A Minimal-Form $ n $-D Memristive Conservative Chaotic System: Modeling, Multiscroll Regulation, and Efficient Circuit Implementation

In recent years, memristive Hamiltonian conservative chaotic systems (MHCCSs) have become a research hotspot in nonlinear dynamics and information security, yet their development remains constrained by complex model structures, limited high-dimensional scalability, and inefficient hardware implementation. To address this, a novel voltage-differencing three-terminal memristor (VDTTM) model is proposed, whose simple operational logic significantly enhances the efficiency of system modeling. Based on this model, this article presents, for the first time, a systematic construction paradigm for the simplest memristive Hamiltonian conservative chaotic system (SMHCCS), which features the fewest polynomial terms and the lowest proportion of nonlinear terms among systems of the same dimension, outperforming those reported in recent studies. Furthermore, the extended multiscroll system based on SMHCCS (SMHCCS-MS) verifies the feasibility of realizing multiscroll generation and multifeature regulation in MHCCSs. Subsequently, the efficient circuit design of the 4-D SMHCCS and SMHCCS-MS was carried out on a field-programmable gate array (FPGA). Experimental results show that the 4-D SMHCCS system outperforms recent reports in terms of resource utilization, throughput, and other performance metrics. Entropy analysis and NIST tests indicate that the systems achieve high randomness. This study provides a novel paradigm for the systematic modeling of MHCCSs and offers new technical avenues for their efficient hardware implementation and secure pseudorandom number generation in resource-constrained environments.