Border-collision bifurcations in one-dimensional discontinuous maps

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 11, 2003, Pages 3341-3351

  Jain, Parag ^a   Banerjee, Soumitro ^b  

^a Stanford University   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Border collision bifurcations; Discontinuous maps; Power electronics

Indexed keywords

CHAOS THEORY; LINEARIZATION; MATHEMATICAL TRANSFORMATIONS; PARAMETER ESTIMATION; POWER ELECTRONICS;

BORDER-COLLISION BIFURCATIONS; DISCONTINUOUS MAPS;

BIFURCATION (MATHEMATICS);

EID: 1442335935     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127403008533     Document Type: Article

References (16)

1. Banerjee, S., Ott, E., Yorke, J. A. & Yuan, G. H. [1997] "Anomalous bifurcations in dc-dc converters: Borderline collisions in piecewise smooth maps," IEEE Power Electronics Specialists' Conf., pp. 1337-1344.
2. Banerjee, S., Karthik, M. S., Yuan, G. H. & Yorke, J. A. [2000a] "Bifurcations in one-dimensional piece-wise smooth maps - theory and applications in switching circuits," IEEE Trans. Circuits Syst.-I 47, 389-393.
3. Banerjee, S., Ranjan, P. & Grebogi, C. [2000b] "Bifurcations in two-dimensional piecewise smooth maps - theory and applications in switching circuits," IEEE Trans. Circuits Syst.-I 47, 633-643.
4. Banerjee, S. & Verghese, G. C. (eds.) [2001] Nonlinear Phenomena in Power Electronics: Attractors, Bifurcation, Chaos, and Nonlinear Control (IEEE Press).
5. Budd, C. & Dux, F. [1994] "Chattering and related behavior in impacting oscillators," Phil. Trans. Roy. Soc. 347, 365-389.
6. Budd, C. [1995] "Grazing in impact oscillators," in Real and Complex Dynamical Systems, eds. Branner, B. & Hjorth, P. (Kluwer Academic Publishers), pp. 47-64.
7. Chin, W., Ott, E., Nusse, H. E. & Grebogi, C. [1995] "Universal behavior of impact oscillators near grazing incidence," Phys. Lett. A201, 197-204.
8. Di Bernardo, M., Feigin, M. I., Hogan, S. J. & Homer, M. E. [1999] "Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems," Chaos Solit. Fract. 10, 1881-1908.
9. Dobson, I. [1995] "Stability of ideal thyristor and diode switching circuits," IEEE Trans. Circuits Syst.-I 42, 517-529.
10. Jalali, S., Dobson, I., Lasseter, R. H. & Venkataraman, G. [1996] "Switching time bifurcations in a thyristor controlled reactor," IEEE Trans. Circuits Syst.-I 43, 209-217.
11. Maggio, G. M., Di Bernardo, M. & Kennedy, M. P. [2000] "Nonsmooth bifurcations in a piecewise linear model of the Colpitts oscillator," IEEE Trans. Circuits Syst.-I 47, p. 1160.
12. Nusse, H. E. & Yorke, J. A. [1992] "Border-collision bifurcations including 'period two to period three' for piecewise smooth maps," Physica D57, 39-57.
13. Nusse, H. E., Ott, E. & Yorke, J. A. [1994] "Border-collision bifurcations: An explanation for observed bifurcation phenomena," Phys. Rev. E49, 1073-1076.
14. Nusse, H. E. & Yorke, J. A. [1995] "Border-collision bifurcations for piecewise smooth one dimensional maps," Int. J. Bifurcation and Chaos 5, 189-207.
15. Rajaraman, R., Dobson, I. & Jalali, S. [1996] "Nonlinear dynamics and switching time bifurcations of a thyristor controlled reactor circuit," IEEE Trans. Circuits Syst.-I 43, 1001-1006.
16. Yuan, G. H., Banerjee, S., Ott, E. & Yorke, J. A. [1998] "Border collision bifurcations in the buck converter," IEEE Trans. Circuits Syst.-I 45, 707-716.