Analysis of the dynamics of a family system in terms of bifurcations

Abstract

Abstract We analyze a simple model for the dynamics of a family system based on a video tape recording of the first interview between the family and a therapist. The model serves as a working example to show the possibility of abrupt transitions beyond a bifurcation point separating different behavioral domains. Such transitions separate one stable, steady state from another or a non-oscillatory state from periodic behavior. A modification of the basic model indicates how the passage through a bifurcation can be suppressed. Bifurcation phenomena sometimes accompanied by oscillations are known to abound in chemical and biological systems. Whereas bifurcations occur in the latter systems as a result of regulatory interactions at the molecular or cellular levels, the model suggests that similar bifurcations may occur on a more global level from interpersonal relations within the family. We compare the predictions of the model with the interventions of the therapist and discuss the relevance of the results to other patterns of family interactions which might also lead to cyclical behavior.