[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()

时滞非线性薛定谔方程的指数同步 及其在光纤保密通信中的应用

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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

时滞非线性薛定谔方程的指数同步 及其在光纤保密通信中的应用

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

卞立双¹, 殷久利² , 田梦姣², 范兴华²

¹南京理工大学自动化学院, 南京 210094; ²江苏大学理学院, 镇江 212013

Keywords:

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

保密通讯;  Melnikov方法;  非线性薛定谔方程;  指数同步

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.

为了进一步探究光纤通信的保密特性, 研究了时滞非线性薛定谔方程的指数同步问题.时滞混沌系统具有产生多个正的李雅普诺夫指数的可能性, 且不受系统维数的限制.首先利用分岔理论进行了同宿轨分析, 研究发现系统存在2条同宿轨, 根据对应关系, 系统存在孤立波.其次, 利用Melnikov方法证明了同宿轨在任意扰动下可以演变为混沌, 进而将混沌信号作为信息传输的载体.系统的Lyapunov指数谱图、相图以及时间序列分析同样证明了混沌的存在性.再次, 设计了指数同步控制器, 实现驱动系统和响应系统的混沌同步, 并利用Lyapunov稳定性理论进行了证明.最后, 利用MATLAB对误差系统进行了数值仿真, 发现误差很快趋向于零.研究结果表明, 所提出的指数同步方案可在1 s内实现驱动系统和响应系统的同步.

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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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