Question

please, be explicit

4. Find all fixed points for each of the following maps and classify them as cobweb for the typical trajectories. a) f(x) 2r(1-); b) f(z) -; c) f(z) ; d) f() 4+ attracting, repelling, or neutral. Draw a

Answer 1

f (x)2a(1 xx 0 or 2(1 x)1x TO

Cobweb diagram is below:

This shows 0.5 is an attracting fixed point

0:6 (0.5, 0.5 0:4 0.2 (0, 0) 02 0.4 0.6 0.8 t

This shows 0 is a repelling fixed point

0.2 |(0, 0) 0.2 -0.2 -0.2 -0:4

2)

3 f (r)x = xx2x 0, t/2

Cobweb diagrams are below:

0.1 |L0, 0) 0.11 0.1 --01

Which means x=0 is a neutral fixed point

and

1.5 |(1.414, 1.414) 1 -0:5 -0.5 0.5 1.5 2 -0.5

0:5 수0104 -1.5 F0.5 0.5 -0.5 --1-5 (-1.414, -1.414

Means both are repelling fixed points

=t/2

c) are the fixed points

f(x) 16 = x = ¢ 44

(0.25, 0.25) 0-2 0.2

So 0.25 is attracting and

(0.75, 0 75) (0.25, 0.25 0.5 LO

So 0.75 is repelling

d)

f(r) 4 x4x2-16x 9 0 4x -0.5,4.5

45, 4.5) 2 4 6 D.5, -05) LO

So 4.5 is attracting and

4- (4:5, 4:5) 2 2 (-0.5, -0:5) 2 LO 4 CN 2

Meaning -0.5 is repelling

$\blacksquare$

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