The first MATLAB file simulates the 2-species Nicholson Bailey
difference equation modified to
include host density dependence (page 85 of Edelstein-Keshet
(Math Models in Biology)
x(n+1) = x(n)*exp(r*(1-x(n)/K)-a*y(n))
y(n+1) = x(n)*(1-exp(-a*y(n)))
r=0.5; (r=host repro rate'), a=0.2; (=search
efficiency
of parasitoid')
K=14.47; (=host carrying capacity); x0=11; ( initial
population
x0 of host)
y0=1; (initial population y0 of parasitoid); n=80;
( time period of run).
The second file draws bifurcation diagram for the model, using the
host
growth rate as
bifurcation parameter.
2: Nlogweb.m
This MATLAB file simulates the discrete logistic equation
x(i+1)=r*x(i)*(1-x(i))
and illustrates cobwebbing analysis.
r=3.8;( growth rate); x0=0.2; (initial population x0); n=80;(end of
time interval).
You can adapt this for the cobwebbing analysis of other difference equations.
3: logbif.m
logbif.m - this MATLAB file simulates
the
logistic difference equation
u(n+1)=a u(n) (1-u(n)) and carries out a
bifurcation
analysis by varying a.
200 different values of a are used between
the
ranges amin and amax
set by the user. A bifurcation plot is
drawn by showing the last 250 points
of a sequence of 1000 simulated points for each
value of a. The initial
condition is fixed at x0=.2
4: Rickerbif.m
5: lypex.m
This file allows you to draw both the bifurcation diagram and Lyapunov