Love dynamics: The case of linear couples

摘要

This paper proposes a minimal model composed of two ordinary differential equations to describe the dynamics of love between two individuals. The equations take into account three mechanisms of love growth and decay: the pleasure of being loved (return), the reaction to the partner's appeal (instinct), and the forgetting processes (oblivion). Under suitable assumptions on the behavior of the individuals, the model turns out to be a positive linear system enjoying, as such, a number of remarkable properties, which are in agreement with common wisdom on the argument. These properties are used to explore the consequences that individual behavior can have on the community structure. The main result along this line is that individual appeal is the driving force that creates order in the community. Possible extensions of this theory of linear love dynamics are briefly discussed.