Complex dynamics and encryption application of memristive chaotic system with various amplitude modulations

The exploration of memristive chaotic system has garnered immense interest and attention in recent years. This paper endeavors to construct a novel four-dimensional memristive chaotic system by incorporating a third-order flux-controlled memristor into a simple chaotic system, leading to the emergence of chaos, periodicity and stability. The dynamic characteristics of the system are manifested through bifurcation diagrams, Lyapunov exponents and phase portraits. The most prominent feature of the system lies in its amplitude modulation, enabling it to achieve varying degrees of amplitude control by modulating the parameters. To validate its practical applicability, a cross-plane color image encryption algorithm has been devised and rigorously subjected to a comprehensive performance analysis. Numerical analysis results show that the NPCR and UACI are 99.6078% and 33.4661%, the correlation coefficients are close to 0, and the maximum information entropy reaches 7.9998. These results conclusively demonstrate the superior efficacy of the system in image encryption.