  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.
