Bifurcations of Fractional-order Diffusionless Lorenz System
Kehui Sun1,2 and J. C. Sprott2
1School of Physics
Science and Technology, Central South University, Changsha 410083 China
2Department of Physics,
University of Wisconsin-Madison, Madison, WI 53706 USA
Received 5 July 2009, Accepted 15 August 2009, Published 30 October 2009
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.