Chaos in the fractional Chua and Chen systems with lowest-order

Abstract

This paper investigates bifurcation and chaos in the fractional-order Chua and Chen systems from the time-domain point of view. The objective is achieved using a decomposition method, which allows the solution of the fractional differential equations to be written in closed form. 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 period-doubling routes to chaos in the fractional Chen system, by virtue of a systematic time-domain analysis of its dynamics.