Nature of the phase-flip transition in the synchronized approach to amplitude death

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

Volumn 82, Issue 4, 2010, Pages

  Karnatak, Rajat ^a   Punetha, Nirmal ^a   Prasad, Awadhesh ^b   Ramaswamy, Ram ^a  

^a JAWAHARLAL NEHRU UNIVERSITY   (India)

^b UNIVERSITY OF DELHI   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ABRUPT CHANGE; AMPLITUDE DEATH; ANTIPHASE; AVOIDED CROSSINGS; EIGENVALUES; EIGENVECTORS; FIXED POINTS; IMAGINARY PARTS; IN-PHASE; JACOBIANS; LIMIT-CYCLE OSCILLATORS; LYAPUNOV EXPONENT; ORDER PARAMETER;

EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS; OSCILLATORS (ELECTRONIC); SYNCHRONIZATION;

PHASE TRANSITIONS;

EID: 78651292736     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.046219     Document Type: Article

References (27)

1. C. Huygens, Horoloquium Oscilatorium (Parisiis, Paris, 1673).
2. M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, Proc. R. Soc. London 458, 563 (2002). 10.1098/rspa.2001.0888
3. K. Bar-Eli, Physica 14D, 242 (1985). 10.1016/0167-2789(85)90182-4
4. R. E. Mirollo and S. H. Strogatz, J. Stat. Phys. 60, 245 (1990) 10.1007/BF01013676
5. G. B. Ermentrout, Physica 41D, 219 (1990). 10.1016/0167-2789(90)90124-8
6. S. H. Strogatz, Nature (London) 394, 316 (1998). 10.1038/28488
7. D. G. Aronson, G. B. Ermentrout, and N. Koppel, Physica 41D, 403 (1990). 10.1016/0167-2789(90)90007-C
8. A. Prasad, Phys. Rev. E 72, 056204 (2005). 10.1103/PhysRevE.72.056204
9. R. Karnatak, R. Ramaswamy, and A. Prasad, Phys. Rev. E 76, 035201 (R) (2007). 10.1103/PhysRevE.76.035201
10. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985). 10.1103/RevModPhys.57.617
11. J. Von Neumann and E. Wigner, Phys. Z. 30, 467 (1929).
12. E. Teller, J. Phys. Chem. 41, 109 (1937). 10.1021/j150379a010
13. V. Ahlers, R. Zillmer, and A. Pikovsky, Phys. Rev. E 63, 036213 (2001). 10.1103/PhysRevE.63.036213
14. H. G. Schuster and P. Wagner, Prog. Theor. Phys. 81, 939 (1989). 10.1143/PTP.81.939
15. E. Niebur, H. G. Schuster, and D. M. Kammen, Phys. Rev. Lett. 67, 2753 (1991). 10.1103/PhysRevLett.67.2753
16. Y. Nakamura, F. Tominaga, and T. Munakata, Phys. Rev. E 49, 4849 (1994). 10.1103/PhysRevE.49.4849
17. - can be stabilized.
18. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. 80, 5109 (1998). 10.1103/PhysRevLett.80.5109
19. D. V. R. Reddy, A. Sen, and G. L. Johnston, Physica 129D, 15 (1999). 10.1016/S0167-2789(99)00004-4
20. 2, at the crossing the frequency of oscillations changes abruptly.
21. F. Ginelli, P. Poggi, A. Turchi, H. Chate, R. Livi, and A. Politi, Phys. Rev. Lett. 99, 130601 (2007). 10.1103/PhysRevLett.99.130601
22. I. Goldhirsch, P.-L. Sulem, and S. A. Orszag, Physica 27D, 311 (1987). 10.1016/0167-2789(87)90034-0
23. J. D. Farmer, Physica 4D, 366 (1982). 10.1016/0167-2789(82)90042-2
24. S. V. Ershov and A. B. Potapov, Physica 118D, 167 (1998). 10.1016/S0167-2789(98)00013-X
25. If D and d are the dimensions of the coupled system and the individual subsystems (D = 2 d), note that the N D dimensional vectors e i (τ) have the property, (a) e j i = e j + d i, for i = 1, 2 before transition and for i = 3, 4 after the transition and, (b) e j i = - e j + d i, for i = 3, 4 before transition and for i = 1, 2 after the transition. where j = k + (n - 1) D, n = 1, 2,... N and k = 1, 2,... d. For our case, D = 4 and d = 2.
26. N. Punetha and R. Ramaswamy (unpublished).
27. A. Prasad, J. Kurths, S. K. Dana and R. Ramaswamy, Phys. Rev. E 74, 035204 (R) (2006). 10.1103/PhysRevE.74.035204