本文在研究一個新Shimizu–Morioka渾沌系統，並運用相圖、散度分析、頻譜分析、平衡點分析、Lyapunov指數等技術，分析此系統的特性與運動行為，接著模擬實際電路與渾沌同步的數值分析。在控制理論部分，利用倒階控制、適應性控制、GYC 部份穩定理論與BGYC 同步方法，設計控制器運用於此渾沌系統，使主系統和從系統可以同步。在驗證提出的模型和控制器後，使用FPGA板實現渾沌信號電路，並藉由此渾沌訊號對圖像作安全加密演算法，並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 new Shimizu–Morioka chaotic system is presented in this study. We use techniques include phase portraits, divergence computing, power spectrum analysis, equilibrium point analysis and Lyapunov exponent to analysis and understanding of the dynamical behaviors of the chaotic system. Furthermore, we simulate the real circuit and chaos synchronization of numerical analysis. In control theory, we utilize backstepping control, adaptive control, GYC partial region stability theory and BGYC synchronization control to make a slave system be synchronized with the new Shimizu–Morioka chaotic system. After validating the proposed model and controller, the chaotic synchronization and encryption are implemented with FPGA board. 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 Shimizu–Morioka system for the image encryption algorithm on FPGA. We change the master 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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