Previously, we had constructed a model for the dynamics of a social group in which individuals make decisions chosen from a cone of possible choices which seem rationally acceptable according to local (individual) criteria. (Abraham, 1988) In this kind of model, synergy appears as a measure of the intersection of individual preference cones and group preference cones. We may call this a microdynamic model, in that the choices of each individual are represented in the model, as in microeconomics.

3.1 Microdynamic bifurcations

If the cones, and thus the dynamics of the group, are changed by a continuous parameter, derived changes are to be expected in the long-term behavior of the model. That is, the map of attractors and basins of the system will be changed by the parameter. Occasionally, particularly abrupt changes may occur, typical of bifurcations familiar from the simpler models of dynamical systems theory. In addition, we may expect unfamiliar bifurcations, special to this category of model, in which choices are made at random within a preference cone, rather than being uniquely determined by a vector.

3.2 Synergy bifurcations

One such bifurcation we might observe is the synergy bifurcation, in which the intersections of preference cones abruptly increase or decrease. We might propose this as an (abstract) model for the transformation of the Kalahari !Kung in the 1970s. Like microeconomic models of this type, the dimension is very large, and simulation is not practical. We now seek a simpler model.