This work provides theoretical conditions guaranteeing that a self-organizing map efficiently 9 develops representations of the input space. The study relies on a neural fields model of spatiotemporal 10 activity in area 3b of the primary somatosensory cortex. We rely on Lyapunov's theory for neural 11 fields to derive theoretical conditions for stability. The theoretical conditions are verified by numerical 12 experiments. The analysis highlights the key role played by the balance between excitation and inhibi-13 tion of lateral synaptic coupling and the strength of synaptic gains in the formation and maintenance 14 of self-organizing maps. 15 16