Romeo and Juliet, part 1

Now, I don't want to write about the womenfolk, and I'm sure you don't want to read my misguided opinions. Sometimes, though, I stumble across a cute math problem, and it begs a quick writeup.

The simple version of the Romeo and Juliet finds the former hopelessly smitten by the latter, hanging on her every word. However, Juliet is the stereotypical flirt, such that the more Romeo wants her, the less she wants him... and vice versa.

the math works out like this:
which works out to a nicely oscillatory solution. Depending on the initial conditions (how passionately they love(+) or hate(-) each other to begin with), Romeo and Juliet's behavior will circle endlessly along the lines of one of these circles... if a and b don't agree, it'll be a little elliptical, but you get the point.

So, when J and R are both positive, they both love each other; however, because Romeo loves Juliet, her love for him quickly wanes. Once Juliet stops loving Romeo, he wants her less and less, until he eventually hates her... it is at this point that Juliet begins to want Romeo, perhaps because Juliet craves attention or simply likes messing with Romeo's head... but I digress.

This is just a simple mathematical model, but damned if you don't see it all the time, especially with those damn wiener kids and their damn emo relationships.