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Unformatted text preview: carrying capacity
P(t) = 0 constant in time  separable  would use partial fractions to solve
solution curve is on (x, y) plane where y*=4 is the
equilibria approached by incr and decr curves increases as
y<4
use y'''>4 y"' = 5
f(5) = 5(45)<0 method: phase line
diagram
 similar to cobwebbing
technique of DTDS
y = y(x) decreases as function of
x is y>4 soln curves moving away from eqm is unstable,
vice versa for moving towards 2< y^ <3, f(y^) <0
then, dy/dx < 0,
and therefore, y(x) decreases
0 <y^ < 2 , f(y^) > 0 , then dy/dx >0
and therefore y(x) increases y>3, f(y).0, dy/dx >0 > y(x) is increasing
as a function of x
soln curve will move away
from the eqm r 2rk/k don't want to use separation don't want to
use phase line
soo, take the derivative
of RHS sub in the eqm values ...
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 Winter '07
 MUNTEANU
 Calculus, Fractions, Derivative, eqm

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