1-D Robust Chaotic Maps Through Systematic Shifting and Halfway Shifted Product

This paper introduces a novel methodology for the generation of robust chaotic 1-D maps with an emphasis on creating an uninterrupted chaotic region and improving the chaotic properties across the entire parameter space. In our proposed technique, we manipulated the chaotic seed maps through systematic shifts, which resulted in pronounced improvements in their chaotic properties. The effectiveness of this approach is demonstrated through a comprehensive analysis employing bifurcation plots, maximum Lyapunov exponent, average Lyapunov exponent, and chaotic ratio. These collectively demonstrate the attainment of a wide uninterrupted chaotic range as well as the improved chaotic characteristics introduced by the shifted maps. Furthermore, the paper explores the effects of combining one of the seed maps and one of the halfway shifted maps by demonstrating that, their product adds additional improvements in chaotic properties. This proposed technique contributes to various applications such as random number generation, chaos-based cryptography, ensuring secure communication, and so on.