The The Van der Pol equation: qualitative and numerical study
This expositive paper aims at the study of nonlinear equations, focused on the van der Pol equation, including deduction, qualitative analysis, and numerical examples. The van der Pol equation is deduced using an electrical circuit as a physical model. The qualitative analysis is divided into two pa...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Costa Rica |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Idioma: | inglés |
| OAI Identifier: | oai:portal.ucr.ac.cr:article/50545 |
| Acceso en línea: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/50545 |
| Access Level: | acceso abierto |
| Palabra clave: | Van der Pol equation Lyapunov function Qualitative analysis Numerical integration Ecuación de Van der Pol Función de Lyapunov Análisis cualitativo integración numérica |
| Sumario: | This expositive paper aims at the study of nonlinear equations, focused on the van der Pol equation, including deduction, qualitative analysis, and numerical examples. The van der Pol equation is deduced using an electrical circuit as a physical model. The qualitative analysis is divided into two parts: the theoretical enunciation and its application. The main theorems used in this study are Poincaré-Bendixson’s and Lyapunov’s. The construction of a Lyapunov function is also performed. Finally, a series of numerical examples are graphically presented using computational tools such as Python and Octave. The phase portraits and temporal behavior of the van der Pol equation are exhibited, along with the basin of attraction obtained experimentally, compared with the basin of attraction yielded by the Lyapunov function. Therefore, the numerical study provides a visual representation of the results stated in the qualitative analysis |
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