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Pàgina inicial > Articles > Articles publicats > Integrability and dynamics of a simplified class B laser system |
Data: | 2023 |
Resum: | 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 ≠ 0, we study its dynamics in the Poincaré ball B 3, i. e. , the interior of this ball is identified with R 3 and its boundary the two-dimensional sphere S 2 is identified with the infinity of R 3. |
Ajuts: | Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agencia Estatal de Investigación PID2021-122954NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113 |
Drets: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Publicat a: | Chaos, Vol. 33, Issue 10 (October 2023) , art. 103119, ISSN 1089-7682 |
10 p, 616.4 KB |