Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

Abstract

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator

“…The validity of the chaos control and the synchronization approach was verified theoretically, and this analysis was also confirmed by some simulations in Figs. [7][8][9][10][11][12][13][14][15][16][17][18]. Finally, as the future direction of this manuscript, we will consider more practical models, which will also be more complicated from the mathematical point of view.…”

“…In [10], an adaptive terminal sliding mode control was applied to the chaotic Chen and hyperchaotic Lorenz systems. In [11], considering the stability theory of Lyapunov, the authors synchronized three nonidentical systems of different dimensions.…”

Secure Communication Using Modified Fractional and Inverse Matrices Synchronization Methods

“…However, in our work, we have considered the projective matrix as non-diagonal matrix with non-constant, time-variant entries too. Certainly, not much work has been done using difference synchronization [3] which happens to be an alternative to combination synchronization.…”

Combination Difference Synchronization between Identical Generalised Lotka-Volterra Chaotic Systems

“…We have arranged the remaining article as: Sec 2: formulates the problem; Sec 3: develops the synchronization theory. Sec 4: conducts the combination difference synchronization scheme [6][7][8]. Sec 5: consists of the discussions regarding numerical simulations and displays the results performed in MATLAB.…”