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0
400
800
1200
1960 1990 2020
moose
wolves
Wolves
0
100
200
300
0 500 1000 1500
Moose
0
400
800
1200
1960 1990 2020
Wolves
Moose
0
100
200
300
0500 1000 1500
0
400
800
1200
1960 1990 2020
Wolves
Moose
0
100
200
300
0 500 1000 1500
©
0 5 10 15
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
t (s)
x (m)
Displacements for mass-spring system
underdamped
critically damped
overdamped
0
1
2
3
02000 4000 6000 8000 10000
0 0.5 1 1.5 2 2.5 3 3.5 4
20
25
30
35
40
t (hr)
T (C)
0 2 4 6 8 10
0
2
4
6
8
10
12
time (min)
Concentration
Reactor concentrations versus time
CA1
CB1
CA2
CB2
y = -10.0054x5 + 117.8991x4 - 389.2741x3 + 275.0587x2 +
1814.1224x
R2 = 1.0000
0
2000
4000
6000
8000
10000
12000
0 1 2 3 4 5 6
0
2
4
6
010000 20000 30000 40000 50000 60000 70000
0 5 10 15 20
-2
-1
0
1
2
3
time (s)
displacement (m)
Displacements (m)
x1
x2
x3
0 5 10 15 20
-1.5
-1
-0.5
0
0.5
1
time (s)
velocity (m/s)
Velocities (m/s)
dx1/dt
dx2/dt
dx3/dt
©
0510 15 20
-20
-10
0
10
20
(a) Lorenz model x versus t
-20 020
-50
0
50
x
y
(b) y versus x
-20 020
0
50
x
z
(c) z versus x
-50 050
0
50
y
z
(d) z versus y
-20 -10 010 20
-50
0
50
-40
-20
0
20
40
x
y
z
©
0 2 4 6 8 10 12 14 16 18 20
-40
-20
0
20
40
60
Lorenz model x versus t
x
y
r = 28
r = 99.96
-20
0
20
-50
0
50
-50
0
50
x
r = 28
y
z
-50
0
50
-100
0
100
-100
0
100
x
r = 99.96
y
z
