Continuous Attractors of Nonlinear Neural Networks with Asymmetric Connection Weights

Abstract

Continuous attractor neural networks with symmetric connection weights have been studied widely. However, there is short of results on continuous attractor neural networks with asymmetric connection weights. This paper studies the networks with asymmetric connection weights. To overcome the difficulties caused by asymmetric connection weights, an interesting new norm is proposed in a general vector space which is not Euclidean space. Then the new distance and attractivity are defined. Finally, the explicit expressions of continuous attractors of Cellular Neural Networks with asymmetric connection weights are obtained.