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 $a,b,c,d [\math] in R: <script type="math/tex"> dX/dt=aX+bY and dY/dt=cX+dY$ 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 Tr(A)2?4?det(A)=0 on a det(A) vs Tr(A) plane and find the corresponding modes of relationships we might encounter and their evolution.