Dynamical analysis of a novel memristor-type chaotic map

Abstract

Abstract As a unique nonlinear component, the discrete memristor, with its simple structure, is associated with the ability to lead to excellent chaotic performance in the construction of chaotic systems. This characteristic has elevated the discrete memristor to a hot topic in the field of chaos. This paper introduces a cosine hyperchaotic map. Numerical simulations reveal its rich dynamical behaviors. The chaotic map exhibits diverse chaotic control models, including partial amplitude control, total amplitude control, initial boosting, and parameter-offset boosting, with dynamical distribution diagrams plotted for amplitude control to quantify the range of amplitude modulation. Additionally, a localized boosting free region is identified, which exhibits extreme sensitivity to initial values. Dual offset parameters are introduced to control this localized boosting free region, enhancing the flexibility of the system. Finally, the map is implemented on STM32 to validate the numerical simulation results.