Dynamical analysis and hardware implementation of discrete memristive chaotic maps based on time-delay closed-loop coupling

Abstract Due to the discrete memristor’s inherent nonlinear and memory characteristics, its application in chaotic systems has attracted extensive attention in recent years. In this paper, a method for constructing a closed-loop structure of multiple discrete memristive chaotic maps via time-delay coupling is proposed, and a time-delay closed-loop system composed of three maps (3-MDCLS) is designed based on this structure. The study reveals that the dynamical behaviors of the system are dependent on the delay length, which is specifically manifested in the morphological variations of attractors, the significant enhancement of hyperchaotic characteristics, and the phenomenon of attractor offset. Further analysis indicates that with the variation of delay length, the regularity of the offset boosting behavior of the system is broken. To verify the physical realizability of the theoretical results, the attractor images of the system under different delay lengths are successfully captured on an oscilloscope. In addition, a class of pseudorandom number generators is designed based on this system, and the NIST tests verify that the randomness of the generated sequences under different delay lengths all meets the standards, thus proving that this structure has favorable reliability and practicability in engineering applications.