In this chapter we present mathematical study of memristor systems. More precisely, we apply local activity theory in order to determine the edge of chaos regime in reaction-diffusion memristor cellular nanoscale networks (RD-MCNN) and in memristor hysteresis CNN (M-HCNN). First we give an overview of mathematical models of memristors, CNN and complexity. Then we consider the above mentioned two models and we develop constructive algorithm for determination of edge of chaos in them. Based on these algorithms numerical simulations are provided. Two applications of M-HCNN model in image processing are presented.
Part of the book: Memristors