本文選題：非線性薛定諤方程 + 混沌同步　； 參考：《江蘇大學》2017年碩士論文

【摘要】：本學位論文主要借助非線性動力學方法對一類非線性薛定諤方程的混沌同步問題進行了研究。通過理論分析和Melnikov方法探究了周期擾動下一類非線性薛定諤方程的混沌存在條件并進行了數值驗證。通過數值仿真,研究不同參數對一類非線性薛定諤方程的混沌同步的影響。本文首先以擾動非線性系統為例分析和模擬了光孤子和怪波脈沖的傳播。當擾動參數超過一定值時,孤子脈沖變成不穩(wěn)定狀態(tài):孤子分裂為兩個分支或改變其變換方向;但怪波脈沖可以恢復其波形并繼續(xù)傳播直至消失。鑒于非線性動力系統易產生混沌,且對混沌具有操控性,本文在后面的研究中對混沌的產生進一步探討,并且設計混沌同步以實現以薛定諤方程為模型的光纖保密通信。其次研究了以擾動的薛定諤方程為模型的光纖保密通信。在含有多重頻率的擾動薛定諤方程中,混沌信號可以從光孤子中產生。理論分析和數值模擬表明,混沌的產生與重數無關。通過反饋控制可以得到混沌同步且同步的速度與非線性薛定諤方程的參數選取有關。由Lyapunov穩(wěn)定性理論,同步誤差可以用非線性矩陣不等式來表示。最后主要研究外部環(huán)境和系統參數對光學保密通信的影響。當光孤子信號受到外部干擾時,可以很容易地產生混沌信號。即使派生系統和原始系統有一些差異時,也可以實現混沌同步。結果表明較小的差異可以導致更快的同步。通過本章還可以得到,改變系統參數可以影響混沌同步的速度,適當的參數對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.
【學位授予單位】：江蘇大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O415.5

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本文編號：2080513