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. This article introduces a new approach to the modeling of social interaction using the mathematics of difference and differential equations. These equations express, in mathematical form, a proposed mechanism of change over time. They do not represent a statistical approach to modeling; rather they are designed to suggest a precise mechanism of change. This method has been used with great success in the biological sciences (Murray, 1989). The method is usually a quantitative approach that requires the modeler to be able to write down in mathematical form, on the basis of some theory, the causes of change in the dependent variables. For example, in the classic predator-prey problem, a modeler writes down that the rate of change in the population densities is some function of the current densities (e.g., Murray, 1989). Although this