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Entropy 2019, 21(4), 384;

Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

Centro de Investigaciones en Óptica, Loma del Bosque 115, 37150 León, Mexico
División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 107, 37150 León, Mexico
Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de León 1144, Paseos de la Montaña, Lagos de Moreno, 47460 Jalisco, Mexico
Author to whom correspondence should be addressed.
Received: 24 October 2018 / Revised: 23 November 2018 / Accepted: 4 December 2018 / Published: 10 April 2019
PDF [1659 KB, uploaded 10 April 2019]


In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element. View Full-Text
Keywords: spatial dynamics; Bogdanov Map; chaos; laser; resonator spatial dynamics; Bogdanov Map; chaos; laser; resonator

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Aboites, V.; Liceaga, D.; Jaimes-Reátegui, R.; García-López, J.H. Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator. Entropy 2019, 21, 384.

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