blob: 346276465f21c8e2473129567c65ef8ed9b01398 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
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
|
