The digraph cell mapping method based on composite cell space

Abstract

In order to improve the accuracy and efficiency，an iterative digraph cell mapping method is presented through introducing the notion of composite cell space. This iterative method can refine any interesting region of cell state space. Because the refining process is performed by algebraic operation，the computer memory does not be increased additionally. Furthermore，the digraph dynamical properties can be preserved in the refining process. In order to implement it easily，an effective algorithm is designed. As an example，the Henon map is taken to demonstrate the validity and efficiency of this method.