Stochastic Nonlinear Dynamics of Interpersonal and Romantic Relationships

TL;DR

This paper develops mathematical stochastic models to analyze the complex dynamics of interpersonal and romantic relationships, revealing behaviors like oscillations and state transitions that deterministic models cannot capture.

Contribution

It introduces stochastic differential equations to model relationship dynamics, incorporating ecological and cultural factors for a more realistic understanding.

Findings

Stochastic models exhibit sustained oscillations in relationship dynamics.

Transitions between stable states are observed in stochastic models.

Deterministic models lack the complex behaviors seen in stochastic simulations.

Abstract

Current theories from biosocial (e.g.: the role of neurotransmitters in behavioral features), ecological (e.g.: cultural, political, and institutional conditions), and interpersonal (e.g.: attachment) perspectives have grounded interpersonal and romantic relationships in normative social experiences. However, these theories have not been developed to the point of providing a solid theoretical understanding of the dynamics present in interpersonal and romantic relationships, and integrative theories are still lacking. In this paper, mathematical models are use to investigate the dynamics of interpersonal and romantic relationships, which are examined via ordinary and stochastic differential equations, in order to provide insight into the behaviors of love. The analysis starts with a deterministic model and progresses to nonlinear stochastic models capturing the stochastic rates and factors (e.g.: ecological factors, such as historical, cultural and community conditions) that affect proximal experiences and shape the patterns of relationship. Numerical examples are given to illustrate various dynamics of interpersonal and romantic behaviors (with emphasis placed on sustained oscillations, and transitions between locally stable equilibria) that are observable in stochastic models (closely related to real interpersonal dynamics), but absent in deterministic models.