BIO2150 Biostatistikk og studiedesign

f x eX

( )

1

2

12

2

#10000 gj.snitt av 10 uniformt fordelte tall

E X x f x dx E X x dx( ) ( ) ( ) .

0

1 11 0

0 5

#10000 gj.snitt av 100 uniformt fordelte tall

nlme

π

[1] 3.148367

dxd t

rx x rx rx 1 2 x t

xe rt

( )

1

11

10

lsoda

Logistisk vekst, forskjellige initialverdier

modell3<-glm(antall~dag+I(dag^2)+I(dag^3),data=fronder,family=poisson)

x r x xn n n 1 1

Sir Robert M. May: Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos (1974)

dBdt

rBK BK

bBP

dPdt

cBP dP

Antall felte kanadisk gaupe 1821-1934

Årstall

Ant

all f

elte

1820 1840 1860 1880 1900 19200

1000

2000

3000

4000

5000

6000

7000

Does a flap of a butterfly´s wings in Brazil set off a tornado in Texas (1972)

dxdt

y x

dyd t

xz rx y

dzd t

xy bz

J. Animal Ecology 47(1978)315-322)

library (rootSolve)

dNdt

rNNK

NN h

1

2

2 2ustabilt

Soetart & Herman 2009

Differensialligninger med tidsforsinkelse (dede)

KNrN

dtdN t

t1 Hutchinsons

ligning

Nicholsons blowflies: populasjonssvingningene i Australsk ullspyflue (Lucilla cuprina)Gurney, W.S.C., Blythe, S.P. & Nisbet, R.M. Nicholson´s blowflies revisited. Science 287 (1980)17-21

Epidemiologisk modell (SIR)

Suseptible S(t)

Infekterte I(t)

Restituerte R(t)

dS dI dR

acSIi

gR

rI

dSd t

i dS acSI gR dId t

acSI dI rI dRdt

rI gR dR

Travelling salesperson problemet (TSP)

Scheffer, M. et al.: Floating plant dominance as a stable state. PNAS 100 (2003) 4040-4045.

FlFahn

nFrdtdF

fff

f

11

SlWbFSahn

nSrdtdS

sss

s

1

1