Bifurcations of Fractional-order Diffusionless Lorenz System

Kehui Sun^1,2 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

ABSTRACT

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.

Ref: K. Sun and J. C. Sprott, Electronic Journal of Theoretical Physics 6, 123-134 (2009)