Yuan Ye, Yu Fei, Tan Bohong, Huang Yuanyuan, Yao Wei, Cai Shuo, Lin Hairong
School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China.
School of Electronic Information, Central South University, Changsha 410083, China.
Chaos. 2025 Jan 1;35(1). doi: 10.1063/5.0238893.
Memristors are commonly used to introduce various chaotic systems and can be used to enhance their chaotic characteristics. However, due to the strict construction conditions of Hamiltonian systems, there has been limited research on the development of memristive Hamiltonian conservative chaotic systems (MHCCSs). In this work, a method for constructing three-terminal memristors is proposed, and the three-terminal memristors are incorporated into the Hamiltonian system, resulting in the development of a class of n-D MHCCS. Based on this method, we model a 4D MHCCS as a standard model for detailed dynamic analysis. The dynamic analysis reveals that the MHCCS exhibits complex dynamic behaviors, including conservativeness, symmetry, chaos depending on parameters, extreme multistability, and chaos under a wide parameter range. The dynamic analysis shows that MHCCS not only retains the favorable characteristics of a conservative system but also has more complex nonlinear dynamics due to the incorporation of memristors, thereby further enhancing its chaotic characteristics. Furthermore, the pseudo-random number generator based on the MHCCS has excellent randomness in terms of the NIST test. Finally, the physical realizability of the system is verified through Field Programmable Gate Array experiments. This study demonstrates that the constructed class of MHCCSs is a good entropy source that can be applied to various chaotic embedded systems, including secure communication, cryptographic system, and pseudo-random number generator.
忆阻器通常用于引入各种混沌系统，并可用于增强其混沌特性。然而，由于哈密顿系统严格的构建条件，关于忆阻哈密顿保守混沌系统（MHCCSs）的发展研究有限。在这项工作中，提出了一种构建三端忆阻器的方法，并将三端忆阻器纳入哈密顿系统，从而开发出一类n维MHCCS。基于此方法，我们将一个4维MHCCS建模为用于详细动态分析的标准模型。动态分析表明，该MHCCS表现出复杂的动态行为，包括保守性、对称性、参数依赖的混沌、极端多稳定性以及在宽参数范围内的混沌。动态分析表明，MHCCS不仅保留了保守系统的良好特性，而且由于纳入了忆阻器而具有更复杂的非线性动力学，从而进一步增强了其混沌特性。此外，基于MHCCS的伪随机数发生器在NIST测试方面具有出色的随机性。最后，通过现场可编程门阵列实验验证了该系统的物理可实现性。这项研究表明，所构建的一类MHCCSs是一种良好的熵源，可应用于各种混沌嵌入式系统，包括安全通信、密码系统和伪随机数发生器。
