Cellular Neural Networks: Dynamics and Modelling

This work deals with theoretical results for studying Cellular Neural Networks (CNNs) concerning its dynamical behaviour. Aspects of CNNs' applications are developed for modelling of some famous nonlinear partial differential equations arising in biology, genetics, neurophysiology, physics, ecology, and so forth. The analysis of CNNs' models is based on the harmonic balance method well known in control theory and in the study of electronic oscillators. Such phenomena as hysteresis, bifurcation and chaos are studied for CNNs. The topics investigated in the book involve several scientific disciplines, such as dynamical systems, applied mathematics, mathematical modelling, information processing, biology and neurophysiology. The reader will find comprehensive discussion on the subject as well as rigorous mathematical analyses of networks of neurons from the view point of dynamical systems. The text is written as a textbook for senior undergraduate and graduate students in applied mathematics. Providing a summary of up-to-date results on dynamics and modelling of CNNs, the book should also be of interest to all researchers in the area.