周期扰动下一类非线性薛定谔方程的混沌同步问题研究

发布时间：2018-06-29 02:52

本文选题：非线性薛定谔方程 + 混沌同步　；参考：《江苏大学》2017年硕士论文

【摘要】：本学位论文主要借助非线性动力学方法对一类非线性薛定谔方程的混沌同步问题进行了研究。通过理论分析和Melnikov方法探究了周期扰动下一类非线性薛定谔方程的混沌存在条件并进行了数值验证。通过数值仿真,研究不同参数对一类非线性薛定谔方程的混沌同步的影响。本文首先以扰动非线性系统为例分析和模拟了光孤子和怪波脉冲的传播。当扰动参数超过一定值时,孤子脉冲变成不稳定状态:孤子分裂为两个分支或改变其变换方向;但怪波脉冲可以恢复其波形并继续传播直至消失。鉴于非线性动力系统易产生混沌,且对混沌具有操控性,本文在后面的研究中对混沌的产生进一步探讨,并且设计混沌同步以实现以薛定谔方程为模型的光纤保密通信。其次研究了以扰动的薛定谔方程为模型的光纤保密通信。在含有多重频率的扰动薛定谔方程中,混沌信号可以从光孤子中产生。理论分析和数值模拟表明,混沌的产生与重数无关。通过反馈控制可以得到混沌同步且同步的速度与非线性薛定谔方程的参数选取有关。由Lyapunov稳定性理论,同步误差可以用非线性矩阵不等式来表示。最后主要研究外部环境和系统参数对光学保密通信的影响。当光孤子信号受到外部干扰时,可以很容易地产生混沌信号。即使派生系统和原始系统有一些差异时,也可以实现混沌同步。结果表明较小的差异可以导致更快的同步。通过本章还可以得到,改变系统参数可以影响混沌同步的速度,适当的参数对加速混沌同步具有重要作用。
[Abstract]:In this dissertation, the chaotic synchronization of a class of nonlinear Schrodinger equations is studied by means of nonlinear dynamics. The existence conditions of chaos for a class of nonlinear Schrodinger equations under periodic perturbation are studied by theoretical analysis and Melnikov method. The effects of different parameters on chaotic synchronization of a class of nonlinear Schrodinger equations are studied by numerical simulation. In this paper, the propagation of solitons and strange waves is analyzed and simulated by taking the perturbation nonlinear system as an example. When the disturbance parameter exceeds a certain value, the soliton pulse becomes unstable: the soliton splits into two branches or changes its transformation direction, but the strange wave pulse can recover its waveform and continue to propagate until it disappears. In view of the chaos is easy to be generated in nonlinear dynamical system and it is controlled by chaos, this paper further discusses the chaos generation in the following research, and designs chaos synchronization to realize the secure communication based on Schrodinger equation. Secondly, the optical fiber secure communication based on the perturbation Schrodinger equation is studied. In the perturbation Schrodinger equation with multiple frequencies, chaotic signals can be generated from optical solitons. Theoretical analysis and numerical simulation show that chaos is independent of multiplicity. The speed of synchronization and synchronization can be obtained by feedback control, which is related to the parameter selection of nonlinear Schrodinger equation. Based on Lyapunov stability theory, synchronization errors can be represented by nonlinear matrix inequalities. Finally, the influence of external environment and system parameters on optical secure communication is studied. Chaotic signals can be easily generated when soliton signals are interfered with. Chaotic synchronization can be achieved even if there are some differences between the derived system and the original system. The results show that smaller differences can lead to faster synchronization. Through this chapter, it can be concluded that changing the system parameters can affect the speed of chaotic synchronization, and the appropriate parameters play an important role in accelerating chaos synchronization.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5

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