Open Access Open Access  Restricted Access Subscription or Fee Access

Active Sliding Mode for Synchronization between A Fractional-order Chaos and Integer-order Liu System

Rui-xin Wang, Bin Wang, Yuan-gui Zhou, Wei-yu Wang


A new four-dimensional (4-D) fractional-order chaotic system is proposed in this paper. Theoretically, a necessary condition for occurrence of chaos is obtained. Numerical investigations on the dynamics of this system have been carried out. It is shown that in case of commensurate system the lowest order of the new fractional-order system to yield chaos is 0.83, and a list of state trajectories is presented with fractional derivative of different areas. Furthermore, based on the fractional stability theory, a new active sliding mode control (ASMC) approach is proposed to realize the chaos synchronization between the fractional-order system and integer-order Liu system. Finally, simulation results are given to demonstrate the effectiveness of the proposed active sliding mode control method. The synchronization process is a smooth transition, and the transition time is very short.


fractional-order system, integer-order system, chaos synchronization, active sliding mode control.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.