Stochastic degradation of the fixed-point version of 2D-chaotic maps

This paper deals with a family of interesting 2D-quadratic maps proposed by Sprott, in his seminal paper [1], 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.Fil: de Micco, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica.; ArgentinaFil: Antonelli, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica.; ArgentinaFil: Larrondo, Hilda Angela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica.; Argentin