A second step towards a stochastic mathematical description of human feelings

This paper deals with a mathematical description of human feelings (such as hostility, or indifference or love) in the trail of a previous one [1]. The discussion carried out there was acknowledged to be somewhat oversimplified, so that the present paper aims at deepening the views it relied upon and at widening the application field of the model, by taking into account the character, the tastes, and possibly the past experiences of each individual involved in a social relationship. Even the word “social” is here understood in a wider sense, ranging from the meaning of a “purely intellectual” and “mainly altruistic” relationship to that of a “quite selfish physical (sexual)” one. From a mathematical viewpoint, the description proposed here still leads to a system of nonlinear integrodifferential stochastic equations. Existence and uniqueness of its solutions, as well as their stability and the possible occurrence of strong instability effects, are not discussed here, and postponed to a future work. The main feature of the paper lies in the explicit introduction of additional parameters related to behaviour, external influences of psychologic as well as practical kind, and the consideration of self-feelings. This leads to introduce and discuss additional relations that are to be considered as “constitutive laws” to identify “psychological types” or “classes” of individuals.