[1] Bian Lishuang, Yin Jiuli, Tian Mengjiao, Fan Xinghua, et al. Exponential synchronization for delayed nonlinear Schrödingerequation and applications in optical secure communication [J]. Journal of Southeast University (English Edition), 2019, 35 (4): 447-452. [doi:10.3969/j.issn.1003-7985.2019.04.007]

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Exponential synchronization for delayed nonlinear Schrödingerequation and applications in optical secure communication()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

35

Issue:

2019 4

Page:

447-452

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2019-12-30

Info

Title:

Exponential synchronization for delayed nonlinear Schrödingerequation and applications in optical secure communication

Author(s):

Bian Lishuang¹;  Yin Jiuli²;  Tian Mengjiao²;  Fan Xinghua²

¹School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
²Faculty of Science, Jiangsu University, Zhenjiang 212013, China

Keywords:

secure communication;  Melnikov method;  nonlinear Schrö dinger equation;  exponential synchronization

PACS:

O231.2

DOI:

10.3969/j.issn.1003-7985.2019.04.007

Abstract:

For further exploring the confidentiality of optical communication, exponential synchronization for the delayed nonlinear Schrödinger equation is studied. It is possible for time-delay systems to generate multiple positive Lyapunov exponents without the limitation of system dimension. Firstly, the homoclinic orbit analysis is carried out by using the bifurcation theory, and it is found that there are two homoclinic orbits in the system. According to the corresponding relationship, solitary waves also exist in the system. Secondly, the Melnikov method is used to prove that homoclinic orbits can evolve into chaos under arbitrary perturbations, and then chaotic signals are used as the carriers of information transmission. The Lyapunov exponent spectrum, phase diagram and time series of the system also prove the existence of chaos. Thirdly, an exponential synchronization controller is designed to achieve the chaotic synchronization between the driving system and the response system, and it is proved by the Lyapunov stability theory. Finally, the error system is simulated by using MATLAB, and it is found that the error tends to zero in a very short time. Numerical simulation results demonstrate that the proposed exponential synchronization scheme can effectively guarantee the chaotic synchronization within 1 s.

References:

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Memo

Memo:

Biographies: Bian Lishuang(1993—), female, Ph.D. candidate; Yin Jiuli(corresponding author), male, doctor, professor, yjl@ujs.edu.cn.
Foundation items: The National Natural Science Foundation of China(No. 71673116, 71690242), the Humanistic and Social Science Foundation from Ministry of Education of China(No.16YJAZH007), the Natural Science Foundation of Jiangsu Province(No. SBK2015021674).
Citation: Bian Lishuang, Yin Jiuli, Tian Mengjiao, et al.Exponential synchronization for delayed nonlinear Schr?dinger equation and applications in optical secure communication[J].Journal of Southeast University(English Edition), 2019, 35(4):447-452.DOI:10.3969/j.issn.1003-7985.2019.04.007.

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