Abstract
By using a linear feedback control technique, we propose a chaos synchronization scheme for nonlinear fractional discrete dynamical systems. Then, we construct a novel 1-D fractional discrete income change system and a kind of novel 3-D fractional discrete system. By means of the stability principles of Caputo-like fractional discrete systems, we lastly design a controller to achieve chaos synchronization, and present some numerical simulations to illustrate and validate the synchronization scheme.
Highlights
Over the last decades, increasing interest has been shown in fractional differential calculus, which has been successfully applied to various fields, such as biology [1], fluid mechanics [2], materials science [3], physics [4], and economics [5]
Fractional discrete calculus has gained more and more attention and a lot of interesting results have emerged in mathematics [6,7,8,9,10,11,12,13], medical science [14], physics [15,16], and so on
Most mentioned synchronization schemes of fractional differential systems can be used in the synchronization of fractional discrete dynamical systems
Summary
Over the last decades, increasing interest has been shown in fractional differential calculus, which has been successfully applied to various fields, such as biology [1], fluid mechanics [2], materials science [3], physics [4], and economics [5]. Just as the linear feedback control technique can be employed to achieve the synchronization of fractional differential systems, one may spontaneously want to know whether or not it can be used to obtain the synchronization of fractional discrete dynamical systems. Xin et al employed the linear feedback control technique to design projective synchronization schemes for chaotic discrete dynamical systems [32] and Entropy 2017, 19, 351; doi:10.3390/e19070351 www.mdpi.com/journal/entropy. The linear feedback control technique will be applied to achieve the synchronization of fractional discrete dynamical systems. Comparing the aforementioned four synchronization schemes for fractional discrete dynamical systems [8,28,29,30], the linear feedback control technique is easier to design and implement but is more intuitive for the simplest linear stability theory of fractional discrete dynamical systems.
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