BIFURCATIONS AND CHAOS IN FRACTIONAL-ORDER SIMPLIFIED LORENZ SYSTEM

KEHUI SUN, XIA WANG
School of Physics Science and Technology, Central South University,
Changsha 410083, P. R. China
kehui@csu.edu.cn; wangxiacsu@163.com

J.C. SPROTT
Department of Physics, University of Wisconsin-Madison,
Madison, WI 53706, USA
sprott@physics.wisc.edu

ABSTRACT

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behavior in the fractional-order simplified Lorenz system using the time-domain scheme. Chaos does exist in this system for a wide range of
fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams, and Lyapunov exponents. Both the system parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this system to yield chaos is 2.62.

Ref: K. Sun, X. Wang, and  J. C. Sprott, International Journal of Bifurcation and Chaos 20, 1209-1219 (2010)

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