|author||bnewbold <firstname.lastname@example.org>||2014-04-22 21:56:02 -0400|
|committer||bnewbold <email@example.com>||2014-04-22 21:56:02 -0400|
add today's lecture notes
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diff --git a/notes/lec09_intro4_stability b/notes/lec09_intro4_stability
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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
+the 'bier_stability.m' script calculates eigenvalues numerically.
+PROJECT: re-write this script in julia