Abstract
In this article two different controllers for the stabilization of a fractional-order discrete system in the left Caputo discrete delta operator sense are given. The first one acts by a fractional proportional pulse control, the second acts by a fractional feedback control. These controllers are applied to fractional-order chaotic discrete dynamical systems to obtain their stability and also we show a comparison with the integer order dynamical systems stability. Some simulations are presented for the fractional logistic map and the fractional Henon map.
Highlights
I N THE last decades, a considerable number of investigations has been devoted to the analysis of chaos control
The control of chaos is understood by the stabilization of discrete or continuous chaotic systems to a steady state or a periodic orbit
Manoeuvres to control chaos have been tested in different branches such as laboratory physics, cardiology and biochemistry
Summary
I N THE last decades, a considerable number of investigations has been devoted to the analysis of chaos control. The control of chaos is understood by the stabilization of discrete or continuous chaotic systems to a steady state or a periodic orbit. Stability analysis using Lyapunov functions and synchronization has been applied in the logistic fractional discrete equation, and in the well-known two-dimensional Henon map [17]. Some investigations have used control methods to chaos fractional discrete maps [18], [19]. QUEZADA-TÉLLEZ et al.: CONTROLLING CHAOS FOR FRACTIONAL-ORDER DISCRETE SYSTEM of momentum to control chaotic dynamics of logistic fractional map. On another hand, in [19] a kicked method is applied on a damped rotator map.
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