Stability analysis of an unsupervised neural network with feedforward and feedback dynamics

We present a new method of analyzing the dynamics of self-organizing neural networks with different time scales based on the theory of flow invariance. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global asymptotic stability of the equilibrium point.