本文透過在順滑二次獨立混沌系統加入一個回授控制，進而產生一個新LC渾沌系統。我們透過相圖，散度分析，頻譜分析，分歧圖和李亞普洛夫指數圖這些技術來分析並了解新的渾沌系統的動力學行為。在控制理論部分，通過應用GYC部分區域穩定理論，渾沌系統的主動牽制控制並減少控制器因子完成同步。利用適應性控制在複數網路實現渾沌系統同步。此外，我們使用渾沌系統在FPGA上的圖像加密演算法已經實現並討論直方圖分析、信息熵分析和差分分析。

The new LC chaotic system is presented in this study by adding a feedback control to smooth quadratic autonomous chaotic system which is discovered. We also discuss the dynamical behaviors of the new LC chaotic system by applying various techniques. These techniques include phase portraits, divergence computing, power spectrum analysis, bifurcation diagrams and Lyapunov exponent diagrams. In the part of control theory, by applying GYC partial region stability theory, active pinning control synchronization and reduce pinning controller factor of chaotic system is accomplished. The synchronization of chaotic system using adaptive complex feedback control in complex networks is proposed. In addition, an Image encryption algorithm on FPGA using the new LC chaotic system is achieved. We also discuss histogram analysis, information entropy analysis and differential attack analysis in this study.

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