A 3D discrete memristor hyperchaotic map with application in dual-channel random signal generator

Abstract

Chaotic systems are widely used in many applications for their pseudo-random sequences of fixed mathematical models. Several academics and engineers prefer using discrete maps for their simplicity in mathematical models and quick implementation. Nevertheless, the easily disrupted chaotic behavior of most discrete maps, such as the Logistic Map, is a significant barrier to their generalization. This paper proposes a 3D parallel memristive logistic map (3D-PMLM) to address this issue. The 3D-PMLM can enhance the complexity of a 1D Logistic map by introducing multidimensional controllable parameters. Performance evaluations demonstrate that the 3D-PMLM has more robust hyperchaotic behavior across a broader range of chaos than existing discrete maps. An experimental platform, based on FPGA and DAC, is put forth to implement the chaotic behavior of 3D-PMLM in hardware. Moreover, the application of 3D-PMLM is further demonstrated through the design and implementation of a dual-channel random signal generator featuring an update period of 1us. The experimental results indicate that the output analog signal is random in three dimensions.