A novel simplest four‐dimensional hyperchaotic system with dual memristors is designed by using a charge‐controlled memristor and a generalized voltage‐controlled memristor. Based on the conventional dynamic analysis method and MATLAB simulation software, the dynamic characteristics of the dual memristor hyperchaotic system such as Lyapunov exponent spectrum, phase diagram, and bifurcation diagram are studied. The novel system is found to exhibit singular nonlinear phenomena, such as limit cycle, state transition and multiple scroll attractor with certain parameter values. Being different from most known chaotic systems, which contain only two isolated unstable equilibrium points, the novel system has an infinite number of unstable equilibriums points and a larger Lyapunov exponent. What is more, the three‐fold function projection synchronization of the dual memristor hyperchaotic system and its application for secure communication is studied. Based on Lyapunov stabilization theory and adaptive sliding mode control method, three driving systems and three response systems are synchronized according to the corresponding scaling function matrix, respectively. In the secure communication system, the message signal is separated into three parts loaded in the different drive systems with different initial conditions to increase the reliability. The corresponding numerical simulations demonstrate the effectiveness of the results obtained.

中文翻译：

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基于三重函数投影同步的新型双忆阻超混沌系统及其在安全通信中的应用

通过使用电荷控制的忆阻器和广义的电压控制的忆阻器，设计了一种具有双忆阻器的新颖，最简单的四维超混沌系统。基于传统的动力学分析方法和MATLAB仿真软件，研究了双忆阻超混沌系统的动力学特性，如李雅普诺夫指数谱，相图和分叉图。发现该新颖系统表现出奇异的非线性现象，例如极限环，状态转变和具有特定参数值的多涡旋吸引子。与仅包含两个孤立的不稳定平衡点的大多数已知混沌系统不同，该新颖系统具有无限数量的不稳定平衡点和更大的Lyapunov指数。更，研究了双忆阻器超混沌系统的三重函数投影同步及其在安全通信中的应用。基于Lyapunov稳定理论和自适应滑模控制方法，分别根据相应的缩放函数矩阵对三个驱动系统和三个响应系统进行同步。在安全通信系统中，将消息信号分为三个部分，分别装入具有不同初始条件的不同驱动系统中，以提高可靠性。相应的数值模拟证明了所得结果的有效性。三个驱动系统和三个响应系统分别根据相应的缩放函数矩阵进行同步。在安全通信系统中，将消息信号分为三个部分，分别装入具有不同初始条件的不同驱动系统中，以提高可靠性。相应的数值模拟证明了所得结果的有效性。三个驱动系统和三个响应系统分别根据相应的缩放函数矩阵进行同步。在安全通信系统中，将消息信号分为三个部分，分别装入具有不同初始条件的不同驱动系统中，以提高可靠性。相应的数值模拟证明了所得结果的有效性。