Synchronization of chaotic networks with time-delayed couplings: An analytic study

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

Volumn 83, Issue 4, 2011, Pages

  Englert, A ^a   Heiligenthal, S ^a   Kinzel, W ^a   Kanter, I ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BERNOULLI MAPS; CHAOS SYNCHRONIZATION; CHAOTIC NETWORK; CHAOTIC SYNCHRONIZATION; CHAOTIC TRAJECTORY; COUPLING MATRIX; DELAY TIME; LANG-KOBAYASHI; MULTIPLE DELAYS; SPECTRAL GAP; TENT MAP; TIME SHIFTS; TIME-DELAYED COUPLINGS;

CHAOTIC SYSTEMS; COUPLINGS; LASERS; SEMICONDUCTOR LASERS;

SYNCHRONIZATION;

EID: 79961045601     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.046222     Document Type: Article

References (57)

1. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
2. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00137-0 366, 1 (2002).
3. A. Balanov, N. Janson, D. Postnov, and O. Sosnovtseva, Synchronization: From Simple to Complex (Springer, Berlin, 2009).
4. E. Mosekilde, Y. Maistrenko, and D. Postnov, Chaotic Synchronization: Application to Living Systems (World Scientific, Singapore, 2002).
5. E. Schöll and H. G. Schuster, eds., Handbook of Chaos Control (Wiley-VCH, Weinheim, 2008).
6. C. W. Wu, Synchronization in Complex Networks of Nonlinear Dynamical Systems (World Scientific, Singapore, 2007).
7. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2008.09.002 469, 93 (2008).
8. P. Colet and R. Roy, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.19.002056 19, 2056 (1994).
9. A. Uchida, F. Rogister, J. Garcfa-Ojalvo, and R. Roy, Prog. Opt. OPLEDP 0079-6638 10.1016/S0079-6638(05)48005-1 48, 203 (2005). (Pubitemid 43624199)
10. G. D. VanWiggeren and R. Roy, Science SCIEAS 0036-8075 10.1126/science.279.5354.1198 279, 1198 (1998). (Pubitemid 28164369)
11. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature (London) NATUAS 0028-0836 10.1038/nature04275 437, 343 (2005). (Pubitemid 41643948)
12. F. M. Atay and T. BIyIkoǧlu, Phys. Rev. E NATUAS 1539-3755 10.1103/PhysRevE.72.016217 72, 016217 (2005). (Pubitemid 41521132)
13. S.-J. Baek and E. Ott, Phys. Rev. E NATUAS 1539-3755 10.1103/PhysRevE.69. 066210 69, 066210 (2004).
14. M. Barahona and L. M. Pecora, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.054101 89, 054101 (2002).
15. J. Jost and M. P. Joy, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.65. 016201 65, 016201 (2001).
16. C. Li, W. Sun, and J. Kurths, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.76.046204 76, 046204 (2007). (Pubitemid 47569184)
17. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.821 64, 821 (1990).
18. F. S. de San Roman, S. Boccaletti, D. Maza, and H. Mancini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3639 81, 3639 (1998).
19. F. M. Atay, J. Jost, and A. Wende, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.144101 92, 144101 (2004).
20. C. U. Choe, T. Dahms, P. Hövel, and E. Schöll, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.81.025205 81, 025205 (2010).
21. M. G. Earl and S. H. Strogatz, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.67.036204 67, 036204 (2003).
22. P. Hövel, M. A. Dahlem, and E. Schöll, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127410026101 20, 813 (2010).
23. I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, EPL 0295-5075 10.1209/0295-5075/93/60003 93, 60003 (2001).
24. J. Kestler, W. Kinzel, and I. Kanter, Phys. Rev. E IJBEE4 1539-3755 10.1103/PhysRevE.76.035202 76, 035202 (2007). (Pubitemid 47510084)
25. W. Kinzel, A. Englert, G. Reents, M. Zigzag, and I. Kanter, Phys. Rev. E IJBEE4 1539-3755 10.1103/PhysRevE.79.056207 79, 056207 (2009).
26. G. Kozyreff, A. G. Vladimirov, and P. Mandel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3809 85, 3809 (2000). (Pubitemid 32027189)
27. C. Masoller and A. C. Marti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.134102 94, 134102 (2005). (Pubitemid 40620475)
28. B. Schmitzer, W. Kinzel, and I. Kanter, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.80.047203 80, 047203 (2009).
29. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2109 80, 2109 (1998).
30. V. Flunkert, S. Yanchuk, T. Dahms, E. Schöll, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.105.254101 105, 254101 (2010).
31. J. Kestler, E. Kopelowitz, I. Kanter, and W. Kinzel, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.77.046209 77, 046209 (2008). (Pubitemid 351561392)
32. I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, W. Kinzel, M. Abeles, and D. Cohen, EPL 0295-5075 10.1209/0295-5075/93/66001 93, 66001 (2011).
33. M. Dhamala, V. K. Jirsa, and M. Ding, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.074104 92, 074104 (2004).
34. E. M. Shahverdiev and K. A. Shore, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.77.057201 77, 057201 (2008). (Pubitemid 351669753)
35. W. Just, E. Reibold, H. Benner, K. Kacperski, P. Fronczak, and J. Hołyst, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(99)00113-9 254, 158 (1999).
36. M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, Phys. Rev. E PYLAAG 1539-3755 10.1103/PhysRevE.81.036215 81, 036215 (2010).
37. A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Academic Press, New York, 1979).
38. S. Gershgorin, Bulletin de l'acad/'emie des Sciences de l'URSS. Classe des sciences mathematiques et na 6, 749 (1931).
39. I. Schur, J. Math. 148, 205 (1917).
40. S. Lepri, G. Giacomelli, A. Politi, and F. T. Arecchi, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90016-7 70, 235 (1994).
41. J. D. Farmer, Physica D PDNPDT 0167-2789 10.1016/0167-2789(82)90042-2 4, 366 (1982).
42. P. Erdös and P. Turan, Ann. Math. ANMAAH 0003-486X 10.2307/1969500 51, 105 (1950).
43. A. Granville, in Equidistribution in Number Theory: An Introduction, edited by, A. Granville, and, Z. Rudnick, (Springer, the Netherlands, 2007).
44. S. Yanchuk and P. Perlikowski, Phys. Rev. E ANMAAH 1539-3755 10.1103/PhysRevE.79.046221 79, 046221 (2009).
45. M. Zigzag, M. Butkowski, A. Englert, W. Kinzel, and I. Kanter, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/85/60005 85, 60005 (2009).
46. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. IEJQA7 0018-9197 10.1109/JQE.1980.1070479 16, 347 (1980).
47. I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.123902 97, 123902 (2006). (Pubitemid 44414738)
48. M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.76.046207 76, 046207 (2007). (Pubitemid 47569172)
49. E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.73.066214 73, 066214 (2006). (Pubitemid 43894395)
50. N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, Opt. Commun. OPCOB8 0030-4018 10.1016/j.optcom.2006.06.055 267, 464 (2006). (Pubitemid 44633275)
51. E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, Phys. Rev. E OPCOB8 1539-3755 10.1103/PhysRevE.74.046201 74, 046201 (2006). (Pubitemid 44520430)
52. I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M. Rosenbluh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.154101 98, 154101 (2007). (Pubitemid 46589307)
53. I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, Opt. Express OPEXFF 1094-4087 10.1364/OE.18.018292 18, 18292 (2010).
54. A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 104.114102 104, 114102 (2010).
55. Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.78.025204 78, 025204 (2008).
56. V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.58.7208 58, 7208 (1998).
57. K. Heun, Z. Math. Phys 45, 23 (1900).