Phase Portraits of the Equation x¨ + axx˙ + bx3 = 0
The second-order differential equation x¨ + axx˙ + bx3 = 0 with a, b ∈ R has been studied by several authors mainly due to its applications. Here, for the first time, we classify all its phase portraits in function of its parameters a and b. This classification is done in the Poincaré disc in order...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:307725 |
| Acceso en línea: | https://ddd.uab.cat/record/307725 https://dx.doi.org/urn:doi:10.1134/S1560354724560053 |
| Access Level: | acceso abierto |
| Palabra clave: | Second-order differential equation Poincaré compactification Global phase portraits |
| Sumario: | The second-order differential equation x¨ + axx˙ + bx3 = 0 with a, b ∈ R has been studied by several authors mainly due to its applications. Here, for the first time, we classify all its phase portraits in function of its parameters a and b. This classification is done in the Poincaré disc in order to control the orbits which scape or come from infinity. We prove that there are exactly six topologically different phase portraits in the Poincar'e disc of the first order differential system associated by the second-order differential equation. Additionally we show that this system is always integrable providing explicitly its first integrals. |
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