Bistability and hysteresis in symmetric 3d piecewise linear oscillators with three zones

International Journal of Bifurcation and Chaos

Volumn 18, Issue 12, 2008, Pages 3633-3645

  Freire, Emilio ^a   Ponce, Enrique ^a   Ros, Javier ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Bifurcation; Bistability; Limit cycles; Piecewise linear systems

Indexed keywords

BIFURCATION (MATHEMATICS); CIRCUIT OSCILLATIONS; DELTA SIGMA MODULATION; HYSTERESIS; LINEAR SYSTEMS; OPTICAL BISTABILITY; OSCILLATORS (ELECTRONIC); OSCILLATORS (MECHANICAL);

ANALYTICAL RESULTS; HYSTERESIS PHENOMENON; LIMIT CYCLE BIFURCATION; LIMIT-CYCLE; PERIODIC OSCILLATION; PIECE-WISE LINEAR SYSTEMS; PIECEWISE LINEAR; STABLE OSCILLATIONS;

PIECEWISE LINEAR TECHNIQUES;

EID: 60749129988     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127408022603     Document Type: Article

References (20)

1. Appleton, E. V. & van der Pol, B. [1922] "On a type of oscillation-hysteresis in a simple triode generator," The London, Edinburgh, and Dublin Philosophical Magazine and J. Sci, Ser. 6, 177-193.
2. Andronov, A. A., Vitt, A. A. & Khaikin, S. E. [1966] Theory of Oscillators (Dover, NY).
3. Carmona, V., Freire, E., Ponce, E. & Torres, F. [2002] "On simplifying and classifying piecewise-linear systems," IEEE Trans. Circuits Syst.-I Fund. Th. Appl. 49, 609-620.
4. Carmona, V., Freire, E., Ponce, E., Ros, J. & Torres, P. [2005] "Limit cycle bifurcation in 3D continuous piecewise linear systems with two zones. Application to Chua's circuit," Int. J. Bifurcation and Chaos 15, 3153-3164.
5. Chow, S. N. & Hale, J. K. [1982] Methods of Bifurcation Theory (Springer-Verlag, NY, Berlin).
6. Chua, L. O. & Ayrom, F. [1985] "Designing nonlinear opamp circuits: A cook-book approach," Int. J. Circuit Th. Appl. 13, 235-268.
7. Chua, L. O. [1993] "Global unfolding of Chua's circuit," WAGE Trans. Fund. E76-A, 704-734.
8. Freire, E., Ponce, E. & Ros, J. [1999] "Limit cycle bifurcation from center in symmetric piecewise-linear systems," Int. J. Bifurcation and Chaos 9, 895-907.
9. Freire, E., Ponce, E. & Ros, J. [2005] "The focus-centerlimit cycle bifurcation in symmetric 3D piecewise linear systems," SIAM J. Appl. Math. 65, 1933-1951.
10. Freire, E., Ponce, E. & Ros, J. [2007] "A biparametric bifurcation in 3D continuous piecewise linear systems with two zones. Application to Chua's circuit," Int. J. Bifurcation and Chaos 17, 445-457.
11. Gonçalves, S., Fusco, C., Bishop, A. R. &: Kenkre, V. M. [2005] "Bistability and hysteresis in the sliding friction of a dimer," Phys. Rev. B 72, 195418, pp. 1-8.
12. Hüppcr, G., Schöll, E. & Reggiani, L. [1989] "Global bifurcation and hysteresis of self-generated oscillations in a microscopic model of nonlinear transport in p-Ge," Solid-State Electron. 32, 1787-1791.
13. Jordan, D. W. & Smith, P. [1999] Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems (Oxford University Press, USA).
14. Kriegsrnann, G. A. [1987] "The rapid bifurcation of the Wien bridge oscillator," IEEE Trans. Circuits Syst. 34, 1093-1096.
15. Lynch, S. [2001] "Multistability, bistability and chaos control," Nonlin. Anal. 47, 4501-4512.
16. Moiola, J. L. & Chen, G. [1996] Hopf Bifurcation Analysis: A Frequency Domain Approach (World Scientific, Singapore).
17. Monagan, M. B., Geddes, K. O., Heal, K. M., Labahn, G., Vorkoetter, S. M., McCarron, J. &: DeMarco, P. [2003] Maple 9 Introductory Programming Guide, Maplesoft, Waterloo, ON.
18. Quarles, T., Newton, A. R., Pederson, D. O. & Sangiovanni- Vincentelli, A. [1993] Spice.3 Version 3f3 User's Manual, Department of Electrical Engineering and Computer Sciences, University of California Berkeley, Berkeley, CA, 1993.
19. 2+ oscillations," Europhys. Lett. 55, 746-752.
20. Wang, J. K. & Khonsari, M. M. [2006] "On the hysteresis phenomenon associated with instability of rotorbearing systems," J. Tribol. 128, 188-196.