Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation

Chaos

Volumn 16, Issue 2, 2006, Pages

  Zhusubaliyev, Zhanybai T ^a   Mosekilde, Erik ^b   Maity, Somnath ^c   Mohanan, Srijith ^c   Banerjee, Soumitro ^c  

^a SOUTHWEST STATE UNIVERSITY   (Russian Federation)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^c INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745711667     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2208565     Document Type: Article

References (61)

1. I. Gumowski and C. Mira, Recurrence and Discrete Dynamic Systems, Lecture Notes in Mathematics Vol. 809 (Springer, Berlin, 1980).
2. J. H. B. Deane and D. C. Hamill, IEEE Trans. Power Electron. 5, 260 (1990).
3. M. Ohnishi and N. Inaba, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 41, 433 (1994).
4. E. Fossas and G. Olivar, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 43, 13 (1996).
5. G. H. Yuan, S. Banerjee, E. Ott, and J. A. Yorke, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 45, 707 (1998).
6. T. Kousaka, T. Ueta, and H. Kawakami, IEEE Trans. Circuits Syst., II: Analog Digital Signal Process. 46, 878 (1999).
7. E. Toribio, A. El Aroudi, G. Olivar, and L. Benadero, IEEE Trans. Power Electron. 15, 1163 (2000).
8. B. Brogliato, Nonsmooth Mechanics - Models, Dynamics and Control (Springer, New York, 1999).
9. A. B. Nordmark, J. Sound Vib. 145, 279 (1991).
10. C. Budd and F. Dux, Philos. Trans. R. Soc. London 347, 365 (1994).
11. B. Thuilot, A. Goswami, and B. Espiau, "Bifurcation and chaos in a simple passive bipedal gait," IEEE International Conference Robotics Automation, Albuquerque, NM, 1997.
12. M. Garcia, A. Chatterjee, A. Ruina, and M. Coleman, J. Biomech. Eng. 120, 281 (1998).
13. J. Keener and J. Sneyd, Mathematical Physiology (Springer, New York, 1998).
14. O. Sosnovtseva and E. Mosekilde, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 1225 (1997).
15. M. I. Feigin, Prikl. Mat. Mekh. 34, 861 (1970) (in Russian).
16. M. I. Feigin, Prikl. Mat. Mekh. 38, 810 (1974) (in Russian).
17. M. I. Feigin, Prikl. Mat. Mekh. 42, 820 (1978) (in Russian).
18. M. I. Feigin, Forced Oscillations in Systems with Discontinuous Nonlinearities (Nauka, Moscow, 1994) (in Russian).
19. H. E. Nusse and J. A. Yorke, Physica D 57, 39 (1992).
20. H. E. Nusse, E. Ott, and J. A. Yorke, Phys. Rev. E 49, 1073 (1994).
21. H. E. Nusse and J. A. Yorke, Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, 189 (1995).
22. M. di Bernardo, M. I. Feigin, S. J. Hogan, and M. E. Homer, Chaos, Solitons Fractals 10, 1881 (1999).
23. S. Banerjee and C. Grebogi, Phys. Rev. E 59, 4052 (1999).
24. S. Banerjee, M. S. Karthik, G. H. Yuan, and J. A. Yorke, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 47, 389 (2000).
25. S. Banerjee, P. Ranjan, and C. Grebogi, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 47, 633 (2000).
26. M. Di Bernardo, C. Budd, and A. Champneys, Nonlinearity 11, 859 (1998).
27. M. di Bernardo, C. J. Budd, and A. R. Champneys, Phys. Rev. Lett. 86, 2553 (2001).
28. M. di Bernardo, C. J. Budd, and A. R. Champneys, Physica D 160, 222 (2001).
29. M. di Bernardo, P. Kowalczyk, and A. Nordmark, Physica D 170, 175 (2002).
30. M. di Bernardo, P. Kowalczyk, and A. Nordmark, Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, 2935 (2003).
31. A. B. Nordmark, Nonlinearity 14, 1517 (2001).
32. P. T. Piironen, L. N. Virgin, and A. R. Champneys, J. Nonlinear Sci. 14, 383 (2004).
33. Nonlinear Phenomena in Power Electronics: Attractors, Bifurcations, Chaos, and Nonlinear Control, edited by S. Banerjee and G. C. Verghese (IEEE Press, Piscataway, NJ, 2001).
34. B. Blazejczyk-Okolewska, K. Czolczynski, T. Kapitaniak, and J. Wojewoda, Chaotic Mechanics in Systems with Impacts and Friction (World Scientific, Singapore, 1999).
35. R. I. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-Smooth Mechanical Systems (Springer, Berlin, 2004).
36. C. K. Tse, Complex Behavior of Switching Power Converters (CRC Press, Boca Raton, FL, 2003).
37. Z. T. Zhusubaliyev and E. Mosekilde, Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems (World Scientific, Singapore, 2003).
38. M. di Bernardo, F. Garofalo, L. Glielmo, and F. Vasca, "Quasi-periodic behaviors in DC-DC converters," in IEEE Power Electronic Special. Conference (IEEE, Piscataway, NJ, 1996), pp. 1376-1381.
39. A. El Aroudi, L. Benadero, E. Toribio and S. Machiche, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 359 (2000).
40. A. E. Aroudi and R. Leyva, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 967 (2001).
41. Z. T. Zhusubaliyev, E. A. Soukhoterin, and E. Mosekilde, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 50, 1047 (2003).
42. A. El Aroudi, M. Debbat, R. Giral, G. Olivar, L. Benadero, and E. Toribio, Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, 1549 (2005).
43. H. Dankowicz, P. Piiroinen, and A. B. Nordmark, Chaos, Solitons Fractals 14, 241 (2002).
44. Yu. L. Maistrenko, V. L. Maistrenko, S. I. Vikul, and L. O. Chua, Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, 653 (1995).
45. W. M. Yang and B. L. Hao, Commun. Theor. Phys. 8, 1 (1987).
46. Z. T. Zhusubaliyev, E. A. Soukhoterin, and E. Mosekilde, Chaos, Solitons Fractals 13, 1889 (2002).
47. I. Sushko, L. Gardini, and T. Puu, Chaos, Solitons Fractals 21, 403 (2004).
48. Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, 3rd ed. (Springer, New York, 2004).
49. A. Agliari, G.-I. Bischi, R. Dieci, and L. Gardini, Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, 1285 (2005).
50. Z. T. Zhusubaliyev and E. Mosekilde, Phys. Lett. A 351, 167 (2006).
51. T. Kapitaniak and Yu. L. Maistrenko, Phys. Rev. E 58, 5161 (1998).
52. M. Dutta, H. E. Nusse, E. Ott, J. A. Yorke, and G.-H. Yuan, Phys. Rev. Lett. 83, 4281 (1999).
53. A. V. Kobzev, Multilevel Pulse Modulation: Theory and Applications to Power Electronics (Nauka, Novosibirsk, 1979).
54. P. M. Bhagwat and V. R. Stefanovic, IEEE Trans. Ind. Appl. IA-19, 1057 (1983).
55. A. V. Kobzev, G. Ya. Mikhal'chenko, and N. M. Muzhitchenko, Modulating Power Supplies of Radioelectronic Devices (Radio i Svyaz, Tomsk, 1990).
56. G. Carrara, S. Gardella, M. Marchesoni, R. Salutari, and G. Sciutto, IEEE Trans. Power Electron. 7, 497 (1992).
57. J. S. Lai and F. Z. Peng, IEEE Trans. Ind. Appl. 32, 509 (1996).
58. F. Z. Peng, IEEE Trans. Ind. Appl. 37, 611 (2001).
59. A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, Not. Am. Math. Soc. 39, 303 (1992).
60. B. Krauskopf and H. M. Osinga, in Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, edited by E. J. Doedel and L. S. Tuckerman (Springer, New York, 2000), pp. 199-208.
61. J. P. England, B. Krauskopf, and H. M. Osinga, SIAM J. Appl. Dyn. Syst. 3, 161 (2004).