On taming chaos using LTI filters

Abstract

In a recent paper [l] the possibility of suppressing chaos using linear time-invariant (LTI) filters is considered with numerical experiments concerning a specific chaotic system (the logistic map) and low-order filters. In this letter, simple arguments based on the frequency response of linear systems and on the Liapunov exponents are used to point out that the experimental result of [l] (i.e., a low-order LTI filter cannot destroy nor delay chaos in the logistic map) has general validity, namely it can be extended to any continuous or discrete-time chaotic system and to LTI filters of any order.