An Amplitude-controllable 3-D Hyperchaotic Map with Homogenous Multistability

Abstract By introducing a sinusoidal function into a three-dimensional map, a hyperchaotic map with three positive Lyapunov exponents is derived. The system has two amplitude controllers, a total controller, and a partial controller. The hyperchaotic map shares a unique structure of two-leaf and three-leaf attractors under united Lyapunov exponents. Furthermore, homogenous multistability is found in the 3-D map, where the initial data determine the attractor structure combined with the distance between any two leaves. Experimental hardware based on STM32 is built to prove the numerical findings. The hyperchaotic map is introduced for color image encryption. The analysis of key space, histogram, information entropy, correlation, and anti-noise infection shows its powerful performance in encryption and security.