A Class of Discrete Memristor Chaotic Maps Based on the Internal Perturbation

Further exploration into the influence of a memristor on the behavior of chaotic systems deserves attention. When constructing memristor chaotic systems, it is commonly believed that increasing the number of memristors will lead to better system performance. This paper proposes a class of chaotic maps with different discrete memristors, achieved through internal perturbation based on the Sine map. The I-V curve of the discrete memristor has a symmetrical structure. The dynamic characteristics of the designed system are analyzed using the chaotic attractor phase diagram, Lyapunov exponent (LE) spectrum, and bifurcation diagram. Numerical simulations demonstrate that internal perturbations of discrete memristors enhance the Sine map's chaotic characteristics, expand the chaos range, and improve the ergodicity and LE value. Moreover, the type of discrete memristors has a significant impact on the dynamic characteristics of the system, while the number of discrete memristors has little influence. Therefore, in this paper, a direction for the design of a discrete memristor chaotic system is provided. Finally, a discrete memristor chaotic map with a simple structure and better performance is selected. Based on this, a pseudo-random sequence generator is designed, and the generated sequence passes the National Institute of Standards and Technology (NIST) test.

Automated summary

This study investigates the influence of discrete memristors on chaotic system behavior and proposes a class of chaotic maps with discrete memristors based on the Sine map. Numerical simulations demonstrate that internal perturbations of discrete memristors enhance the Sine map's chaotic characteristics, expand the chaos range, and improve ergodicity and the Lyapunov exponent. The type of discrete memristors significantly impacts the dynamic characteristics of the system, while the number of discrete memristors has little influence. Therefore, this study provides a direction for the design of discrete memristor chaotic systems.