A dynamical model of social interaction

Abstract

The present study proposes a mathematical model for the dynamic change of social inter action between two persons. Even though social interaction has essentially a dynamic aspect which varies through time and across situations, the traditional psychology has never succeeded in treating this dynamic change. First, we assume some hypotheses on basic rules for the dynamic change of social interaction. Then those hypotheses are integrated into a simple system of differential equations; a dynamical system. Each coefficient of terms in the system represents personalities of two persons. In accordance with various combinations of values of the coefficients, social interaction between the two persons brings out a variety of dynamic phases which are represented in the phase space of the dynamical system. Furthermore, a concept of dynamic personalities, which vary according to situations, is defined using a non-linear dynamical system. Finally, the relation between the present model and the method which constructs a dynamical system using an MDS, is discussed.