Dynamical Analysis of Therapist-Client Interactions
Dynamic nonlinear mathematical equations allow investigators to deeply understand complex systems that are apt to change. They can be used to determine the stable steady states or points of homeostasis within the system (i.e., the relationship). These steady states function as an anchor that brings the system back to homeostasis if the system is perturbed or if it has been moved away from homeostasis by a force. Liebovitch and his associates (Liebovitch et al., 2008) modified Gottman’s dynamic nonlinear equations to study the dynamics of conflicts between two parties (which could be individuals or groups). They determined how the dynamics of such conflicts and their emergent properties depended on the actions of each person. Our modeling of the therapeutic relationship constitutes a concrete extension of these results to a different social interaction. In this chapter, we will outline an ongoing research project (described in some detail in the previous chapter) that employs mathematical modeling to discover what underlies a successful therapeutic relationship. We will then discuss, through the use of case studies, the issues related to the parameters generated, the graphical displays of the derived models, and the indices of model fit. Specifically, we present three therapy sessions from two separate case studies to illustrate the mathematical modeling, the difference in the model parameters, and a graphical representation of each.
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