Design and dynamics of discrete dual-memristor chaotic maps and its application in speech encryption

Recently, the design and application of discrete memristors (DMs) have become one of the most innovative research hotspots. Compared with single-memristor chaotic maps, dual-memristor chaotic maps can exhibit more complex dynamical behaviors, stronger memory characteristics, and a more flexible structure. In this paper, we design two types of dual-memristor chaotic maps based on the modulation and switching. Each map is further categorized into two types according to the DM, and the corresponding Simulink models are built. Dynamical behaviors of these systems are analyzed using bifurcation diagrams, Lyapunov exponent spectra (LEs), 2-D bifurcation diagrams, attractor phase diagrams, and SE complexity measuring. Numerical results show that the proposed chaotic maps have rich dynamics. And when different DMs are introduced, dynamics of the modulation maps are different, but for the switching maps, dynamical behaviors are similar. Meanwhile, the PSIM analogue circuit is used to verify the physical realizability of the proposed model and circuits one of the proposed modulation mapping systems is designed. The simulation results are consistent with the numerical simulation results. Finally, an application of voice encryption is carried out, and its security and performance are analyzed. It shows that the designed chaotic maps have potential engineering application value.