Abstract—Networks of threshold elements whose inputs are assigned positive and negative (inhibitory) weights and outputs take the values 0 and 1 are considered. A stationary ensemble is defined as a connected subnetwork of a threshold network for which the unit state (1, 1, …, 1) = 1 is stable. The transfer of an ensemble into the state 1 is called switching on. Necessary and sufficient conditions for a network to be an ensemble are given. It is shown that, in the proposed model, the switching on of one of two ensembles having common elements does not necessarily lead to the switching on of the other.