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Chaos control in the fractional order logistic map via impulses

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Nonlinear Dynamics, 98(2), 1219–1230 (2019) .

Full text: http://dx.doi.org/10.1007/s11071-019-05257-2

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Pre-print (draft before peer review) - added by Marius Florin Danca

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Abstract

In this paper the chaos control in the discrete logistic map of fractionalorder is obtained with an impulsive control algorithm. The underlying discreteinitial value problem of fractional order is considered in terms of Caputo deltafractional difference. Every∆steps, the state variable is instantly modi ed withthe same impulse value, chosen from a bifurcation diagram versus impulse. Itis shown that the solution of the impulsive control is bounded. The numericalresults are veri ed via time series, histograms, and the 0-1 test. Several examplesare considered

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