Integrability and dynamics of a simplified class B laser system
A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [Opt. Commun. 51, 308–314 (1984)] and Politi et al. [Phys. Rev. A 33, 4055 (1986)], and still n...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/397062 |
| Acceso en línea: | https://hdl.handle.net/2117/397062 https://dx.doi.org/10.1063/5.0169342 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomials Dynamics Integral equations Polinomis Dinàmica Equacions integrals Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [Opt. Commun. 51, 308–314 (1984)] and Politi et al. [Phys. Rev. A 33, 4055 (1986)], and still nowadays, it attracts the interest of the researchers. In this paper, we characterize its dynamics near infinity for all values of the parameters. When a = 0, the partial integrability was already proved by Oppo and Politi [Z. Phys. B Con. Mat. 59, 111–115 (1985)]. Here, we prove that for a = 0, it is completely integrable with two independent first integrals given by Liouvillian functions, and we present a complete study of its dynamics. When a 6 = 0, we study its dynamics in the Poincaré ball B3, i.e., the interior of this ball is identified with R3 and its boundary the two-dimensional sphere S2 is identified with the infinity of R3. |
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