Research Article

Cognitive Neurodynamics

, Volume 5, Issue 3, pp 265-275

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Mathematical model of the dynamics of psychotherapy

  • Larry S. LiebovitchAffiliated withCharles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences, Center for Molecular Biology and Biotechnology, Department of Psychology, Florida Atlantic UniversityDivision of Mathematics and Natural Sciences, Department of Physics, Queens College, City University of New York
  • , Paul R. PelusoAffiliated withCollege of Education, Department of Counselor Education, Florida Atlantic University
  • , Michael D. NormanAffiliated withCharles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences, Florida Atlantic University Email author 
  • , Jessica SuAffiliated withCharles E. Schmidt College of Science, Florida Atlantic University
  • , John M. GottmanAffiliated withThe Gottman Institute, University of Washington


The success of psychotherapy depends on the nature of the therapeutic relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. Previously Gottman et al. used a very similar approach (physical-sciences paradigm) for modeling and making predictions about husband–wife relationships. Given that this novel approach shed light on the dyadic interaction between couples, we have applied it to the study of the relationship between therapist and client. The results of our computations provide a new perspective on the therapeutic relationship and a number of useful insights. Our goal is to create a model that is capable of making solid predictions about the dynamics of psychotherapy with the ultimate intention of using it to better train therapists.


Nonlinear phenomena Dynamical systems Dynamical systems theory Ordinary differential equations Biological systems Psychotherapy