Stability analysis of a self-organizing 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 are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory, singular perturbation theory, or those based on supervised synaptic learning. 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 exponential stability of the equilibrium point.