本文透過在原本的Genesio渾沌系統增加一個回授控制，進而產生一個新的Genesio渾沌系統。我們通過應用各種技術來討論此新渾沌系統的動力學行為。這些技術包括相圖、平衡點分析、散度分析、頻譜分析、分歧圖及Lyapunov指數圖，然後在電路板上生成渾沌信號。在控制理論部分，通過應用適應性控制、順滑控制完成同步，以及利用適應性順滑控制新的Genesio渾沌系統。另外我們也利用單向和雙向耦合控制完成此新的Genesio渾沌系統的同步控制。我們也在FPGA板上實現渾沌信號電路，並藉由此渾沌訊號對圖像作安全加密演算法。而且，我們成功利用耦合同步控制在FPGA板上進行圖像解密演算法。在這項研究中，我們將渾沌主系統轉成數位訊號，進而對圖像加密，並利用同步後的從系統對圖像進行解密。

The chaotic system is proposed in this study by adding a feedback control to the Genesio chaotic system. We discuss the dynamical behaviors of the new Genesio chaotic system by applying various techniques. These techniques include phase portraits, equilibrium point analysis, divergence computing, power spectrum analysis, bifurcation diagrams and Lyapunov exponent diagrams. We also generate the chaotic signals of the new Genesio system on realized circuit board. In control theory, we utilize the adaptive control, the sliding mode control to complete synchronization. We also control the new Genesio chaotic system by the adaptive sliding mode control. Besides, we also use unidirectional and mutual control to make a slave system be synchronized with the new Genesio system. We implement the chaotic signal circuits by using FPGA board and implement these chaotic signals for image secure encryption algorithm. In addition, we successfully utilize the synchronization of the coupled control with the new Genesio system for the image encryption algorithm on FPGA. We change the maser chaotic system to digital signals and use them to encrypt the image and use the digital signals of the synchronized slave system to decrypt the image in this study.

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