A novel methodology for the empirical analysis of processes in psychotherapy was developed and tested. This method is based on the Fokker-Planck equation (FPE), a probabilistic model that detects the deterministic and stochastic components of a process. The deterministic component is given by the potential function underlying the process. The FPE application can be used to visualize the attractor (or in the case of multistability, attractors) of the dynamics, and the sources of stochasticity. The FPE app can also be employed in two-dimensional systems, for example, client's and therapist's coupled processes; then the method is run on the cross-correlations of the time series. Signatures were defined that merge the functions retrieved from the methodology into numerical values, and may serve to detect associations with conventional self-report measures of psychotherapy. The method was tested in a case series where client's and therapist's heart rate, heart rate variability and respiration were monitored in 20 psychotherapy sessions. The FPE app works well with time series of high resolution and adequate observation numbers, which renders it applicable to nonverbal and physiological time series.
Keywords: Fokker-Planck equation; attractor; dynamical systems theory; physiology; psychotherapy process.