A family of robust chaotic S-unimodal maps based on the Gaussian function

Abstract

This research paper introduces a family of one-dimensional S-unimodal maps based on the Gaussian function, designed to exhibit robust chaos across a wide range of parameters. These maps are developed to display robust chaos by avoiding multiple fixed points that are primarily responsible for the coexisting attractors in 1D maps. The parameter space analysis reveals that chaotic behaviour is sustained across the entire parameter space, except for a very narrow region. The study employs a comprehensive computational approach, including quantitative measures such as sample entropy, Lyapunov exponent, and invariant measures. The uniformly higher values of sample entropy, uniform positive values of the Lyapunov exponent, and the existence of invariant measures in a region of parameter space confirm the presence of robust chaos in these maps. Such a promising class of robust chaotic maps may be potentially used in diverse fields such as chaos-based cryptography, pseudo-random number generation, communication systems, and more.