Convergence analysis of cellular neural networks with unbounded delay

Cellular neural networks (CNNs) have been successfully applied in many areas such as classification of patterns, image processing, associative memories, etc. Since they are inherently local in nature, they can be easily implemented in very large scale integration. In the processing of static images, CNNs without delay are often applied whereas in the processing of moving images, CNNs with delay have been found more suitable. This paper proposes a more general model of CNNs with unbounded delay, which may have potential applications in processing such motion related phenomena as moving images, and studies global convergence properties of this model. The dynamic behaviors of CNNs, especially their convergence properties, play important roles in applications. This paper: (1) introduces a class of CNNs with unbounded delay; (2) gives some interesting properties of a network's output function; (3) establishes relationships between a network's state stability and its output stability; and (4) obtains simple and easily checkable conditions for global convergence by functional differential equation methods.