Mathematics of marital conflict: qualitative dynamic mathematical modeling of marital interaction

This article presents a new nonstatistical mathematical approach to modeling marital interaction by means of nonlinear difference equations. The application made of this modeling process in this article is to generate theory in order to understand J. M. Gottman and R. W. Levenson's (1992) report of the ability of one variable derived from a balance view of marital interaction to predict marital dissolution in a prospective study. Parameters are introduced that reflect uninfluenced husband and wife set points, emotional inertia, and influence function. These parameters are subjected to various examinations of validity with other data that reflect patterns of marital interaction and the cascade toward marital dissolution. Results suggest the hypothesis that unstable marriages are characterized at Time 1 by a mismatch in husband and wife influence functions. The modeling method makes it possible to fit a couple's equations under one set of conditions, then to simulate the couple's interaction under different conditions, and then to conduct experiments to test the validity of these simulations. The method provides a new approach toward the building of theory in family psychology