Abstract The present study proposes a new fractional-order hyperchaotic memristor oscillator. The proposed system is studied through numerical simulations and analyses, such as the Lyapunov exponents, bifurcation diagrams, and phase portraits. Then, using the sliding mode concept, a robust adaptive control scheme is designed to synchronize the proposed system. The adaptation mechanism is implemented to estimate the unknown parameters of the slave system. Then, the output of the proposed adaptation mechanism is used for the control scheme. The stability of the closed-loop system is proven via a fractional version of the Lyapunov stability theorem and Barbalat's lemma. Numerical simulations of synchronization are shown to investigate the performance of the developed control technique on the uncertain fractional-order hyperchaotic memristor oscillator. Finally, as an engineering application, the proposed fractional-order system is implemented for voice encryption. In this regard, to show the appropriate performance of the proposed system for voice encryption, statistical characteristic of the encryption and decryption processes are performed through different methods including correlation, entropy, root mean square, and root sum of squares.

中文翻译：

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一种新的分数阶超混沌忆阻器振荡器：动态分析、鲁棒自适应同步及其在语音加密中的应用

摘要 本研究提出了一种新的分数阶超混沌忆阻振荡器。通过数值模拟和分析，如李雅普诺夫指数、分岔图和相图，研究了所提出的系统。然后，使用滑模概念，设计稳健的自适应控制方案来同步所提出的系统。自适应机制用于估计从系统的未知参数。然后，所提出的自适应机制的输出用于控制方案。通过 Lyapunov 稳定性定理和 Barbalat 引理的分数版本证明了闭环系统的稳定性。显示了同步的数值模拟，以研究开发的控制技术对不确定分数阶超混沌忆阻器振荡器的性能。最后，作为工程应用，所提出的分数阶系统用于语音加密。在这方面，为了显示所提出的语音加密系统的适当性能，加密和解密过程的统计特性通过不同的方法来执行，包括相关性、熵、均方根和平方根和。