Bifurcation analysis of a circuit-related piecewise-affine map

Abstract

In this paper, a two-parameter bifurcation analysis of a piecewise-affine map is carried out. Such a map derives from a well-known map, which has good features from its circuit implementation point of view and good statistical properties in the generation of pseudo-random sequences. The considered map is a generalization of it, and the bifurcation parameters take into account some common circuit implementation non-idealities or mismatches. In view of a robust design of the map, this bifurcation analysis should come before a statistical analysis, to find a set of parameters ensuring both robust chaotic dynamics and robust statistical properties.