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.

Implementation of an improved chaotic encryption algorithm for real-time embedded systems by using a 32-bit microcontroller

“…Although the chaotic dynamic is well analyzed by several techniques such as Lyapunov exponent, cobweb plots, Jacobian analysis, autocorrelation, histograms, etc., the authors do not presented a cryptosystem based on the chaotic sequence for security purposes. In the same year, San-Um and Ketthong [27] proposed a generalization of four chaotic maps with absolute value nonlinearity. In a similar form that [25] , an experimental implementation of the chaotic waveform generator is performed by using an Arduino microcontroller and the chaotic sequence is analyzed by using similar techniques.…”

Implementation of a Hyperchaotic System with Hidden Attractors into a Microcontroller

“…Also, in 2014, the same authors proposed a generalization of four chaotic maps with absolute value nonlinearity [26], which is experimentally implemented by using an Arduino microcontroller. Furthermore, Andreatos and Volos in 2014 presented a microcontroller implementation of a text encryption algorithm based on a chaotic Chua system [27].…”

Research on encryption algorithms in terahertz communication systems

“…The pseudo-random sequence generated by it has good randomness, and one-dimensional chaotic mapping is simple in design and low in computational cost, making it easier to generate pseudo-random sequences [12][13] [14] . In this paper, a simple one-dimensional absolute value nonlinear mapping proposed in document [15] is improved, and the expression is generalized.…”