Bounds for a new chaotic system and its application in chaos synchronization

This paper has investigated the localization problem of compact invariant sets of a new chaotic system with the help of the iteration theorem and the first order extremum theorem. If there are more iterations, then the estimation for the bound of the system will be more accurate, because the shape of the chaotic attractor is irregular. We establish that all compact invariant sets of this system are located in the intersection of a ball with two frusta and we also compute its parameters. It is a great advantage that we can attain a smaller bound of the chaotic attractor compared with the classical method. One numerical example illustrating a localization of a chaotic attractor is presented as well.