Continuous-time CNN Research Articles

DYNAMICS FOR DISCRETE-TIME CELLULAR NEURAL NETWORKS

This presentation investigates the dynamics of discrete-time cellular neural networks (DT-CNN). In contrast to classical neural networks that are mostly gradient-like systems, DT-CNN possesses both complete stability and chaotic behaviors as different parameters are considered. An energy-like function which decreases along orbits of DT-CNN as well as the existence of a globally attracting set are derived. Complete stability can then be concluded, with further analysis on the sets on which the energy function is constant. The formations of saturated stationary patterns for DT-CNN are shown to be analogous to the ones in continuous-time CNN. Thus, DT-CNN shares similar properties with continuous-time CNN. By confirming the existence of snap-back repellers, hence transversal homoclinic orbits, we also conclude that DT-CNN with certain parameters exhibits chaotic dynamics, according to the theorem by Marotto.

Computing with Front Propagation: Active Contour And Skeleton Models In Continuous-Time CNN

In this paper, a linear CNN template class is studied with a symmetric feedback matrix capable of generating trigger-waves, a special type of binary traveling-wave. The qualitative properties of these waves are examined and some simple control strategies are derived based on modifying the bias and feedback terms in a CNN template. It is shown that a properly controlled wave-front can be efficiently used in segmentation, shape and structure detection/recovery tasks. Shape is represented by the contour of an evolving front. An algorithmic framework is discussed that incorporates bias controlled trigger-waves in tracking the active contour of the objects during rigid and non-rigid motion. The object skeleton (structure) is obtained as a composition of stable annihilation lines formed during the collision of trigger wave-fronts. The shortest path problem in a binary labyrinth is also formulated as a special type of skeletonization task and solved by combined trigger-wave based techniques.

A VLSI-oriented continuous-time CNN model

This paper presents an analysis of the stability and convergence properties of the full signal range (FSR) CNN model. These properties are demonstrated to be similar to those of the Chua-Yang model and the I/O mapping of known applications is shown to be unaffected by the modification introduced in this new model. In this modified CNN model the dynamic range of the cell state variables equals the dynamic range of the cell output variables and is invariant with the application. This feature results in simpler circuit implementations, thus allowing higher cell densities and improving the robustness of CNN integrated circuits. The FSR CNN model is particularly well suited for programmable CNN integrated circuits.