Variable Thresholds in the Chaotic Cellular Neural Network

The chaotic cellular neural network (C-CNN) has complex dynamics, including chaos, oscillations, and stable fixed points. Chaotic dynamics can help the network avoid local minima and reach the global optimum. Hence chaos can improve the performance of cellular neural networks (CNNs) on problems that have local minima in energy (cost) functions. We investigate the effect of variable thresholds in the C-CNN. We show that this threshold cannot be too large if one wishes to produce chaotic dynamics in the C-CNN, which is important to studies of chaotic communication and combinatorial optimization problem. We are particularly interested in variable thresholds because Shi and Wang (2005) showed that the objectives of the frequency assignment problem (FAP) can be mapped into thresholds of the neural network, which resulted in superior performance compared to traditional penalty approaches.