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Página principal > Artículos > Artículos publicados > Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems |
Fecha: | 2020 |
Resumen: | The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed non-autonomous n-dimensional discontinuous piecewise smooth differential system. As a fundamental hypothesis, it is assumed that the unperturbed system has a manifold Z ⊂ Rn of periodic solutions satisfying dim(Z) < n. Then, we apply this result to study limit cycles bifurcating from periodic solutions of linear differential systems, x0 = Mx, when they are perturbed inside a class of discontinuous piecewise polynomial differential systems with two zones. More precisely, we study the periodic solutions of the following differential system x0 = Mx + εFn 1 (x) + ε2Fn 2 (x), in Rd+2 where ε is a small parameter, M is a (d+2)×(d+2) matrix having one pair of pure imaginary conjugate eigenvalues, m zeros eigenvalues, and d−m non-zero real eigenvalues. |
Ayudas: | Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-0410 |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Averaging method ; Filippov system ; Limit cycle ; Nonsmooth dynamical system ; Nonsmooth polynomial differential systems ; Periodic orbit ; Polynomial differential system |
Publicado en: | Revista Matemática Iberoamericana, Vol. 36, Núm. 1 (2020) , p. 291-318, ISSN 0213-2230 |
Postprint 31 p, 575.7 KB |