Using dynamical systems mathematical modeling to examine the impact emotional expression on the therapeutic...

Objective: The purpose of this paper is to describe an approach to dynamical systems (DS) using a set of differential equations, and how an application of these equations can be used to address a critical element of the therapeutic relationship. Using APA's Three Approaches to Psychotherapy with a Female Client: The Next Generation and Three Approaches to Psychotherapy with a Male Client: The Next Generation videos, DS models were created for each of the six sessions with expert clinicians (Judith Beck, Leslie Greenberg, and Nancy McWilliams) from the three theoretical approaches. Method: A second-by-second observational coding system of the emotional exchanges of the therapists and clients was used as the data for the equations. Results: DS modeling allowed for a side-by-side comparison between the three approaches as well as between the two clients. Examining the graphs created by plotting the results of the DS equations (in particular, phase-space portraits) revealed that there were similarities among the three theoretical approaches, and there were notable differences between the two clients. Conclusions: DS modelling can provide researchers and clinicians with a powerful tool to investigate the complex phenomenon that is psychotherapy.