Phase synchronizations: Transitions from high-to low-dimensional tori through chaos

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 10, 2000, Pages 2399-2414

  Hu, Bambi ^a,b   Zheng, Zhigang ^a,c  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b University of Houston   (United States)

^c BEIJING NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034560539     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400001535     Document Type: Article

References (57)

1. Acebron, J. A., Bonilla, L. L., Leo, S. D. & Spigler, R. [1998] "Breaking the symmetry in bimodal frequency distributions of globally coupled oscillators," Phys. Rev. E57(5), 5287-5290.
2. Acebron, J. A. & Spigler, R. [1998] "Adaptive frequency model for phase-frequency synchronization in large populations of globally coupled nonlinear oscillators," Phys. Rev. Lett. 81(11), 2229-2232.
3. Anonishi, T., Kurata, K. & Okada, M. [1999] "Statistical mechanics of an oscillator associative memory with scattered nature frequencies," Phys. Rev. Lett. 82(13), 2800-2803.
4. Bonilla, L. L., Vicente, C. J. P., Ritort, F. & Soler, J. [1998] "Exactly solvable phase oscillator models with synchronization dynamics," Phys. Rev. Lett. 81(17), 3643-3646.
5. Carr, T. W. & Schwartz, I. B. [1998] "Pn measure of disorder in globally coupled oscillators," Physica D115, 321-340.
6. Cohen, A. H., Holmes, P. J. & Rand, R. [1982] "The nature of the coupling between segmental oscillators of the Lamprey spinal generator for locomotion: A mathematical model," J. Math. Biol. 13, 345-369.
7. Crawford, J. D. [1995] "Scaling and singularities in the entrainment of globally coupled oscillators," Phys. Rev. Lett. 74(21), 4341-4344.
8. Daido, H. [1988] "Lower critical dimension for populations of oscillators with randomly distributed frequencies: A renormalization-group analysis," Phys. Rev. Lett. 61(2), 231-234.
9. Daido, H. [1992] "Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions," Phys. Rev. Lett. 68(7), 1073-1076.
10. Daido, H. [1994] "Generic scaling at the onset of macroscopic mutual entrainment in limit cycle oscillators with uniform all-to-all coupling," Phys. Rev. Lett. 73(5), 760-763.
11. Daido, H. [1996] "Multibranch entrainment and scaling in large populations of coupled oscillators," Phys. Rev. Lett. 77(7), 1406-1409.
12. Ermentrout, G. B. [1985] "The behavior of rings of coupled oscillators," J. Math. Biol. 23, 55-74.
13. Grebogi, C., Ott, E. & Yorke, J. A. [1985] "Attractors on an N-torus: Quasiperiodicity versus chaos," Physica D15, p. 354.
14. Glass, L. & Mackey, M. C. [1988] From Clocks to Chaos, the Rhythm of Life (Princeton University, NJ).
15. Haken, H. [1983] Advanced Synergetics (Springer-Verlag, Berlin).
16. Hao, B. L. [1989] Elementary Symbolic Dynamics and Chaos in Dissipative Systems (World Scientific, Singapore).
17. Hong, H., Choi, M. Y., Yi, J. & Soh, K. S. [1999] "Inertia effects on periodic synchronization in a system of coupled oscillators," Phys. Rev. E59(1), 353-363.
18. Hu, G., Yang, J. Z., Ma, W. Q. & Xiao, J. H. [1998] "Hopf bifurcation from chaos and generalized winding numbers of critical modes," Phys. Rev. Lett. 81(24), 5314-5317.
19. Hu, B., Zheng, Z. & Hu, G. [1999a] "Phase synchronization: Dynamical manifestation," unpublished.
20. Hu, B., Zheng, Z. & Hu, G. [1999b] "Phase synchronization in coupled chaotic oscillators: A dynamical analysis," unpublished.
21. Hugenii, G. [1673] Horoloquim Oscilatorium (Parisiis, France).
22. Ichimaru, S. [1980] Basic Principles of Plasma Physics: A Statistical Approach (Addison-Wesley, MA).
23. Kopell, N. & Ermentrout, G. B. [1986] "Symmetry and phaselocking in chains of weakly coupled oscillators," Commun. Pure Appl. Math. 39, 623-660.
24. Kuramoto, Y. [1984] Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin).
25. Lee, K. J., Kwak, Y. & Lim, T. K. [1998] "Phase jumps near a phase synchronization transition in systems of two coupled chaotic oscillators," Phys. Rev. Lett. 81(2), 321-324.
26. Matthews, P. C. & Strogatz, S. H. [1990] "Phase diagram for the collective behavior of limit-cycle oscillators," Phys. Rev. Lett. 65(14), 1701-1704.
27. Neiman, A., Pel, X., Russell, D., Wojtenek, W., Wilkens, L., Moss, F., Braun, H. A., Huber, M. T. & Voigt, K. [1999] "Synchronization of the noisy electrosensitive cells in the paddlefish," Phys. Rev. Lett. 82(3), 660-663.
28. Omata, S., Yamaguchi, Y. & Shimizu, H. [1988] "Entrainment among coupled limit cycle oscillators with frustration," Physica D31, 397-408.
29. Osipov, G. V., Pikovsky, A. S., Rosenblum, M. G. & Kurths, J. [1997] "Phase synchronization effect in alattice of nonidentical Rössler oscillators," Phys. Rev. 55(3), 2353-2361.
30. Parlitz, U., Junge, L., Lauterborn, W. & Kocarev, L. [1996] "Experimental observation of phase synchronization," Phys. Rev. E54(2), 2115-2117.
31. Pecora, L. M. & Carroll, T. L. [1990] "Synchronization in chaotic systems," Phys. Rev. Lett. 64(6), 821-824.
32. Pikovsky, A. S., Rosenblum, M. G. & Kurths, J. [1997a] "Synchronization in globally coupled chaotic oscillators," Europhys. Lett. 34(3), 165-170.
33. Pikovsky, A. S., Rosenblum, M. G., Osipov, G. V. & Kurths, J. [1997b] "Phase synchronization of chaotic oscillators by external driving," Physica D104, 219-238.
34. Pikovsky, A. S., Osipov, G. V., Rosenblum, M. G., Zaks, M. & Kurths, J. [1997c] "Attractor-repeller-collision and eyelet intermittency at the transition to phase synchronization," Phys. Rev. Lett. 79(1), 47-50.
35. Ritort, F. [1998] "Solvable dynamics in a system of interacting random tops," Phys. Rev. Lett. 80(1), 6-9.
36. Rogers, J. L. & Wille, L. T. [1996] "Phase transitions in nonlinear oscillator chains," Phys. Rev. E54(3), R2193-R2196.
37. Rosa, Jr. E., Ott, E. & Hess, M. H. [1998] "Transition to phase synchronization of chaos," Phys. Rev. Lett. 80(8), 1642-1645.
38. Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. [1996] "Phase synchronization of chaotic oscillators," Phys. Rev. Lett. 76(11), 1804-1807.
39. Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. [1997] "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78(22), 4193-4196.
40. Ruelle, D. & Takens, F. [1971] "On the nature of turbulence," Commun. Math. Phys. 20, p. 167.
41. Sakaguchi, H., Shinmoto, S. & Kuramoto, Y. [1987] "Local and global self-entrainments in oscillator lattices," Prog. Theor. Phys. 77(5), 1005-1010.
42. Sakaguchi, H., Shinmoto, S. & Kuramoto, Y. [1988] "Mutual entrainment in oscillator lattices with nonvariational type interaction," Prog. Theor. Phys. 79(5), 1069-1079.
43. Schafer, C., Rosenblum, M. G., Kurths, J. & Abel, H. [1998] "Heartbeat synchronized with ventilation," Nature 392(6673), 239-240.
44. Strogatz, S. H. & Mirollo, R. E. [1988a] "Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies," Physica D31, 143-168.
45. Strogatz, S. H. & Mirollo, R. E. [1988b] "Collective synchronization in lattices of nonlinear oscillators with randomness," J. Phys. A21, L699-L705.
46. Strogatz, S. H., Mirollo, R. E. & Matthews, P. C. [1992] "Coupled nonlinear oscillators below the synchronization threshold: Relaxation be generalized Landau damping," Phys. Rev. Lett. 68(18), 2730-2733.
47. Takana, H.-A., Lichtenberg, A. J. & Oishi, S. [1997] "First-order phase transition resulting from finite inertia in coupled oscillator systems," Phys. Rev. Lett. 78(11), 2104-2107.
48. Tang, D. Y. & Heckenberg, N. R. [1997] "Synchronization of mutually coupled chaotic systems," Phys. Rev. E55(6), 6618-6623.
49. Tass, P. [1997] "Phase and frequency shifts in a population of phase oscillators," Phys. Rev. E56(2), 2043-2060.
50. Tass, P., Rosenblum, M. G., Weule, J., Kurths, J., Pikovsky, A., Volkmann, J., Schnitzer, A. & Freund, H. J. [1998] "Detection of m : n phase locking from noisy data: Application to magnetoencephalography," Phys. Rev. Lett. 81(15), 3291-3294.
51. Wiesenfeld, K. & Hadley, P. [1989] "Attractor crowding in oscillatory arrays," Phys. Rev. Lett. 62(12), 1335-1338.
52. Wiesenfeld, K., Colet, P. & Strogatz, S. H. [1996] "Synchronization transitions in a disordered Josephson series array," Phys. Rev. Lett. 76(3), 404-407.
53. Winfree, A. T. [1990] Geometry of Biological Time (Springer-Verlag, NY).
54. Yalcmkaya, T. & Lai, Y. C. [1997] "Phase characterization of chaos," Phys. Rev. Lett. 79(20), 3885-3888.
55. Young, M. K. S. & Strogatz, S. H. [1999] "Time delay in the Kuramoto model of coupled oscillators," Phys. Rev. Lett. 82(3), 648-651.
56. Zheng, Z., Hu, G. & Hu, B. [1998] "Phase slips and phase synchronization of coupled oscillators," Phys. Rev. Lett. 81(24), 5318-5321.
57. Zheng, Z., Hu, B. & Hu, G. [2000] "Collective phase slips and phase synchronizations in coupled oscillator systems," Phys. Rev. E62, 402-408.