A mathematical model of psychotherapy: An investigation using dynamic non-linear equations to model the therapeutic relationship

Abstract

Mathematical models, such as the one developed by Gottman et al. (1998, 2000, 2002) to understand the interaction between husbands and wives, can provide novel insights into the dynamics of the therapeutic relationship. A set of nonlinear equations were used to model the changing emotional state of a therapist and client. The results suggest: (1) The person that is most responsive to the other achieves the most positive state, (2) the emotional state of the client oscillates before reaching its final state, (3) therapy is least successful when the therapist starts from a negative state, and (4) there is an inverse relationship between models that change only the influence parameter and models that change only the inertia parameter, creating a series of four basic models to work with. These theoretical models require further, empirical investigation to test the derived parameters. If validated, or revised based on observations of therapist-client relationships in development, they could provide specific direction in creating successful therapeutic relationships for training clinicians and those already in practice.

Psychotherapy Is Chaotic—(Not Only) in a Computational World

“…One distinctive feature of the current approach compared to that of Liebovitch et al (2011; Peluso et al, 2012), which focused on the co-evolution of emotional valences expressed by a therapist and his client, is that the current approach focuses on the psychological processes of clients in relation to their own experiences. The differential equations which were defined by the Libovich et al group consist of segments of linear functions each defining the gradient of emotional changes which the client exerts on the therapist and vice versa.…”

Complexity analysis of sustainable peace: mathematical models and data science measurements

“…It can also be the back end for an interactive interface for policy makers to study the consequences of different interventions in the system. Extending previous mathematical models of networked systems [11][12][13][14][15] to analyze a CLD, we determine the value x i of each peace factor from:…”

Dynamical Systems Theory in Psychology: Assistance for the Lay Reader is Required

“…For example, Peluso et al (2012, 51), presented non-linear dynamical models of the changes over time of psychotherapist and client emotional valences, in which each participant’s emotional valence was modeled as deterministic functions of both the other participant’s emotional valence and their own emotional valence at the immediately preceding time.…”

“…When results are presented from simulations in the absence of empirical data (e.g., Peluso et al, 2012), showing a few representative time series plots of the simulated data could help readers gain a better sense of how the patterns described in other ways (e.g., other plots, text descriptions) would look in empirical data. Readers might be able to get some sense of the plausibility of the model based on the look of these simulated time series plots.…”