In this manuscript, we investigate the dynamics of Memristor Cellular Nonlinear Networks, focusing on the complex behaviors of 2-terminal locally active volatile threshold switches, known as volatile memristors, using a circuit-theoretic approach. We show that a cell within the array equipped with an NbO2-based volatile threshold switch can exhibit both oscillatory and static dynamics depending on the parameters of the Memristor Cellular Nonlinear Network. We utilize the latter to design an M-CNN for image processing that performs edge detection on binary input images.