https://doi.org/10.1140/epjd/s10053-022-00435-1
Regular Article - Optical Phenomena and Photonics
Pyragas method and chaos in higher-order nonlinear Schrödinger equation in an optical fiber
1
Higher Teachers’ Training College, University of Maroua, P.O. Box 55, Maroua, Cameroon
2
Faculty of Sciences, University of Maroua, P.O. Box 814, Maroua, Cameroon
3
National Advanced School of Engineering, University of Maroua, P.O. Box 46, Maroua, Cameroon
4
The Abdus Salam International Centre for Theoretical Physics, P.O. Box 538, Strada costiera 11, I-34014, Trieste, Italy
Received:
16
March
2022
Accepted:
6
June
2022
Published online:
20
June
2022
Various dynamic behaviors of the higher-order nonlinear Schrödinger (HNLS) equation are investigated in an optical fiber. The governing model is converted into the planar dynamical system with the help of Galilean transformation. Through the effective potential and their corresponding phase portrait, the effects of the self-phase modulation and the quintic nonlinearity on the unperturbed system are addressed. Moreover, we performed different numerical tools such as time series, phase portraits as well as the Poincaré section, which show that the perturbed system transits from the quasi-periodic state to the chaotic state according to the frequency 
and the strength of the external perturbation 
. The chaotic phenomena can be controlled by using the Pyragas method. This work finds its applications in broadband telecommunications which extend in the infrared spectral region, the doping of optical fiber as well as the encryption of information.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022
