Equilibrium Points Neck Tie

Are those the behaviors of linearized two-dimensional systems of differential equations in the neighborhood of an equilibrium point on your tie or are you just happy to see me? Ha! That joke just never gets old. Source, sprial, and saddle (the "three s's" as our diffy-q prof used to call them). Technically, there's five behaviors if you differentiate (zing!) between spiral-in and spiral-out and between sources and sinks (and more if you include trivial solutions) but that made the design kinda crowded and you couldn't make out the glyphozoids very well because they were so small. When strangers on the bus point this out, it will give you practice in the six most useful words in all of mathematics: "Meh, it's just a sign flip." Addendum: Some of you have noted that we omitted centers. Feel free to view these as spirals with zero real part if it makes you feel better. And, yes, we're assuming the determinant of the Jacobian is non-zero here. And the eigenvalues are distinct. Jeez, ya nerdz. IT'S A TIE NOT A DISSERTATION.