The generalization of mathematically simple and robust chaotic maps with absolute value nonlinearity

Abstract

This paper presents a generalization of four chaotic maps with absolute value nonlinearity. The proposed four maps are mathematically simple through the use of absolute value nonlinearity which is in a category of piecewise-linear nonlinearity. Moreover, the proposed maps exhibits robust chaos as there is an absence of periodic windows and coexisting attractors in neighborhood of parameter spaces. Dynamic properties are described in terms of Cobweb plots, bifurcations, Lyapunov exponents, and chaotic waveforms in time domain. Experimental results utilize the Ardino microcontroller to generate chaotic waveforms with a relatively flat spectrum in frequency domain. The application in random-bit generator that passes all NIST standard tests is also included.