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diff --git a/lectures/lec13_bistability4 b/lectures/lec13_bistability4 new file mode 100644 index 0000000..f0c6363 --- /dev/null +++ b/lectures/lec13_bistability4 @@ -0,0 +1,20 @@ + +Bistability in 2 variable systems + +review: mutual activation (positive feedback loop) + and mutual inhibition (negative feedback loop) + +[review of simple mutual activitation and inhibition physical systems] + +when doing analysis, often want to plot nullclines in phase (aka, variable) +space. the nullcline of a variable is a curve in phasespace where the time derivative of the given variable is zero. + +find these by expressing the differential of the variable (w/r/t time) as a +symbolic expression (probably involving both variables) and solving for equals +0. then we will analyse the intersecting points (which are equilibria, though +not necessarily stable). might need to plot nullcline for varying "other"/free +variables to find a state where there are 3x (or more) intersections, which are +bistable systems. + +overall a bit confused; shouldn't this lecture have come earlier, before the +stability analysis? oh, no, that was a single variable system. |