Four Novel Dual Discrete Memristor-Coupled Hyperchaotic Maps

Abstract

Unlike the high-dimensional hyperchaotic system based on a continuous memristor, the low-dimensional map coupled by discrete memristor (DM) and traditional chaotic map can also generate hyperchaos. However, the hyperchaotic map constructed by two DMs has not attracted much attention. To this end, a generalized two-dimensional dual DM-coupled hyperchaotic mapping model is reported in this paper, and four specific maps are provided. The proposed maps have line invariant points, which can be interpreted as allowing arbitrary real values for the initial condition associated with the DM, and the stability is investigated in detail. Furthermore, the coupling strength-dependent and initial condition-dependent complex dynamics of four maps are studied by numerical simulations, and the dynamical performance is evaluated from the perspective of quantitative analysis. It is shown that the considered maps are capable of exhibiting the three characteristic fingerprints of memristors in arbitrary parameter spaces, and this characteristic has gained attention for the first time. In particular, the complete control of the considered maps by variable substitution is performed, which can generate arbitrary switched hyperchaotic behaviors. In addition, four pseudo-random number generators are designed based on the proposed maps, and the randomness is tested by using the NIST SP800-22 software. In general, the proposed maps can not only generate abundant dynamical behaviors, but also enrich the DM circuits and provide a reference for applications based on chaos. Finally, the developed digital hardware circuit implementation platform verifies the results of the numerical method.