Stochastic Degradation of the Fixed-point version of 2D-Chaotic Maps

M. ANTONELLI; H. A. LARRONDO; L. DE MICCO

CHAOS, SOLITONS AND FRACTALS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2017 vol. 104 p. 477 - 484

0960-0779

This paper deals with a family of interesting 2D-quadratic maps proposed by Sprott, in his seminal paper, related to ``chaotic art". Our main interest about these maps is their great potential for using them in digital electronic applications, because they present multiple chaotic attractors depending on the selected point in the parameter´s space. Only results for the analytical representation of these maps have been published in the open literature. Consequently the objective of this paper is to extend the analysis to the digital version, to make possible the hardware implementation in a digital medium, like field programmable gate arrays (FPGA) in fixed-point arithmetic.Our main contributions are: (a) the study of the domains of attraction in fixed-point arithmetic, in terms of period lengths and statistical properties; (b) the determination of the threshold of the bus width that preserves the integrity of the domain of attraction and (c) the comparison between two quantifiers based on respective probability distribution functions (PDFs) and the well known maximum Lyapunov exponent (MLE) to detect the above mentioned threshold.