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+nullclines: set of points in phase space where one derivative is zero.
+    can often be derived analytically.
+    the intersections of nullclines are even more interesting; an intersection
+    in a 2-D phase space is a fixed point (equilibria)
+
+vectors in a vector field area point in the same direction (quadrant) until a
+nullcline is crossed. the area is a "discrete region".
+
+"stable-limit cycle" is when there is a stable closed curve in phase space (as
+oopposed to, eg, a fixed point)
+
+how to find if stable vs unstable?
+
+take the jacobian, and find the eigenvalues of the jacobian at the limit point.
+if real parts are all positive, then unstable. if all negative, then stable. if
+complex eigenvalues have positive real parts, then there is a stable limit
+cycle.
+
+the 'bier_stability.m' script calculates eigenvalues numerically.
+
+PROJECT: re-write this script in julia