Dynamical analysis of continous self-organizing cortical maps

Based on Amaris(1,2) mathematical formulation of the self-organization of synaptic efficacies and neural response fields under the influence of external stimuli we show that if the map is a contraction, then the system has a unique equilibrium which is globally asymptotically stable; consequently the system acts as a stable encoder of external input stimuli. The system converges to a fixed point representing the steady-state of the neural activity which has as an upper bound the superposition of the spatial integrals of the weight function between neighbouring neurons and the stimulus autocorrelation function.