This paper presents a finite-time adaptive synchronization strategy for a class of new hyperchaotic systems with unknown slave system’s parameters. Based on the finite-time stability theory, an adaptive control law is derived to make the states of the new hyperchaotic systems synchronized in finite-time. Numerical simulations are presented to show the effectiveness of the proposed finite time synchronization scheme.

Chaos synchronization has attracted increasing attention since the pioneering work of Pecora and Carroll [

However, in real-world application, it is usually expected that two systems can synchronize as quickly as possible and the finite-time control is an efficient technique [

Recently, a new 4D dynamical system is proposed [

Phase portraits of the four-wing hyperchaotic attractor for

Assume that a continuous, positive-definite function

In order to achieve master-slave synchronization of Dadras system, the master and slave systems are defined with the subscripts

Let

Our goal is to design controllers

Define

In order to achieve the synchronization, we select the following control laws and the update rules for three uncertain parameters

For any initials, the two systems (

Choose the following Lyapunov function candidate:

The differential of the Lyapunov function along the trajectory of the error system (

From Lemma

From the proof of Theorem

Although the synchronization scheme is designed for Dadras systems, it can be used in two other identical hyperchaotic systems and even two different hyperchaotic systems.

Numerical simulation results are presented to show the effectiveness of the proposed finite-time synchronization method. Fourth-order Runge-Kutta method is used and the time step size is

States of the master and slave systems without control.

States of the master and slave systems with the designed controller.

Synchronization errors between the master and slave systems with the designed controller.

Adaptive parameters

This paper has addressed the finite-time adaptive synchronization of Dadras hyperchaotic systems. Based on finite-time stability theory, the proposed scheme can assure the states of slave system to track the states of the master system in finite time. From the process of proof we can see that this method can be extended to other hyperchaotic systems such as Rössler hyperchaotic system and Lü hyperchaotic system.

The authors declare that there is no conflict of interests regarding the publication of this paper.