Some more robustness conditions for the invariant density of a class of 1D maps under additive noise

Abstract

Circuits based on chaotic maps are increasingly appealing to synthesize signals with prescribed statistical features. However, in their implementation one should not forget that electronic noise can affect the statistics, even by a large amount. Although dealing with the effects of noise on a strongly nonlinear system can be hard, it has recently been proved that classes of chaotic maps exist whose invariant density is completely insensitive to it, a property that makes them particularly well suited for implementation. This paper builds upon that initial framework, offering a wider set of sufficient conditions for general noise robustness. It also illustrates that other noise robustness mechanisms exist when the particular (yet reasonable) assumption of symmetrically distributed noise is made.