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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.

By introducing new concepts, this paper presents a new classification of transient cells for the digraph cell mapping dynamical system. Based on this new classification, the approximation problem of the invariant manifolds of dynamical system is discussed in detail. In order to improve the efficiency and speed of computing, an effective algorithm is given to complete the above classification. As an illustrative example, Henon map is taken to demonstrate the validity of the modified digraph cell mapping method.

Based on the adaptive slide mode control method, we investigated the robust synchronization for a class of chaotic systems with random perturbations. This approach can be applied to may chaotic systems; and the upper bound of random perturbations is not necessarily known in advance and it is estimated through an adaptive control process. Finally, two-scroll chaotic system, Lorenz system and hyperchaotic Rssler system are taken as examples to illustrate the effectiveness of the proposed method.

Using the integral-observer approach, chaos synchronization is achieved for a class of chaotic systems when both the parameters and the output of the system are perturbed. Based on Lyapunov stability theory and LMI technique, we give the sufficient criterion, which can make the drive system and the response system globally exponentially synchronized. In the end, we take MLC chaotic system as an example to verify the effectiveness of the proposed method.