Spatio-Temporal Dynamics in Cellular Neural Networks

Abstract

Analog Parallel Architectures like Cellular Neural Networks (CNN’s) have been thoroughly studied not only for their potential in high-speed image processing applications but also for their rich and exciting spatio-temporal dynamics. An interesting behavior such architectures can exhibit is spatio-temporal filtering and pattern formation, aspects that will be discussed in this work for a general structure consisting of linear cells locally and homogeneously connected within a specified neighborhood. The results are generalizations of those regarding Turing pattern formation in CNN’s. Using linear cells (or piecewise linear cells working in the central linear part of their characteristic) allows the use of the decoupling technique – a powerful technique that gives significant insight into the dynamics of the CNN. The roles of the cell structure as well as that of the connection template are discussed and models for the spatial modes dynamics are made as well.