Analysis of a Novel Amplitude-Controlled Memristive Hyperchaotic Map and Its Utilization in Image Encryption

In this paper, a global amplitude-controlled discrete hyperchaotic memristive map is designed utilizing the hyperbolic tangent function. This map exhibits fixed points arranged in a line along the y-axis, and the stability distributions of these fixed points are delineated based on variations in both the initial conditions of the map and the parameter plane. The dynamic characteristics of the map were examined through the analysis of its 2D dynamics and the largest Lyapunov exponent (LE) distribution. The existence of multistability was robustly confirmed through a comprehensive analysis of the basin of attraction, the spectra of LE that depend on initial values, bifurcation diagrams, and trajectory plots. Additionally, the amplitude of the map can be adjusted both globally and locally through manipulation of the non-bifurcation parameter. Subsequently, a digital circuit powered by a microcontroller was designed to embody the map. In comparison to recent maps, the newly devised map exhibits superior efficacy in the realm of image encryption applications.