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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 Matemática Aplicada II)
Ros, Javier (Universidad de Sevilla. Departamento 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.
Nota: Número d'acord de subvenció MINECO/MTM2008-03437
Nota: Número d'acord de subvenció AGAUR/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 ; preprint
Matèria: Harmonic balance ; Kalman’s conjecture ; Limit cycles ; Periodic orbit ; Piecewise linear differential systems
Publicat a: Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, Vol. 74 (2011) , p. 6712-6727, ISSN 0362-546X

DOI: 10.1016/

44 p, 528.6 KB

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