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Diffstat (limited to 'notes/lec09_intro4_stability')
| -rw-r--r-- | notes/lec09_intro4_stability | 22 |
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diff --git a/notes/lec09_intro4_stability b/notes/lec09_intro4_stability deleted file mode 100644 index 3462764..0000000 --- a/notes/lec09_intro4_stability +++ /dev/null @@ -1,22 +0,0 @@ - -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 |