Design of a Weighted Average Chaotic System for Robust Chaotic Operation

Abstract

In this paper, we propose a novel technique to attain a robust 1-D chaotic system. The robustness of the system is characterized by the presence of an uninterrupted chaotic region throughout the entire parameter space with excellent chaotic properties. This wide chaotic region is a crucial characteristic for practical applications where parameter disturbance may push the system out of chaotic operation. Our proposed system is comprised of the weighted average of multiple 1-D chaotic seed maps and is a generalized framework for developing robust chaos using any number of seed maps. The uninterrupted chaotic range and improved chaotic entropy is demonstrated using the bifurcation plot, Lyapunov exponent, Shannon entropy, correlation coefficient, and Kolmogorov entropy. We also demonstrate how cascading can be used to further improve the ergodicity of the proposed system. The proposed method can be useful in many applications such as chaos-based cryptography, secure communication, reconfigurable logic gate, random number generation, and so on.