Stabilization of a steady state in network oscillators by using diffusive connections with two long time delays

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

Volumn 81, Issue 1, 2010, Pages

  Konishi, Keiji ^a   Kokame, Hideki ^a   Hara, Naoyuki ^a  

^a Osaka Prefecture University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL RESULTS; CIRCUIT MODELS; COUPLING STRENGTHS; DELAY TIME; IN-NETWORK; LONG TIME DELAYS; NETWORK TOPOLOGY; PROPORTIONAL RELATION; SMALL WORLD NETWORKS; STEADY STATE; TWO DELAYS;

ELECTRIC NETWORK TOPOLOGY; LINEAR STABILITY ANALYSIS; TIME DELAY;

STABILIZATION;

EID: 75349086493     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.016201     Document Type: Article

References (73)

1. T. Endo and S. Mori, IEEE Trans. Circuits Syst. 23, 100 (1976). 10.1109/TCS.1976.1084183
2. Y. Nishio and A. Ushida, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 42, 678 (1995). 10.1109/81.473574
3. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization (Cambridge University Press, London, 2001).
4. P. Holmes, R. Full, D. Koditschek, and J. Guckenheimer, SIAM Rev. 48, 207 (2006). 10.1137/S0036144504445133
5. A. Ishiguro, M. Shimizua, and T. Kawakatsub, Rob. Auton. Syst. 54, 641 (2006). 10.1016/j.robot.2006.02.011
6. Y.-W. Hong and A. Scaglione, IEEE J. Sel. Areas Commun. 23, 1085 (2005). 10.1109/JSAC.2005.845418
7. Y. Yamaguchi and H. Shimizu, Physica D 11, 212 (1984). 10.1016/0167-2789(84)90444-5
8. D. Aronson, G. Ermentout, and N. Kopell, Physica D 41, 403 (1990). 10.1016/0167-2789(90)90007-C
9. K. Konishi, Phys. Lett. A 341, 401 (2005). 10.1016/j.physleta.2005.04.094
10. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. 80, 5109 (1998). 10.1103/PhysRevLett.80.5109
11. S. Strogatz, Nature (London) 394, 316 (1998). 10.1038/28488
12. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. 85, 3381 (2000). 10.1103/PhysRevLett.85.3381
13. R. Herrero, M. Figueras, J. Rius, F. Pi, and G. Orriols, Phys. Rev. Lett. 84, 5312 (2000). 10.1103/PhysRevLett.84.5312
14. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Physica D 129, 15 (1999). 10.1016/S0167-2789(99)00004-4
15. K. Konishi, Phys. Rev. E 70, 066201 (2004). 10.1103/PhysRevE.70.066201
16. R. Dodla, A. Sen, and G. L. Johnston, Phys. Rev. E 69, 056217 (2004). 10.1103/PhysRevE.69.056217
17. M. Mehta and A. Sen, Phys. Lett. A 355, 202 (2006). 10.1016/j.physleta. 2006.01.104
18. K. Konishi, Phys. Rev. E 68, 067202 (2003). 10.1103/PhysRevE.68.067202
19. K. Konishi, Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 2781 (2007). 10.1142/S0218127407018750
20. F. M. Atay, Phys. Rev. Lett. 91, 094101 (2003). 10.1103/PhysRevLett.91. 094101
21. F. Atay, Physica D 183, 1 (2003). 10.1016/S0167-2789(03)00154-4
22. F. M. Atay, J. Differ. Equations 221, 190 (2006). 10.1016/j.jde.2005.01. 007
23. F. M. Atay and O. Karabacak, SIAM J. Appl. Dyn. Syst. 5, 508 (2006). 10.1137/060652531
24. A. Prasad, Phys. Rev. E 72, 056204 (2005). 10.1103/PhysRevE.72.056204
25. K. Konishi, K. Senda, and H. Kokame, Phys. Rev. E 78, 056216 (2008). 10.1103/PhysRevE.78.056216
26. J. Yang, Phys. Rev. E 76, 016204 (2007). 10.1103/PhysRevE.76.016204
27. Y. Song, J. Wei, and Y. Yuan, J. Nonlinear Sci. 17, 145 (2007). 10.1007/s00332-006-0802-1
28. S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, and J.-M. Liu, IEEE J. Sel. Top. Quantum Electron. 10, 936 (2004). 10.1109/JSTQE.2004.837013
29. R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J.-M. Liu, Phys. Rev. E 73, 047201 (2006). 10.1103/PhysRevE.73.047201
30. G. Chen and X. Dong, From Chaos to Order (World Scientific, Singapore, 1998).
31. H. Schuster, Handbook of Chaos Control (Wiley-VCH, New York, 1999). 10.1002/3527607455
32. E. Scholl and H. Schuster, Handbook of Chaos Control (Wiley-VCH, New York, 2008).
33. B. R. Andrievskii and A. L. Fradkov, Autom. Remote Control (Engl. Transl.) 64, 673 (2003). 10.1023/A:1023684619933
34. B. R. Andrievskii and A. L. Fradkov, Autom. Remote Control (Engl. Transl.) 65, 505 (2004). 10.1023/B:AURC.0000023528.59389.09
35. K. Pyragas, Phys. Lett. A 170, 421 (1992). 10.1016/0375-9601(92)90745-8
36. K. Pyragas, Philos. Trans. R. Soc. London, Ser. A 364, 2309 (2006). 10.1098/rsta.2006.1827
37. K. Gu and S. Niculescu, ASME J. Dyn. Syst., Meas., Control 125, 158 (2003). 10.1115/1.1569950
38. H. Nakajima, Phys. Lett. A 232, 207 (1997). 10.1016/S0375-9601(97)00362-9
39. W. Just, Physica D 142, 153 (2000). 10.1016/S0167-2789(00)00051-8
40. B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, and E. Schöll, Phys. Rev. Lett. 98, 114101 (2007). 10.1103/PhysRevLett.98.114101
41. W. Just, B. Fiedler, M. Georgi, V. Flunkert, P. Hövel, and E. Schöll, Phys. Rev. E 76, 026210 (2007). 10.1103/PhysRevE.76.026210
42. C. M. Postlethwaite and M. Silber, Phys. Rev. E 76, 056214 (2007). 10.1103/PhysRevE.76.056214
43. K. Pyragas, Phys. Rev. Lett. 86, 2265 (2001). 10.1103/PhysRevLett.86.2265
44. K. Pyragas, V. Pyragas, I. Z. Kiss, and J. L. Hudson, Phys. Rev. E 70, 026215 (2004). 10.1103/PhysRevE.70.026215
45. A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Chaos 8, 782 (1998). 10.1063/1.166357
46. P. Hövel and E. Schöll, Phys. Rev. E 72, 046203 (2005). 10.1103/PhysRevE.72.046203
47. T. Dahms, P. Hövel, and E. Schöll, Phys. Rev. E 76, 056201 (2007). 10.1103/PhysRevE.76.056201
48. H. Kokame, K. Hirata, K. Konishi, and T. Mori, Int. J. Control 74, 537 (2001). 10.1080/00207170010017275
49. H. Kokame, K. Hirata, K. Konishi, and T. Mori, IEEE Trans. Autom. Contr. 46, 1908 (2001). 10.1109/9.975474
50. K. Hirata, H. Kokame, K. Konishi, and H. Fujita, Proceedings of American Control Conference, 2001, pp. 25-27.
51. V. Z. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, Phys. Rev. E 73, 046205 (2006). 10.1103/PhysRevE.73.046205
52. T. Ushio, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 43, 815 (1996). 10.1109/81.536757
53. K. Konishi and H. Kokame, Phys. Lett. A 248, 359 (1998). 10.1016/S0375-9601(98)00673-2
54. S. Yamamoto, T. Hino, and T. Ushio, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 785 (2001). 10.1109/81.928162
55. A. Kittel, Z. Naturforsch., A: Phys. Sci. 49, 843 (1994).
56. T. Hikihara and T. Kawagoshi, Phys. Lett. A 211, 29 (1996). 10.1016/0375-9601(95)00925-6
57. S. Yanchuk, M. Wolfrum, P. Hövel, and E. Schöll, Phys. Rev. E 74, 026201 (2006). 10.1103/PhysRevE.74.026201
58. A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004). 10.1103/PhysRevLett.93.264101
59. A. Ahlborn and U. Parlitz, Phys. Rev. E 72, 016206 (2005). 10.1103/PhysRevE.72.016206
60. A. Ahlborn and U. Parlitz, Opt. Lett. 31, 465 (2006). 10.1364/OL.31.000465
61. K. Konishi and H. Kokame, Proceedings of the 15th International IEEE Workshop on Nonlinear Dynamics of Electronic Systems, 2007, pp. 249-252.
62. C. Masoller and A. C. Martí, Phys. Rev. Lett. 94, 134102 (2005). 10.1103/PhysRevLett.94.134102
63. T. Omi and S. Shinomoto, Phys. Rev. E 77, 046214 (2008). 10.1103/PhysRevE.77.046214
64. A. Tobbens and U. Parlitz, Phys. Rev. E 78, 016210 (2008). 10.1103/PhysRevE.78.016210
65. K. Konishi and H. Kokame, Proceedings of the International Symposium on Nonlinear Theory and its Applications, 2008, pp. 528-531.
66. K. Konishi, H. Kokame, and N. Hara, Proceedings of the Second IFAC Meeting Related to Analysis and Control of Chaotic Systems, 2009 (unpublished).
67. T. Matsumoto, L. Chua, and M. Komuro, IEEE Trans. Circuits Syst. 32, 797 (1985). 10.1109/TCS.1985.1085791
68. C. Moore and M. E. J. Newman, Phys. Rev. E 61, 5678 (2000). 10.1103/PhysRevE.61.5678
69. A. Hastings, J. Math. Biol. 21, 35 (1984). 10.1007/BF00275221
70. W. Murdoch, R. Nisbet, S. Blythe, W. Gurney, and J. D. Reeve, Am. Nat. 129, 263 (1987). 10.1086/284634
71. K. Blyuss, Y. Kyrychko, P. Hövel, and E. Schöll, Eur. Phys. J. B 65, 571 (2008). 10.1140/epjb/e2008-00371-x
72. J. Lu, Z. Ma, and L. Li, Commun. Nonlinear Sci. Numer. Simul. 14, 3037 (2009). 10.1016/j.cnsns.2008.10.026
73. Although a counter example of the odd-number property for UPOs on time-continuous systems has been reported in, the property is valid for UFPs.