Coupled systems of non-smooth differential equations

Jacquemard, Alain; Tonon, Durval J.

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Coupled systems of non-smooth differential equations

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Author(s):	Jacquemard, Alain ^[1] ; Tonon, Durval J. ^[2] Total Authors: 2
Affiliation:	^[1] Univ Bourgogne, Inst Math Bourgogne, CNRS, UMR 5584, Dijon - France ^[2] Univ Fed Goias, IME, BR-74001970 Goiania, Go - Brazil Total Affiliations: 2
Document type:	Journal article
Source:	BULLETIN DES SCIENCES MATHEMATIQUES; v. 136, n. 3, p. 239-255, APR-MAY 2012.
Web of Science Citations:	4
Abstract
We study the geometric qualitative behavior of a class of discontinuous vector fields in four dimensions. Explicit existence conditions of one-parameter families of periodic orbits for models involving two coupled relay systems are given. We derive existence conditions of one-parameter families of periodic solutions of systems of two second order non-smooth differential equations. We also study the persistence of such periodic orbits in the case of analytic perturbations of our relay systems. These results can be seen as analogous to the Lyapunov Centre Theorem. (C) 2012 Elsevier Masson SAS. All rights reserved. (AU)

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