Role of delay for the symmetry in the dynamics of networks

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

Volumn 83, Issue 4, 2011, Pages

  D'Huys, O ^a   Fischer, I ^b   Danckaert, J ^a   Vicente, R ^c,d  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b UNIVERSITAT DE LES ILLES BALEARS   (Spain)

^c MAX PLANCK INSTITUTE FOR BRAIN RESEARCH   (Germany)

^d FRANKFURT INSTITUTE FOR ADVANCED STUDIES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION POINTS; SPATIOTEMPORAL PATTERNS; STEADY STATE SOLUTION; SYMMETRY-BREAKING;

BIFURCATION (MATHEMATICS);

EID: 79961052345     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.046223     Document Type: Article

References (41)

1. M. Golubitsky and I. Stewart, The Symmetry Perspective (Birkhäuser, Basel, 2003).
2. S. Kondo and R. Asai, Nature (London) NATUAS 0028-0836 10.1038/376765a0 376, 765 (1995).
3. A. M. Turing, Philos. Trans. R. Soc. London Ser. B PTRBAE 0962-8436 10.1098/rstb.1952.0012 237, 37 (1952).
4. D. K. Kondepudi, R. J. Kaufman, and N. Singh, Science SCIEAS 0036-8075 10.1126/science.250.4983.975 250, 975 (1990).
5. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Part 1, Vol. 5 of Course of Theoretical Physics (Pergamon, New York, 1994).
6. R. D. Averitt, Nature Phys. SCIEAS 1745-2473 10.1038/nphys1768 6, 639 (2010).
7. R. Yusupov, T. Mertelj, V. V. Kabanov, S. Brazovskii, P. Kusar, J.-H. Chu, I. R. Fisher, and D. Mihailovic, Nature Phys. SCIEAS 1745-2473 10.1038/nphys1738 6, 681 (2010).
8. J. J. Collins and I. N. Stewart, J. Nonlinear Sci. JNSCEK 0938-8974 10.1007/BF02429870 3, 349 (1993).
9. K. Ito and Y. Nishiura, Phys. Rev. E JNSCEK 1539-3755 10.1103/PhysRevE.77.036224 77, 036224 (2008). (Pubitemid 351466159)
10. J. Kestler, W. Kinzel, and I. Kanter, Phys. Rev. E JNSCEK 1539-3755 10.1103/PhysRevE.76.035202 76, 035202 (2007). (Pubitemid 47510084)
11. S. A. Campbell, Y. Yuan, and S. D. Bungay, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/18/6/022 18, 2827 (2005). (Pubitemid 41483202)
12. L. Chen and K. Aihara, IEEE Trans. Circuits Syst. I ITCAEX 1057-7122 10.1109/TCSI.2002.1001949 49, 602 (2002). (Pubitemid 34711460)
13. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. IEJQA7 0018-9197 10.1109/JQE.1980.1070479 16, 347 (1980).
14. G. Orosz, R. E. Wilson, R. Szalai, and G. Stépan, Phys. Rev. E IEJQA7 1539-3755 10.1103/PhysRevE.80.046205 80, 046205 (2009).
15. M. Dhamala, V. K. Jirsa, and M. Ding, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.074104 92, 074104 (2004).
16. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3381 85, 3381 (2000).
17. T. Erneux, Applied Delay Differential Equations (Springer, New York, 2009).
18. S. Yanchuk and P. Perlikowski, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.79.046221 79, 046221 (2009).
19. P. Pue-on, Ph.D. thesis, Suranaree University of Technology, 2007.
20. D. Fan and J. Wei, Math. Prob. Eng. 1024-123X 10.1155/2009/950251 2009, 950251 (2009).
21. G. Orosz and G. Stépán, J. Nonlinear Sci. 0938-8974 10.1007/s00332-004-0625-4 14, 505 (2004). (Pubitemid 40881205)
22. B. F. Redmond, V. G. LeBlanc, and A. Longtin, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(02)00423-2 166, 131 (2002). (Pubitemid 34715754)
23. T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.795 86, 795 (2001). (Pubitemid 32159792)
24. S. Tang, R. Vicente, M. Chiang, C. Mirasso, and J. Liu, IEEE J. Sel. Top. Quantum Electron. IJSQEN 1077-260X 10.1109/JSTQE.2004.837013 10, 936 (2004). (Pubitemid 40010765)
25. I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.123902 97, 123902 (2006). (Pubitemid 44414738)
26. 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)
27. A. S. Landsman and I. B. Schwartz, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.75.026201 75, 026201 (2007). (Pubitemid 46203549)
28. J. Buldu, M. Torrent, and J. Garcia-Ojalvo, J. Lightwave Technol. JLTEDG 0733-8724 10.1109/JLT.2007.895555 25, 1549 (2007). (Pubitemid 46971445)
29. M. Peil, L. Larger, and I. Fischer, Phys. Rev. E JLTEDG 1539-3755 10.1103/PhysRevE.76.045201 76, 045201 (2007). (Pubitemid 47569155)
30. A. Wagemakers, J. Buldu, and M. Sanjuan, Chaos CHAOEH 1054-1500 10.1063/1.2737820 17, 023128 (2007).
31. R. Vicente, L. Gollo, C. Mirasso, I. Fischer, and G. Pipa, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0809353105 105, 17157 (2008).
32. V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.254101 105, 254101 (2010).
33. C. U. Choe, T. Dahms, P. Hövel, and E. Schöll, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.81.025205 81, 025205 (R) (2010).
34. O. D'Huys, R. Vicente, J. Dankaert, and I. Fischer, Chaos 1054-1500 10.1063/1.3518363 20, 043127 (2010).
35. M. C. Mackey and L. Glass, Science SCIEAS 0036-8075 10.1126/science. 267326 197, 287 (1977).
36. S. Yanchuk, M. Wolfrum, P. Hövel, and E. Schöll, Phys. Rev. E SCIEAS 1539-3755 10.1103/PhysRevE.74.026201 74, 026201 (2006). (Pubitemid 44943751)
37. P. Perlikowski, S. Yanchuk, O. V. Popovych, and P. A. Tass, Phys. Rev. E SCIEAS 1539-3755 10.1103/PhysRevE.82.036208 82, 036208 (2010).
38. 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).
39. F. Rogister, P. Mégret, O. Deparis, M. Blondel, and T. Erneux, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.24.001218 24, 1218 (1999).
40. Y. Liu and J. Ohtsubo, IEEE J. Quantum Electron. IEJQA7 0018-9197 10.1109/3.631270 33, 1163 (1997).
41. G. Van der Sande, M. C. Soriano, I. Fischer, and C. R. Mirasso, Phys. Rev. E IEJQA7 1539-3755 10.1103/PhysRevE.77.055202 77, 055202 (2008). (Pubitemid 351705634)