Controlling Chaos for a Fractional-Order Discrete System

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.

Keywords

• Caputo delta difference
• chaos
• discrete fractional calculus
• Mittag–Leffler