A New Matrix Projective Synchronization of Fractional-Order Discrete-Time Systems and its Application in Secure Communication

Abstract

In this study, it is proposed that a new matrix projective synchronization of fractional-order (FO) chaotic maps in discrete-time. A new synchronization error is introduced and a control law is constructed, which makes the synchronization error converge towards zero in sufficient time under the stability theory of linearization method of FO systems. Numerical simulation results are presented to illustrate the feasibility of the scheme. Finally, a secure communication scheme based on FO discrete-time (FODT) systems was proposed.

Chaos in the Real World: Recent Applications to Communications, Computing, Distributed Sensing, Robotic Motion, Bio-Impedance Modelling and Encryption Systems

“…In [11], a matrix projective synchronization scheme for fractional-order maps is presented. A novel synchronization error is introduced, and a control algorithm is designed to stabilize the error dynamics at the origin.…”

“…A novel synchronization error is introduced, and a control algorithm is designed to stabilize the error dynamics at the origin. The synchronization of fractional maps is exploited for a secure communication application, which includes speech encryption over a public channel [11].…”

“…The manuscript is organized as follows. In Section 2 the applications of chaos to communications are illustrated [2][3][4][5][6][7][8][9][10][11][12], including the use of chaos in radar-based systems and underwater acoustic channels. Section 3 highlights how chaos may represent a promising approach in sensing applications [13], whereas Section 4 illustrates different applications of chaos in robotic motion [14][15][16].…”

Bifurcation Analysis and Fractional PD Control of Gene Regulatory Networks with sRNA

“…So it is fit for describing systems with recollection and historical dependence processes and can represent and simulate natural objects more precisely. As an arbitrary extension of integral calculus on order, fractional calculus has shown substantial advantages and broad application background in many fields such as power systems [4,5], biological systems [6,7], secure communication [8,9], finance [10,11] and physics [12,13]. The development and application of fractional calculus theory have injected new vitality into studying gene regulatory networks.…”