In this paper we first made an overview of memristor computing. Then we presented the dynamics of hysteresis CNN model with memristor synapses (M-HCNN). In order to study the dynamics of the obtained M-HCNN model we applied theory of local activity. In this way we determined the edge of chaos domain in the parameters set for the model under consideration. The processing results do not change under the variations of the memristor weights. This is due to the influence of the binary quantization of the output signals. However, in order to obtain stable solution we need more iterations when some variations arise in the templates. This can reflect in the speed of the M-HCNN performance without change of the quality of the final results.