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| -rw-r--r-- | notes/lec09_intro4_stability | 22 |
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diff --git a/notes/lec09_intro4_stability b/notes/lec09_intro4_stability new file mode 100644 index 0000000..3462764 --- /dev/null +++ b/notes/lec09_intro4_stability @@ -0,0 +1,22 @@ + +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 |