**diff options**

author | bnewbold <bnewbold@robocracy.org> | 2014-04-22 21:56:02 -0400 |
---|---|---|

committer | bnewbold <bnewbold@robocracy.org> | 2014-04-22 21:56:02 -0400 |

commit | dc65fcce38ad89549692696c3fc8f2265dbf981a (patch) | |

tree | 983370280083838a5e558f9b0f8617501f22b115 | |

parent | 8128bc12611df99c8b1249ef4f986cef3216401b (diff) | |

download | dmmsb2014-dc65fcce38ad89549692696c3fc8f2265dbf981a.zip dmmsb2014-dc65fcce38ad89549692696c3fc8f2265dbf981a.tar.gz |

add today's lecture notes

-rw-r--r-- | notes/lec09_intro4_stability | 22 |

1 files changed, 22 insertions, 0 deletions

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 |