On periodic orbits of 3d symmetric piecewise linear systems with real triple eigenvalues

International Journal of Bifurcation and Chaos

Volumn 19, Issue 7, 2009, Pages 2391-2399

  Ponce, E ^a   Ros, J ^a  

^a UNIVERSIDAD DE SEVILLA   (Spain)

Author keywords

Periodic orbits; Piecewise linear systems; Saturated systems

Indexed keywords

BIFURCATION (MATHEMATICS); EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS;

APPROXIMATE METHODS; BIFURCATION PARAMETER; GLOBAL BIFURCATIONS; PERIODIC ORBITS; PIECE-WISE LINEAR SYSTEMS; SATURATED SYSTEMS; STABLE PERIODIC ORBITS; SYMMETRIC PERIODIC ORBITS;

PIECEWISE LINEAR TECHNIQUES;

EID: 70350605736     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127409024165     Document Type: Article

References (15)

1. Aguirre, B., Alvarez-Ramírez, J., Ferńandez, G. & Súarez, R. [1997] "First harmonic analysis of linear control systems with high-gain saturating feedback," Int. J. Bifurcation and Chaos 7, 2501-2510.
2. Alvarez, J. & Curiel, L. E. [1997] "First harmonic analysis of linear control systems with high-gain saturating feedback," Int. J. Bifurcation and Chaos 7, 1811-1822.
3. Barnett, S. & Cameron, R. G. [1985] Introduction to Mathematical Control Theory, 2nd edition (Clarendon Press, Oxford).
4. Basso, M. & Genesio, R. [2003] "Analysis and control of limit cycle bifurcations," Bifurcation Control, eds. Chen, G., Hill, D. J. & Yu, X., LNCIS, Vol.293 (Springer, Berlin), pp. 127-154.
5. 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.
6. Carmona, V., Freire, E., Ponce, E., Ros, J. & Torres, F. [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.
7. 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.
8. 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.
9. Freire, E., Ponce, E. & Ros, J. [2008] "Bistability and hysteresis in symmetric 3D piecewise linear oscillators with three zones," Int. J. Bifurcation and Chaos 18, 3633-3645.
10. Genesio, R. & Tesi, A. [1992] "Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems," Automatica 28, 531-548.
11. Khalil, H. K. [1992] Nonlinear Systems (Macmillan, NY).
12. Leonov, G. A., Burkin, I. M. & Shepeljavyi, A. I. [1996] Frequency Methods in Oscillation Theory (Kluwer, Dordrecht).
13. Llibre, J. & Ponce, E. [1996] "Global first harmonic bifurcation diagram for odd piecewise linear control systems," Dyn. Stab. Syst. 11, 49-88.
14. Moreno, I. & Súarez, R. [2004] "Existence of periodic orbits of stable saturated systems," Syst. Contr. Lett. 51, 293-309.
15. Rapp, P. E. & Mees, A. I. [1977] "Spurious predictions of limit cycles in a non-linear feedback system by the describing function method," Int. J. Contr. 26, 821-829.