J.L. Adams, T.T. Hartley, and C.F. Lorenzo (USA)
Fractional-Order Calculus, Fractional-Order System, Chua System, Chaos, Low-Order Chaos 1 A Review of Fractional-Order Operators Two commonly used definitions for the fractional-order differintegral are the Grunwald definition and the Riemann Liouville definition [1] [2] [3]. In this paper the fractional order derivative is assumed to be that of Riemann and Li ouville. The Riemann-Liouville definition for integration of noninteger order is d−q dt−q f(t) = 1 Γ(q) t 0 (t − τ) q−1 f(τ
The conventional understanding of order holds that the or der of a system is the degree of its highest order deriva tive. This paper presents a system whose order is less than two which exhibits chaotic characteristics. Specifically, a fractional-order Chua system of order 1.9 is shown to un dergo period doubling bifurcation and eventually displays a double scroll attractor. The chaotic behavior is predicted theoretically, and then demonstrated through simulation.
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