Magdalena Szafrańska-Łęczycka, University of Warsaw, Poland
Katarzyna Szymańska-Dębowska, Lodz University of Technology, Poland
Urszula Foryś, University of Warsaw, Poland

Abstract: In this paper we introduce a mathematical model of psychotherapy where the proposed continuous dynamical system describes the relationship between the client and the therapist based on dyadic interactions modeling. The model also incorporates the influence representing the external environment of the client's state. It was assumed that given that influence is negative. In order to reflect possible instability of the client's state, we describe the client who can demonstrate other mental comorbidities. Additionally, this assumption depicts the fact that his/her preferable state can be not unique. We analyse basic properties of the model and use it to study various scenarios of final results of psychotherapy.

Keywords: psychotherapy, dyadic interactions, dynamical system, local and global stability, instability