Determination of edge of chaos in hysteresis CNN model with memristor synapses

This paper deals with Hysteresis Cellular Nonlinear Networks (HCNN) with memristor synapses. First, we consider the hysteresis phenomena in a memristive system. We introduce HCNN model working in relaxation oscillator mode, in which the resistor is replaced by a memristor. Edge of chaos regime is determined for the HCNN model based on local activity theory. Numerical simulations and applications are presented in order to illustrate the obtained theoretical results.