H. Lai, "Transition from intermittency to periodicity in lag synchronization in coupled Rossler oscillators," Phys. Rev. E 65, 036202 (2002).
17. P. Cvitanović, "Periodic orbits as the skeleton of classical and quantum chaos," Physica D 51, 138-151 (1991).
18. N. F. Rulkov, "Images of synchronized chaos: experiments with circuits," Chaos 6, 262-279 (1996).
19. O. V. Sosnovtseva, A. G. Balanov, T. E. Vadivasova, V. V. Astakhov, and E. Mosekilde, "Loss of lag synchronization in coupled chaotic systems," Phys. Rev. E 60, 6560-6565 (1999).
20. P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as a Dynamical System (Birkhäuser, Basel, 1980).
21. B. R. Hunt and E. Ott, "Optimal periodic orbits of chaotic systems," Phys. Rev. Lett. 76, 2254-2257 (1996).
22. P. Schmeicher and F. K. Diakonos, "General approach to the localization of unstable periodic orbits in chaotic dynamical systems," Phys. Rev. E 57, 2739-2746 (1998).
23. E. R. Rosa, E. Ott, and M. H. Hess, "Transition to phase synchronization of chaos," Phys. Rev. Lett. 80, 1642-1645 (1998).
24. E. Barreto and P. So, "Mechanisms for the development of unstable dimension variability and the breakdown of shadowing in coupled chaotic systems." Phys. Rev. Lett. 85, 2490-2493 (2000).