A study is presented of a set of coupled nets proposed to function as a global competitive network. One net, of hidden nodes, is composed solely of inhibitory neurons and is excitatorily driven and feeds back in a disinhibitory manner to an input net which itself feeds excitatorily to a (cortical) output net. The manner in which the former input and hidden inhibitory net function so as to enhance outputs as compared with inputs, and the further enhancements when the cortical net is added, are explored both mathematically and by simulation. This is extended to learning on cortical afferent and lateral connections. A global wave structure, arising on the inhibitory net in a similar manner to that of pattern formation in a negative laplacian net, is seen to be important to all of these activities. Simulations are only performed in one dimension, although the global nature of the activity is expected to extend to higher dimensions. Possible implications are briefly discussed.