Bifurcation and chaos in the fractional Chua and Chen systems with very low order

Abstract

The aim of this work is to analyze the chaotic behaviors in the fractional-order Chua and Chen systems via a time-domain approach. The objective is achieved using a decomposition method, which allows the solution of the fractional differential equations to be written in closed form. Specifically, by taking advantage of the capabilities given by time-domain analysis, the paper illustrates three remarkable findings: i) chaos exists in the fractional Chua system with very low order, that is, 0.03, which represents the lowest order reported in literature for any dynamical system studied so far; ii) chaos exists in the fractional Chen system with order as low as 0.24, which represents the smallest value reported in literature for the Chen system; iii) it is feasible to show the occurrence of pitchfork bifurcations and perioddoubling routes to chaos in the fractional Chen system, by virtue of a systematic time-domain analysis of its dynamics.