Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension
The orbits of the reversible differential system ˙x = -y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = -y, ˙y = x,...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:169449 |
| Acceso en línea: | https://ddd.uab.cat/record/169449 https://dx.doi.org/urn:doi:10.1080/14689367.2015.1102868 |
| Access Level: | acceso abierto |
| Palabra clave: | Averaging theory Discontinuous polynomial differential system Limit cycle Periodic orbit |
| Sumario: | The orbits of the reversible differential system ˙x = -y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = -y, ˙y = x, ˙z = 0, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y. |
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