Bifurcation sets of symmetrical continuous piecewise linear systems with three zones

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 12, Issue 8, 2002, Pages 1675-1702

  Freire, Emilio ^a   Ponce, Enrique ^a   Rodrigo, Francisco ^a   Torres, Francisco ^a  

^a Escuela Universitaria Politecnica   (Spain)

Author keywords

Invariant closed curves; Piecewise linear systems; Poincar half maps

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; OSCILLATIONS; SET THEORY; VECTORS;

PIECEWISE LINEAR SYSTEMS;

LINEAR SYSTEMS;

EID: 0036696771     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127402005509     Document Type: Article

References (18)

1. Andronov, A., Vitt, A. & Khaikin, S. [1966] Theory of Oscillations (Pergamon Press, Oxford), Chap. 8, pp. 443-582.
2. Chua, L.O. & Deng, A. [1986] "Canonical piecewise linear modeling," IEEE Trans. Circuits Syst. 33, 511-525.
3. Freire, E., Ponce, E., Rodrigo, F. & Torres, F. [1998] "Bifurcations sets of continuous piecewise linear systems with two zones," Int. J. Bifurcation and Chaos 8(11), 2073-2097.
4. Freire, E., Ponce, E. & Ros, J. [1999] "Limit cycle bifurcation from center in symmetric piecewise-linear systems," Int. J. Bifurcation and Chaos 9(5), 895-907.
5. Freire, E., Rodrigo, F. & Torres, F. [2001] "On the existence of limit cycles in an analog circuitry for the Van der Poi and Fitzhugh-Nagumo equations," in preparation.
6. Hartman, P. [1982] Ordinary Differential Equations (Birkäuser, Boston).
7. Keener, J.P. [1983] "Analog circuitry for the Van der Pol and Fitzhugh-Nagumo equations," IEEE Trans. Syst. Man Cybern. 13(5), 1010-1014.
8. Kriegsmann, G.A. [1987] "The rapid bifurcation of the Wien bridge oscillator," IEEE Trans. Circuits Syst. CAS-34, 1093-1096.
9. Liénard, A. [1928] "Etude des oscillations entretenues," Revue Générale d'Electricité XXIII 21, 901-912; XXIII 23, p. 946.
10. Liénard, A. [1928] "Etude des oscillations entretenues," Revue Générale d'Electricité XXIII 21, 901-912; XXIII 23, p. 946.
11. Llibre, J. & Ponce, E. [1999] "Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields," Nonlin. Anal. 36, 623-653.
12. Llibre, J. & Sotomayor, J. [1996] "Phase portraits of planar control systems," Nonlin. Anal. TMA 27, 1177-1197.
13. 2," Memorandum UCB/ERL M90/29, University of California at Berkeley.
14. Madan, R.N. [1993] Chua's Circuit: A Paradigm for Chaos, World Scientific Series on Nonlinear Science, Serie B (World Scientific, Singapore).
15. Marsden, J. & McCracken, M. [1976] The Hopf Bifurcation and Its Applications, Appl. Math. Sci., Vol. 19 (Springer-Verlag, NY).
16. Mees, A.I. & Chua, L.O. [1979] "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. Circuits Syst. 26, 235-254.
17. Robinson, C. [1995] Dynamical Systems (CRC Press, Boca Raton, FL).
18. Teruel, A.E. [2000] Clasificación topológica de una familia de campos vectoriales lineales a trozos en el plano, PhD dissertation, Universitat Autònoma de Barcelona, Barcelona Spain (in Spanish).