A class of <i>n</i>-D Hamiltonian conservative chaotic systems with three-terminal memristor: Modeling, dynamical analysis, and FPGA implementation

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.