Limit cycle bifurcation in 3D continuous piecewise linear systems with two zones. Application to Chua's circuit

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 10, 2005, Pages 3153-3164

  Carmona, V ^a   Freire, E ^a   Ponce, E ^a   Ros, J ^a   Torres, F ^a  

^a UNIVERSIDAD DE SEVILLA   (Spain)

Author keywords

Bifurcations; Limit cycles; Piecewise linear systems

Indexed keywords

EID: 29244445839     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405014027     Document Type: Article

References (13)

1. 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.
2. Chow, S. N. & Hale, J. K. [1982] Methods of Bifurcation Theory (Springer-Verlag).
3. Chua, L. O. & Lin, G. [1990] "Canonical realization of Chua's circuit family," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 37, 885-902.
4. Chua, L. O., Wu, C. W., Huang, A. & Zhong, G.-Q. [1993] "A universal system for studying and generating chaos -Part I: Routes to chaos," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 40, 732-744.
5. 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.
6. 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.
7. Kahlert, C. & Rossler, O. E. [1985] "Analytical properties of Poincaré halfmaps in a class of piecewise-linear dynamical system," Z. Naturforsch. A40, 1011-1025.
8. Kennedy, M. P. [1993] "Three steps to chaos -Part II: A Chua's circuit premier," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 40, 657-674.
9. Khalert, C. [1988] "The ranges of transfer and return maps in three-region piecewise-linear dynamical systems," J. Circuit Th. Appl. 16, 11-23.
10. Kriegsmann, G. A. [1987] "The rapid bifurcation of the Wien bridge oscillator," IEEE Trans. Circuits Syst. 34, 1093-1096.
11. n," Int. J. Bifurcation and Chaos 14, 2843-2851.
12. Quarles, T., Newton, A. R., Pederson, D. O. & Sangiovanni- Vincentelli, A. [1993] Spice3 Version 3f3 User's Manual, Department of Electrical Engineering and Computer Sciences, University of California Berkeley, Ca., 94720.
13. Wilkinson, J. H. [1965] The Algebraic Eigenvalue Problem (Oxford University Press).