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
[email protected];
[email protected]
J.C. SPROTT
Department of Physics,
University of
Wisconsin-Madison,
Madison, WI 53706, USA
[email protected]
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)
The complete paper is available
in PDF format.
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