  Using the predictor-corrector scheme, the fractional order diffusionless
Lorenz system is investigated numerically. The effective chaotic range of the
fractional order diffusionless system for variation of the single control
parameter is determined. The route to chaos is by period-doubling bifurcation
in this fractional order system, and some typical bifurcations are observed,
such as the flip bifurcation, the tangent bifurcation, an interior crisis
bifurcation, and transient chaos. The results show that the fractional-order
diffusionless Lorenz system has complex dynamics with interesting
characteristics.
