Let X(t) be my attraction to a girl and Y(t) be a girls attraction to me, where positive values indicate love and negative values indicate hate. Constructing a linear system with parameters [math]a,b,c,d[\math] in R:

[math]dX/dt = aX + bY[/math] and [math]dY/dt = cX + dY[/math]. I know personally my b<0 and a>0 for example; I am disinterested in those interested in me, and the more I am interested in someone the more I become interested, given social/physical proximity which is an assumption of this model.

We can plot the function [math]Tr(A)^2-4*det(A)=0[/math] on a det(A) vs Tr(A) plane and find the corresponding modes of relationships we might encounter and their evolution.