Academic Guidance 2015
Mathematics and Population Biology

F. Takasu
Dept. Information and Computer Sciences, Nara Women's University

Exponential growth model

fn[x_]=R x/.R->1.1

seq = NestList[fn,1,30]

ListPlot[seq]

ListLogPlot[seq]

seqLog = Log[seq]

ListPlot[seqLog]

Discrete Logistic Model

logistic = r(1-x/k)x/.{r->3.5, k->100}

fn[x_]= logistic

fn[1]

seq = NestList[fn,1,50]

ListPlot[seq,PlotRange->All,Joined->True]

pList={};
AppendTo[pList,{seq[[1]],0}];
Do[
AppendTo[pList,{seq[[i]],seq[[i+1]]}];
AppendTo[pList,{seq[[i+1]],seq[[i+1]]}],{i,1,Length[seq]-1}
]

gCobWeb=ListPlot[pList,Joined->True,PlotStyle->RGBColor[1,0,0]]

g = Plot[{x, logistic},{x,0,100}]

Show[gCobWeb, g,AspectRatio->1,PlotRange->All]

Ricker Logistic Model

logistic =Exp[ r(1-x/k)]x/.{r->2.0, k->1}

fn[x_]= logistic

fn[1]

seq = NestList[fn,0.001,50]

ListPlot[seq,PlotRange->All,Joined->True]

pList={};
AppendTo[pList,{seq[[1]],0}];
Do[
AppendTo[pList,{seq[[i]],seq[[i+1]]}];
AppendTo[pList,{seq[[i+1]],seq[[i+1]]}],{i,1,Length[seq]-1}
]

gCobWeb=ListPlot[pList,Joined->True,PlotStyle->RGBColor[1,0,0]]

g = Plot[{x, logistic},{x,0,3}]

Show[gCobWeb, g,AspectRatio->1,PlotRange->All]