Algebraic determination of limit cycles in 3-dimensional piecewise linear differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ponce, Enrique (Universidad de Sevilla. Departamento de Matemática Aplicada II)
Ros Padilla, Javier (Universidad de Sevilla. Departamento de Matemática Aplicada II)

Data:	2011
Resum:	We study a one-parameter family of symmetric piecewise linear differential systems in R^3 which is relevant in control theory. The family, which has some intersection points with the adimensional family of Chua's circuits, exhibits more than one attractor even when the two matrices defining its dynamics in each zone are stable, in an apparent contradiction with the 3-dimensional Kalman's conjecture. For these systems we characterize algebraically their symmetric periodic orbits and obtain a partial view of the one-parameter unfolding of its triple-zero degeneracy. Having at our disposal exact information about periodic orbits of a family of nonlinear systems, which is rather unusual, the analysis allows us to assess the accuracy of the corresponding harmonic balance predictions. Also, it is shown that certain conditions in Kalman's conjecture can be violated without losing the global asymptotic stability of the origin.
Ajuts:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Nota:	Agraïments: The second and third authors are partially supported by an MEC/FEDER grant number MTM2009-07849
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Harmonic balance ; Kalman's conjecture ; Limit cycles ; Periodic orbit ; Piecewise linear differential systems
Publicat a:	Nonlinear Analysis : Theory, Methods and Applications, Vol. 74 (2011) , p. 6712-6727, ISSN 0362-546X

DOI: 10.1016/j.na.2011.06.051

Postprint 44 p, 528.6 KB

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