Chaos in Fractional-order Autonomous Nonlinear Systems
Wajdi M. Ahmad
Department of Electrical and Electronics Engineering,
of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates
J. C. Sprott
Department of Physics, University
Wisconsin, Madison, WI 53706, USA
(Accepted 19 September 2002)
We numerically investigate chaotic behavior in autonomous nonlinear
of fractional order. Linear transfer function approximations
fractional integrator block are calculated for a set of fractional
in (0, 1], based on frequency domain arguments, and the resulting
models are studied. Two chaotic models are considered in this
an electronic chaotic oscillator, and a mechanical chaotic "jerk"
In both models, numerical simulations are used to demonstrate that
different types of model nonlinearities, and using the proper
chaotic attractors are obtained with system orders as low as
Consequently, we present a conjecture that third-order chaotic
systems can still produce chaotic behavior with a total system of
2 + eps, 1 > eps > 0, using the appropriate control
effect of fractional order on the chaotic range of the control
is studied. It is demonstrated that as the order is decreased,
chaotic range of the control parameter is affected by contraction
Robustness against model order reduction is demonstrated.
Ref: W. M. Ahmad and J. C. Sprott,
Solitons and Fractals
16, 339-351 (2003)
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