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Entropy 2019, 21(4), 384; https://doi.org/10.3390/e21040384

Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

1
Centro de Investigaciones en Óptica, Loma del Bosque 115, 37150 León, Mexico
2
División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 107, 37150 León, Mexico
3
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
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Abstract

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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