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