Skip to main content

Dynamical Analysis of Therapist-Client Interactions

  • Chapter
  • First Online:
Mathematical Modeling of Social Relationships

Part of the book series: Computational Social Sciences ((CSS))


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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Paul R. Peluso .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Peluso, P.R., Baker, A.Z., Sauer, A., Peluso, J.P. (2018). Dynamical Analysis of Therapist-Client Interactions. In: Strawinska-Zanko, U., Liebovitch, L. (eds) Mathematical Modeling of Social Relationships. Computational Social Sciences. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-76764-2

  • Online ISBN: 978-3-319-76765-9

  • eBook Packages: Social SciencesSocial Sciences (R0)

Publish with us

Policies and ethics