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Presentation
Made by Me
Pavel Lazukin
Competitive Predator-Prey Model
Why I chose this
• It was a requirement pass this class• This was the only topic I picked
Assumptions
• Births are instantaneous
• There is unlimited amount of space
• There is unlimited supply of food for the bison
bHCaHdt
dH mCcbHC
dt
dC
Predator-Prey System
Phase Plane
Prey
Pre
dato
r
Predator and Prey versus time
t
Pre
da
tor
an
d P
rey
My Predator-Prey Model
BcbWdWW 11'1
BcbWdWW 22'2
BcWBcWgBB 21'
0
510
1520
25
0
5
10
15
50
100
150
200
W1
W2
B
0 5 10 15 20
0
50
100
150
200
t
W1, W
2, and
B
W1
W2
B
Logistic Growth Model
1
1111
'1 K
WKWrW
2
2222
'2 K
WKWrW
Competition Model
1
2121111
'1 K
WWKWrW
2
1212222
'2 K
WWKWrW
17 17.05 17.1 17.15 17.2 17.25
13
13.5
14
14.5
15
15.5
W1
W2
0 5 10 15 20
13
13.5
14
14.5
15
15.5
16
16.5
17
17.5
t
W1 a
nd W
2
W1
W2
= death rate of wolf pack 1
= competition between the two wolf packs and wolf pack 1 carrying capacity
= birth rate of wolf pack 1 proportional to the amount of bison
= death rate of wolf pack 2
= competition between the two wolf packs and wolf pack 2 carrying capacity
= birth rate of wolf pack 2 proportional to the amount of bison
= birth rate of bison
= death of bison due to wolf pack 1 eating them
= death of bison due to wolf pack 2 eating them
1dW
1
2121111 K
WWKWr
What different things mean
BcbW1
2dW
2
1212222 K
WWKWr
BcbW2
gB
BcW1
BcW2
Final Model
BcbWK
WWKWrdWW 1
1
21211111
'1
BcbWK
WWKWrdWW 2
2
12122222
'2
BcWBcWgBB 21'
0
5
10
15
20
0
5
10
15
40
60
80
100
120
140
160
180
W1
W2
B
0 5 10 15 20
0
20
40
60
80
100
120
140
160
180
t
W1, W
2, and
B
W1
W2
B
Conclusion
• Wolfs, bison and other wolfs reach the equilibrium
So that means births and deaths seem to stop.
• =happily ever after
Another Conclusion
• Impossible in real life because humans and their technological advances exist
The End
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