Analysis of saddle-node bifurcations in an interpersonal relationship model

This paper presents a model of affective interpersonal relationships among secure individuals. The model consists of three main factors: oblivion, response to a partner's affection, and perception of the partner's characteristics. A simple return function is employed for a detailed formal mathematical analysis. The paper demonstrates the existence of a saddle-node bifurcation related to individuals' perceptions of their partner's attributes. This work indicates that improving the perception of a partner's qualities can lead to an enhancement in the relationship.