  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 complete bifurcation diagram of the system.
We compare the results of the model to psychological data on a single,
recurrently depressed patient that was administered the two types of therapies
considered (viz., coping-focused vs. affect-focused). The model leads to the
prediction that stabilization at a normal state may rely on evaluating one's
emotional state through an historical ongoing emotional state rather than in a
narrow present window. The simple mathematical model proposed here offers a
theoretically grounded quantitative framework for investigating the temporal
process of change and parameters of resilience to relapse.
