Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force

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

Volumn 78, Issue 6, 2008, Pages

  Senthilkumar, D V ^a,c   Srinivasan, K ^b   Thamilmaran, K ^a   Lakshmanan, M ^a  

^a BHARATHIDASAN UNIVERSITY   (India)

^b NATIONAL INSTITUTE OF TECHNOLOGY   (India)

^c UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLE FORMATION; CONTROL SYSTEM ANALYSIS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; ELECTRON TUBES; EXPERIMENTS; LYAPUNOV METHODS; NETWORKS (CIRCUITS); PARAMETER ESTIMATION; TELECOMMUNICATION NETWORKS;

CONTROL PARAMETERS; ELECTRONIC CIRCUITS; FOURIER AMPLITUDES; LYAPUNOV EXPONENTS; NON-SINUSOIDAL; NUMERICAL AND EXPERIMENTAL STUDIES; NUMERICAL DATUMS; POINCARE; QUASIPERIODIC; QUASIPERIODIC FORCES; SPECTRAL DISTRIBUTIONS; SQUARE WAVES; STRANGE NONCHAOTIC ATTRACTORS;

DISTRIBUTION FUNCTIONS;

EID: 58149233952     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.066211     Document Type: Article

References (63)

1. C. Grebogi, E. Ott, S. Pelikan, and J. A. Yorke, Physica D 13, 261 (1984). 10.1016/0167-2789(84)90282-3
2. F. J. Romeiras and E. Ott, Phys. Rev. A 35, 4404 (1987); 10.1103/PhysRevA.35.4404
3. F. J. Romeiras, A. Bondeson, E. Ott, T. M. Andonsen, Jr., and C. Grebogi, Physica D 26, 277 (1987). 10.1016/0167-2789(87)90229-6
4. A. Bondeson, E. Ott, and T. M. Antonsen, Jr., Phys. Rev. Lett. 55, 2103 (1985); 10.1103/PhysRevLett.55.2103
5. Y. C. Lai, Phys. Rev. E 53, 57 (1996). 10.1103/PhysRevE.53.57
6. M. Ding, C. Grebogi, and E. Ott, Phys. Rev. A 39, 2593 (1989); 10.1103/PhysRevA.39.2593
7. M. Ding and J. A. Scott Relso, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 533 (1994).
8. J. F. Heagy and W. L. Ditto, J. Nonlinear Sci. 1, 423 (1991); 10.1007/BF02429848
9. J. I. Staglino, J. M. Wersinger, and E. E. Slaminka, Physica D 92, 164 (1996). 10.1016/0167-2789(95)00273-1
10. T. Yalcinkaya and Y. C. Lai, Phys. Rev. Lett. 77, 5039 (1996). 10.1103/PhysRevLett.77.5039
11. T. Kapitaniak and J. Wojewoda, Attractors of Quasiperiodically Forced Systems (World Scientific, Singapore, 1993).
12. A. Venkatesan, M. Lakshmanan, A. Prasad, and R. Ramaswamy, Phys. Rev. E 61, 3641 (2000). 10.1103/PhysRevE.61.3641
13. A. Venkatesan and M. Lakshmanan, Phys. Rev. E 55, 5134 (1997); 10.1103/PhysRevE.55.5134
14. A. Venkatesan and M. Lakshmanan, Phys. Rev. E 58, 3008 (1998). 10.1103/PhysRevE.58.3008
15. A. Prasad, V. Mehra, and R. Ramaswamy, Phys. Rev. Lett. 79, 4127 (1997); 10.1103/PhysRevLett.79.4127
16. A. Prasad, V. Mehra, and R. Ramaswamy, Phys. Rev. E 57, 1576 (1998). 10.1103/PhysRevE.57.1576
17. A. S. Pikovsky and U. Feudel, Chaos 5, 253 (1995); 10.1063/1.166074
18. U. Feudel, J. Kurths, and A. S. Pikovsky, Physica D 88, 176 (1995); 10.1016/0167-2789(95)00205-I
19. A. S. Pikovsky and U. Feudel, J. Phys. A 27, 5209 (1994); 10.1088/0305-4470/27/15/020
20. S. P. Kuznetsov, A. S. Pikovsky, and U. Feudel, Phys. Rev. E 51, R1629 (1995); 10.1103/PhysRevE.51.R1629
21. A. Witt, U. Feudel, and A. S. Pikovsky, Physica D 109, 180 (1997). 10.1016/S0167-2789(97)00168-1
22. V. S. Anishchenko, T. E. Vadivasova, and O. Sosnovtseva, Phys. Rev. E 53, 4451 (1996); 10.1103/PhysRevE.53.4451
23. O. Sosnovtseva, U. Feudel, J. Kurths, and A. S. Pikovsky, Phys. Lett. A 218, 225 (1996); 10.1016/0375-9601(96)00399-4
24. S. Kuznetsov, U. Feudel, and A. Pikovsky, Phys. Rev. E 57, 1585 (1998). 10.1103/PhysRevE.57.1585
25. K. Kaneko, Prog. Theor. Phys. 71, 140 (1984);
26. T. Nishikawa and K. Kaneko, Phys. Rev. E 54, 6114 (1996). 10.1103/PhysRevE.54.6114
27. A. Venkatesan and M. Lakshmanan, Phys. Rev. E 63, 026219 (2001). 10.1103/PhysRevE.63.026219
28. B. R. Hunt and E. Ott, Phys. Rev. Lett. 87, 254101 (2001); 10.1103/PhysRevLett.87.254101
29. J. W. Kim, S. Y. Kim, B. R. Hunt, and E. Ott, Phys. Rev. E 67, 036211 (2003); 10.1103/PhysRevE.67.036211
30. S. Y. Kim, W. Lim, and E. Ott, Phys. Rev. E 67, 056203 (2003); 10.1103/PhysRevE.67.056203
31. W. Lim and S. Y. Kim, J. Korean Phys. Soc. 3, 514 (2004).
32. J. F. Heagy and S. M. Hammel, Physica D 70, 140 (1994). 10.1016/0167-2789(94)90061-2
33. A. Prasad, R. Ramaswamy, I. I. Satija, and N. Shah, Phys. Rev. Lett. 83, 4530 (1999). 10.1103/PhysRevLett.83.4530
34. C. S. Zhou and T. L. Chen, Europhys. Lett. 38, 261 (1997); 10.1209/epl/i1997-00235-7
35. R. Ramaswamy, Phys. Rev. E 56, 7294 (1997); 10.1103/PhysRevE.56.7294
36. R. Chacon and A. M. Gracia-Hoz, Europhys. Lett. 57, 7 (2002). 10.1209/epl/i2002-00533-6
37. S. Y. Kim and W. Lim, J. Phys. A 37, 6477 (2004). 10.1088/0305-4470/37/ 25/004
38. T. Kapitaniak and L. O. Chua, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 423 (1997). 10.1142/S0218127497000297
39. T. Yang and K. Bilimgut, Phys. Lett. A 236, 494 (1997); 10.1016/S0375-9601(97)00833-5
40. Z. Liu and Z. Zhua, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 1383 (1996); 10.1142/S0218127496000801
41. Z. Zhua and Z. Liu, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 227 (1997). 10.1142/S0218127497000169
42. A. Venkatesan, K. Murali, and M. Lakshmanan, Phys. Lett. A 259, 246 (1999). 10.1016/S0375-9601(99)00456-9
43. W. L. Ditto, M. L. Spano, H. T. Savage, S. N. Rauseo, J. F. Heagy, and E. Ott, Phys. Rev. Lett. 65, 533 (1990); 10.1103/PhysRevLett.65.533
44. T. Zhou, F. Moss, and A. Bulsara, Phys. Rev. A 45, 5394 (1992); 10.1103/PhysRevA.45.5394
45. W. X. Ding, H. Deutsch, A. Dinklage, and C. Wilke, Phys. Rev. E 55, 3769 (1997); 10.1103/PhysRevE.55.3769
46. J. A. Ketoja and I. Satija, Physica D 109, 70 (1997). 10.1016/S0167-2789(97)00160-7
47. K. Thamilmaran, D. V. Senthilkumar, A. Venkatesan, and M. Lakshmanan, Phys. Rev. E 74, 036205 (2006). 10.1103/PhysRevE.74.036205
48. A. Prasad, S. S. Negi, and R. Ramaswamy, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 291 (2001); 10.1142/S0218127401002195
49. A. Prasad, A. Nandi, and R. Ramaswamy, Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 3397 (2007). 10.1142/S0218127407019123
50. U. Feudel, S. Kuznetsov, and A. Pikovsky, Strange Nonchaotic Attractors: Dynamics between Order and Chaos in Quasiperiodically Forced Systems (World Scientific, Singapore, 2006).
51. T. Zhou, F. Moss, and A. Bulsara, Phys. Rev. A 45, 5394 (1992). 10.1103/PhysRevA.45.5394
52. W. X. Ding, H. Deutsch, A. Dinklage, and C. Wilke, Phys. Rev. E 55, 3769 (1997). 10.1103/PhysRevE.55.3769
53. J. A. Ketoja and I. Satija, Physica D 109, 70 (1997). 10.1016/S0167-2789(97)00160-7
54. G. Ruiz and P. Parmananda, Phys. Lett. A 367, 478 (2007). 10.1016/j.physleta.2007.03.053
55. S. Graziani, P. Silar, and M. J. Daboussi, BMC Evol. Biol. 2, 18 (2004).
56. D. Dubnau and R. Losick, Mol. Microbiol. 61, 564 (2006). 10.1111/j.1365-2958.2006.05249.x
57. A. R. Bulsara, E. Jacobs, T. Zhou, F. Moss, and L. Kiss, J. Theor. Biol. 154, 531 (1991); 10.1016/S0022-5193(05)80396-0
58. A. Longtin, A. Bulsara, D. Pierson, and F. Moss, Biol. Cybern. 70, 569 (1994). 10.1007/BF00198810
59. V. Chinarov and M. Menzinger, BioSystems 55, 137 (2000). 10.1016/S0303-2647(99)00091-X
60. Z. M. Ge and W. Y. Leu, Chaos, Solitons Fractals 20, 502 (2004).
61. G. D. VanWiggeren and R. Roy, Science 279, 1198 (1998); 10.1126/science.279.5354.1198
62. G. D. VanWiggeren and R. Roy, Phys. Rev. Lett. 81, 3547 (1998). 10.1103/PhysRevLett.81.3547
63. K. Thamilmaran, D. V. Senthilkumar, M. Lakshmanan, and A. Ishaq Ahmed, Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, 2 (2005).