Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
The following differential quadratic polynomial differential system dx/dt=y-x, dy/dt=2y-y/y-1(2-yy-5y-4/y-1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of rad...
| 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:289972 |
| Acceso en línea: | https://ddd.uab.cat/record/289972 https://dx.doi.org/urn:doi:10.3390/appliedmath4010004 |
| Access Level: | acceso abierto |
| Palabra clave: | Isotropic star Polynomial differential equation Phase portrait Poincaré disc |
| Sumario: | The following differential quadratic polynomial differential system dx/dt=y-x, dy/dt=2y-y/y-1(2-yy-5y-4/y-1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. First, we classify all the topologically non-equivalent phase portraits in the Poincaré disc of these quadratic polynomial differential systems for all values of the parameter y∈R∖{1}. Second, using the information of the different phase portraits obtained we classify the possible limit values of m(r)/r and 4πr2ρ of an isotropic star when r decreases. |
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