四維度的Chen – Lee 系統的渾沌動力分析及其廣義同步

Abstract

本文透過增加一組控制方程式在Chen – Lee渾沌系統，進而產生一個新的四維度的Chen – Lee渾沌系統。我們運用創新的方法來分析及呈現四維度Chen – Lee系統的3D相圖及其投影圖，使我們對於四維度Chen – Lee系統有更清楚的了解。藉由系統參數的變動我們可以獲得動態更為複雜的四維度Chen – Lee系統，此參數同時也是一組隨著時間改變的渾沌訊號。本文也探討四維度Chen – Lee系統的控制與同步，並利用GYC部分區域穩定理論來達成適應性控制，除此之外也將基因演算法(Genetic Algorithm)應用至適應性控制來達成同步。在本文中，此渾沌系統被加以實現於電路上，除了四維度Chen – Lee系統的電路模擬以及電路同步模擬外，也實際將四維度Chen – Lee系統的電子電路實現化，並以示波器觀察此系統實際相位圖。

A new four dimensional chaotic system is presented in this study by adding one more feedback control equation to the Chen – Lee system which is discovered by Chen and Lee in 2004. We use an innovative technique to present the 3-dimensional phase portraits and its projection simultaneously in order to have a better understanding of the four dimensional Chen – Lee system. A more complicated four dimensional Chen – Lee system with uncertain chaotic parameter is proposed. By applying GYC partial region stability theory, adaptive generalized chaos synchronization of the four dimensional Chen – Lee system is accomplished; in addition, the adaptive control is also accomplished by applying genetic algorithm. Furthermore, the adaptive control of the four dimensional Chen – Lee system is implemented on electronic circuit. An electronic circuit board of the four dimensional Chen – Lee system is realized in this thesis.