We study a formal model describing network interaction of heterogeneous agents with many inputs and many outputs (MIMO agents). The paper presents a continuation of the research. The introduced model has a large number of parameters, which complicates its analytical study. The simulation demonstrated that by varying the values of agent parameters, it is possible to achieve funda-mentally different dynamics of nodes activity in a network. For different parameters, it is possible to obtain the predominance of one activity type in the whole network, the periodic change of different types, attenuation, and the involvement of the entire network, or its parts, in the stationary activity of one or different types. This research is devoted to the analytical study of the reduced model to determine the key properties for generating various kinds of behavior. The model itself has also undergone some significant changes. We consider small networks of agents and describe the conditions under which they can generate stable activity patterns. We introduce the concepts of ensemble and rhythmic activity generator for several activity types.