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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.
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