Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems

Abstract

The effects of using frequency-domain approximation in numerical simulation of fractional-order systems are analytically studied. The main aim in the study is to determine the number, location and stability property of the equilibriums in a fractional-order system and its frequency-based approximating counterpart. The comparison shows that the original fractional-order system and its frequency-based approximation may differ from each other in some or all issues considered in the study. Unfortunately, these differences can lead to wrong consequences in some special cases such as detecting chaos in the fractional-order systems. It is shown that using the frequency-domain approximation methods can conceal chaotic behaviour for a chaotic fractional-order system or display chaos for a non-chaotic one. Therefore one should be careful and conservative in using these methods to recognise chaos in the fractional-order systems.