Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems
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 differentia...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:224217 |
| Acceso en línea: | https://ddd.uab.cat/record/224217 https://dx.doi.org/urn:doi:10.4171/rmi/1131 |
| Access Level: | acceso abierto |
| Palabra clave: | Averaging method Filippov system Limit cycle Nonsmooth dynamical system Nonsmooth polynomial differential systems Periodic orbit Polynomial differential system |
| Sumario: | 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. |
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