Chaos in a fractional order modified Duffing system

In this paper, the chaotic behaviors in a fractional order modified Duffing system are studied numerically by phase portraits, Poincaré maps and bifurcation diagrams. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0, 1], based on frequency domain arguments. The total system orders found for chaos to exist in such systems are 1.8, 1.9, 2.0 and 2.1.