tonight's lectures

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+Stability analysis for multi-variate systems
+
+could do a crude thing: chose points (on nullclines) near an equilibrium and
+integrate to see if there is convergence or divergence.
+
+jacobians! horray. the eigenvalues determine stability. stable if both real
+parts of eigenvalues are negative; otherwise unstable.
+
+claims that analytical evaluation of jacobians is hard but numerical is easy.
+hmm.
+
+the above is the algebaic way.
+
+geometric way is to calculate gradient w/r/t to time in the areas around and
+between nullclines (by calculating at zero/zero and/or very far away at
+inf/inf, then "flipping" every time a null cline is crossed (which makes sense
+because these are points were derivative is zero). the arrows/gradient "points
+to" the stable intersections.
+
+aka, vector looks like:   | d[A]/dt |
+                          |         |
+                          | d[B]/dt |
+
+can also do one-dimensional analysis on individual nullcline lines, again using
+"flip if crossing (other) nullclines" trick