Abstract
For the chaotic system, it is very difficult to take a treatment of it, because of the crisp map of this system is required though it is unknown in some cases. In this work, we extended the concept of Unstable Periodic Orbits(UPO) which is a outstanding characteristic in chaos and proposed a concept of the plural Unstable Periodic Regions(UPR). By this proposed concept, we can have the knowledge of the quantitative and the qualitative of chaos step on different viewpoint. An application of this concept is also shown as the control in chaos with a situation that the dynamics of the chaotic control system is unknown. By this concept and the results of the numerical simulations of the application with proposed concept, the other way of the treatment of chaos were shown up.
