Oscillatory and rotary synchronization of chaotic autonomous phase systems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 6 2, 2003, Pages

  Hu, Bambi ^a,b   Osipov, Grigory V ^a,c   Yang, Hong Liu ^a   Kurths, Jürgen ^d  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b University of Houston   (United States)

^c LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

^d UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; DIFFUSION; LYAPUNOV METHODS; MATHEMATICAL MODELS; PHASE LOCKED LOOPS; PHASE SPACE METHODS; SYNCHRONIZATION; TOPOLOGY;

AUTONOMOUS CONTINUOUS TIME PHASE SYSTEM; CHAOTIC AUTONOMOUS PHASE SYSTEM; GENERALIZED CHAOTIC PHASE SYNCHRONIZATION; OSCILLATORY-ROTARY SYNCHRONIZATION; PHASE VARIABLE DIFFUSION; REAL CHAOTIC PHASE SYNCHRONIZATION;

CHAOS THEORY;

EID: 45849155616     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (54)

1. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983)
2. A.S. Pikovsky, Z. Phys. B: Condens. Matter 55, 149 (1984)
3. L.M. Pecora and T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)
4. V.S. Anishchenko, T.E. Vadivasova, D.E. Postnov, and M.A. Safonova, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 633 (1992)
5. B.R. Hunt and E. Ott, Phys. Rev. Lett. 76, 2254 (1996)
6. L.M. Pecora et al., Chaos 7, 520 (1997).
7. V.S. Afraimovich, N.N. Verichev, and M.I. Rabinovich, Radiophys. Quantum Electron. 29, 747 (1986)
8. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995)
9. L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
10. Int. J. Bifurcation Chaos Appl. Sci. Eng. 10 (2000), special focus issue on phase synchronization, edited by J. Kurths.
11. Chaos 7 (1997), special focus issue on chaotic synchronization, edited by L. Pecora.
12. A.S. Pikovsky, M.G. Rosenblum, and J. Kurths, Synchronization-A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
13. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, and C.S. Zhou, Phys. Rep. 366, 1 (2002).
14. A.S. Pikovsky, Sov. J. Commun. Technol. Electron. 30, 85 (1985).
15. E.F. Stone, Phys. Lett. A 163, 367 (1992).
16. M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
17. U. Parlitz, L. Junge, W. Lauterbron, and L. Kocarev, Phys. Rev. E 54, 2115 (1996).
18. A.S. Pikovsky, M.G. Rosenblum, G.V. Osipov, and J. Kurths, Physica D 104, 219 (1997).
19. G.V. Osipov, A.S. Pikovsky, M.G. Rosenblum, and J. Kurths, Phys. Rev. E 55, 2353 (1997).
20. R.C. Elson et al., Phys. Rev. Lett. 81, 5692 (1998)
21. V. Makarenko and R. Llinas, Proc. Natl. Acad. Sci. U.S.A. 95, 15474 (1998)
22. B. Blasius, A. Huppert, and L. Stone, Nature (London) 399, 354 (1999)
23. C. Schäfer, M.G. Rosenblum, J. Kurths, and H.H. Abel, ibid. 392, 239 (1998)
24. P. Tass et al., Phys. Rev. Lett. 81, 3291 (1998)
25. F. Morman, K. Lehnertz, P. David, and Ch.E. Elger, Physica D 144, 358 (2000)
26. C.M. Ticos, E. Rosa, Jr., W.B. Pardo, J.A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000)
27. E. Allaria, F.T. Arechi, A.D. Garbo, and R. Meucci, ibid. 86, 791 (2001)
28. I. Kiss and J. Hudson, Phys. Rev. E 64, 046215 (2001).
29. H.L. Yang, Phys. Rev. E 63, 026213 (2001).
30. G.V. Osipov, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 88, 054102 (2002).
31. G.V. Osipov and J. Kurths, Phys. Rev. E 65, 016216 (2002).
32. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1992).
33. As the phase system we consider the system that has as variables only phase or angle variable and it time derivatives.
34. B/C + ℏ/2erC dφ/dt + I/C sin φ=0, which after some parameter substitutions can be easily reduced to Eq. (1).
35. P. Hadley and M.R. Beasley, Appl. Phys. Lett. 50, 621 (1987).
36. Phase-Locked Loops and Their Applications, edited by W.C. Lindsey and M.K. Simon (IEEE Press, New York, 1978).
37. Note that phase and frequency lockign are not always identical in chaotic systems.
38. A. Pikovsky and P. Grassberger, J. Phys. A 24, 4587 (1991)
39. R. Brown, N.F. Rulkov, and N.B. Tufillaro, Phys. Rev. E 50, 4488 (1994)
40. P. Ashwin, J. Buescu, and I. Stewart, Phys. Lett. A 193, 126 (1994)
41. P. Ashwin, J. Buescu, and I. Stewart, Nonlinearity 9, 703 (1996)
42. N.F. Rulkov and M.M. Sushchik, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 625 (1997).
43. V.V. Matrosov, Tech. Phys. Lett. 22-23, 4 (1996)
44. T. Endo, J. Franklin Inst. B331, 1859 (1994)
45. A. Sato and T. Endo, in Proc. NDES'94, Krakow, Poland, 1994, edited by W. Schwarz and A.C. Davies (unpublished), p. 117
46. A.K. Kozlov and V.D. Shalfeev, in Proc. NDES'95, Dublin, Ireland, 1995, edited by M.P. Kennedy (unpublished), p. 233
47. N. Smith, C. Crowley, and M. Kennedy, in Proc. NDES'96, Seville, Spain, 1996, edited by A. Rodriguez-Vazquez (unpublished), p. 27
48. M.V. Korzinova, V.V. Matrosov, and V.D. Shalfeev, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 963 (1999).
49. V.D. Shalfeev and G.V. Osipov, in Proc. NDES'97, Moscow, Russia, 1997, edited by W. Shakhguildian (unpublished), p. 139.
50. V.D. Shalfeev, V.V. Matrosov Radiophys. Quantum Electron. 41, 1033 (1998).
51. A.S. Pikovsky, G.V. Osipov, M.G. Rosenblum, M.A. Zaks, and J. Kurths, Phys. Rev. Lett. 79, 47 (1997).
52. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, G.V. Osipov, I.Z. Kiss, and J.L. Hudson, Phys. Rev. Lett. 89, 264102 (2002).
53. G. Nash, Phase Locked Loop, Design Fundamentals (Motorolla Inc., Phoenix, AZ, 1994).
54. We consider only 1:1 synchronization.