The Unreasonable Effectiveness of the Chaotic Tent Map in Engineering Applications

From decimal expansion of real numbers to complex behaviour in physical, biological and human-made systems, deterministic chaos is ubiquitous. One the simplest examples a nonlinear dynamical system that exhibits well known 1-dimensional piecewise linear Tent map. The map (and their skewed cousins) are instances larger family maps namely Generalized Luröth Series (GLS) which studied for rich number theoretic ergodic properties. In this work, we discuss unreasonable effectiveness generalizations (GLS maps) applications electronics, communication computer engineering. To list few these applications: (a) GLS-coding: lossless data compression algorithm i.i.d sources Shannon optimal fact generalization popular Arithmetic Coding used image standard JPEG2000; (b) GLS as neurons recently proposed Neurochaos Learning architecture delivers state-of-the-art performance classification tasks; (c) ideal candidates chaos-based computing since they can simulate XOR, NAND other gates dense storage information efficient search retrieval; (d) Noise-resistant versions useful signal multiplexing presence noise error detection; (e) shown be cryptographic protocols - joint encryption also generating pseudo-random numbers. unique properties features Map enable wide variety engineering will investigated. A open problems indicated well.