Bifurcations of fractional-order diffusionless Lorenz system

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.