PapersNo Access
BIFURCATION OF INVARIANT CONES IN PIECEWISE LINEAR HOMOGENEOUS SYSTEMS
https://doi.org/10.1142/S0218127405013423Cited by:40
Abstract
Invariant surfaces in three-dimensional continuous piecewise linear homogeneous systems with two pieces separated by a plane are detected. The Poincaré map associated to this plane transforms half-straight lines passing through the origin into half-straight lines of the same type. The invariant half-straight lines under this map determine invariant cones for which the existence, stability and bifurcation are studied. This analysis lead us to consider some questions about the topological type and stability of the origin.
References
-
V. N. Afanas'ev , V. B. Kolmanosvskii and V. R. Nosov , Mathematical Theory of Control Systems Design ( Kluwer Academic Publishers , 1995 ) . Google Scholar -
A. A. Andronov , A. Vitt and S. Khaikin , Theory of Oscillations ( Pergamon Press , Oxford , 1966 ) . Crossref, Google Scholar - Commun. Math. Phys. 79, 573 (1981). Crossref, ISI, Google Scholar
-
S. Barnet and R. G. Cameron , Introduction to Mathematical Control Theory ( Oxford University Press , NY , 1985 ) . Google Scholar - J. Math. Anal. Appl. 172, 463 (1993). Crossref, ISI, Google Scholar
- Carmona, V. [2002] Bifurcaciones en Sistemas Lineales a Trozos, Ph. D. Dissertation, Universidad de Sevilla (in Spanish) . Google Scholar
- IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 49, 609 (2002). Crossref, ISI, Google Scholar
- IMA J. Appl. Math. 69, 71 (2004). Crossref, ISI, Google Scholar
- Int. J. Bifurcation and Chaos 8, 2073 (1998). Link, ISI, Google Scholar
- Int. J. Bifurcation and Chaos 8, 1675 (2002). ISI, Google Scholar
-
J. Guckenheimer and P. Holmes , Nonlinear Oscillationsô Dynamical Systemsô and Bifurcations of Vector Fields ( Springer-Verlag , NY , 1985 ) . Google Scholar - J. Diff. Eqs. 95, 183 (1992). Crossref, ISI, Google Scholar
- Z. Naturforsch-A 40, 1011 (1985). Crossref, Google Scholar
- J. Circuit Th. Appl. 16, 11 (1988). Crossref, ISI, Google Scholar
- Amer. J. Math. 85, 225 (1963). Google Scholar
-
Z. Zhang , Qualitative Theory of Differential Equations ,Translations of Mathematical Monographs 101 ( American Mathematical Society , Providence, RI , 1992 ) . Google Scholar
