Adaptive fixed-time difference synchronization for different classes of chaotic dynamical systems

Abstract

This article examines adaptive fixed-time difference synchronization for various
classes of chaotic dynamical systems. The adaptive fixed-time control technique has been used in
this article to investigate the difference synchronization for the Sprott chaotic system, both with
and without delay. The fixed settling time (T) have been estimated successfully. It is also shown
that the trajectories of error states approach to the origin within a fixed time (T). The theoretical
analysis is validated by simulating Sprott chaotic systems both with and without delay. On the
other hand, various nonlinear chaotic systems are explored for difference synchronization in
discrete chaotic systems. Several chaotic maps, including Tinkerbell, Henon, and Hitzl-Zele,
have been used to achieve synchronization in these discrete systems. The numerical results are
presented graphically, verifying the theoretical outcomes of difference synchronization for
various classes of chaotic dynamical systems