Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

Abstract

This paper concerns the problem of fixed-time synchronization(FxS) of master-slave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand. Distinguished from the conventional fixed-time control schemes, the proposed controller don't contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.

Realizing stochastic fixed-time synchronization between two nonlinear chaotic finance systems

“…have deployed the fixed-time integral SMC technique to stabilize the CFS [35]. Recently, Ma et al have designed the adaptive fixed-time control(AFC) scheme to synchronize drive-response CFSs [36].…”

“…(1) Distinguished from the works of [11]- [22] and [34,36], this investigation considers the influence of noise perturbations in the response CFS, and proposes the definition of SFxS between the drive-response CFSs for the first time;…”