Suppressing chaos in discontinuous systems of fractional order by active control

Marius-F. Danca and Roberto Garrappa

Applied Mathematics and Computation, 2015, vol. 257, issue C, 89-102

Abstract: In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov’s convex regularization and via differential inclusions, the underlying discontinuous initial value problem is first recast in terms of a set-valued problem and hence it is continuously approximated by using Cellina’s Theorem for differential inclusions. For chaos control, an active control technique is implemented so that the unstable equilibria become stable. As example, Shimizu–Morioka’s system is considered. Numerical simulations are obtained by means of the Adams–Bashforth–Moulton method for differential equations of fractional-order.

Keywords: Discontinuous chaotic systems of fractional order; Filippov regularization; Cellina’s Theorem; Sigmoid function; Differential equations of fractional-order; Chaos control (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:89-102

DOI: 10.1016/j.amc.2014.10.133

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