3.3 Bifurcations in piecewise-smooth maps

Nonlinear Phenomena in Power Electronics: Attractors, Bifurcations, Chaos, and Nonlinear Control

Volumn , Issue , 2001, Pages 73-88

  Banerjee, Soumitro ^a   Grebogi, Celso ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL ENGINEERING; ELECTRONICS ENGINEERING; ELECTRONICS INDUSTRY;

PIECEWISE SMOOTH MAPS;

CHAOS THEORY;

EID: 0041812205     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1109/9780470545393.ch3     Document Type: Chapter

References (16)

1. S. Banerjee and K. Chakrabarty, Nonlinear modeling and bifurcations in the boost converter, IEEE Trans. on Power Electronics, vol. 13, no. 2, pp. 252-260, 1998.
2. S. Banerjee, E. Ott, J. A. Yorke, and G. H. Yuan, Anomalous bifurcations in de-de converters: Borderline collisions in piecewise smooth maps, Power Electronics Specialists’ Conference, pp. 1337-1344, 1997.
3. G. H. Yuan, S. Banerjee, E. Ott, and J. A. Yorke, Border collision bifurcations in the buck converter, IEEE Trans. on Circuits and Systems-I, vol. 45, no. 7, pp. 707-716, 1998.
4. W. C. Y. Chan and C. K. Tse, Study of bifurcations in current programmed de/de boost converters: From quasiperiodicity to period doubling, IEEE Trans. on Circuits and Systems-I, vol. 44, no. 12, pp. 1129-1142, 1997.
5. G. Olivar, Chaos in the buck converter. PhD diss., Technical University of Catalonia, Barcelona, Spain, 1997. Servei de Publicacions de la Ul’C (3640).
6. H. E. Nusse and J. A. Yorke, Border-collision bifurcations including “period two to period three” for piecewise smooth maps, Physica D, vol. 57, pp. 39-57, 1992.
7. H. E. Nusse, E. Ott, and J. A. Yorke, Border-collision bifurcations: An explanation for observed bifurcation phenomena, Physical Review E, vol. 49, pp. 1073-1076, 1994.
8. W. Chin, E. Ott, H. E. Nusse, and C. Grebogi, Universal behavior of impact oscillators near grazing incidence, Physics Letters A, vol. 201, pp. 197-204, 1995.
9. G. H. Yuan, Shipboard crane control, simulated data generation and border collision bifurcations. PhD diss., University of Maryland, College Park, USA, 1997.
10. S. Banerjee and C. Grebogi, Border collision bifurcations in two-dimensional piecewise smooth maps, Physical Review E, vol. 59, no. 4, pp. 4052-4061, 1999.
11. F. Takens, Transition from periodic to strange attractors in constrained equations, in Dynamical Systems and Bifurcation Theory M. Camacho, M. Pacifico, and F. Takens, eds., vol. 160 of Pitman Research Notes in Mathematics Series, pp. 399-421, Longman Scientific and Technical, 1987.
12. H. E. Nusse and J. A. Yorke, Border-collision bifurcations for piecewise smooth one dimensional maps, Int. J. Bifurcation and Chaos, vol. 5, no. 1, pp. 189-207, 1995.
13. Y. L. Maistrenko, V. L. Maistrenko, and L. O. Chua, Cycles of chaotic intervals in a timedelayed Chua’s circuit, Int. J. Bifurcation and Chaos, vol. 3, pp. 1573-1579, 1993.
14. S. Banerjee, J. A. Yorke, and C. Grebogi, Robust chaos, Physical Review Letters, vol. 80, pp. 3049-3052, 1998.
15. S. Banerjee, P. Ranjan, and C. Grebogi, Bifurcations in two-dimensional piecewise smooth maps: Theory and applications in switching circuits. IEEE Trans. on Circuits and SystemsI, vol. 47, no. 5, pp. 633-643, 2000.
16. M. di Bernardo, M. I. Feigin, S. J. Hogan, and M. E. Homer, Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems, Chaos, Solitons &Fractals, vol. 10, no. 11, 1999.