Towards mathematical models in psychology: A stochastic description of human feelings

The paper deals with a mathematical description of human feelings (such as hostility, or indifference or love) toward other human beings. The discussion is carried out in a somewhat simplified scheme, by describing the psychological state of each individual by only one state variable, conceived as a kind of measure of its feelings. This is, however, to be meant as simply a first step towards a more comprehensive description of human psychology, taking into account character, tastes and possibly past experiences of each individual involved in a social relation. For the simplified description here developed, we propose a system of nonlinear integro-differential stochastic equations, aiming at giving at least a probabilistic forecast of the evolution of reciprocal feeling of two relating individuals. Thus, the solution of the system will be a couple of probability density functions, for which we present a short preliminary discussion of existence and uniqueness as well as of stability and the possible occurrence of strong instability effects. A number of numerical simulations are presented to test the significance of the model and some ways to extend the scheme, by introducing a number of additional external as well as internal parameters that can reasonably be assumed to influence the reciprocal feelings, are suggested and discussed, with special attention to the concept of stochastic constitutive laws for the feelings.