On the Dynamical Interplay of Positive and Negative Affects.

Emotional disorders and psychological flourishing are the result of complex interactions between positive and negative affects that depend on external events and the subject's internal representations. Based on psychological data, we mathematically model the dynamical balance between positive and negative affects as a function of the response to external positive and negative events. This modeling allows the investigation of the relative impact of two leading forms of therapy on affect balance. The model uses a delay differential equation to analytically study the bifurcation diagram of the system. We compare the results of the model to psychological data on a single, recurrently depressed patient who was administered the two types of therapies considered (coping focused versus affect focused). The model leads to the prediction that stabilization at a normal state may rely on evaluating one's emotional state through a historical ongoing emotional state rather than in a narrow present window. The simple mathematical model proposed here offers a theoretical framework for investigating the temporal process of change and parameters of resilience to relapse.