%
% logweb.m - this MATLAB file solves the 
% discrete logistic equation x(i+1)=r*x(i)*(1-x(i))
% and illustrates cobwebbing analysis for two 
% points chosen by the user to illustrate the
% stretching and folding of a non-linear map
% The user is prompted to read in the value
% of r to use as well as two initial values
% x0 and z1 which must be in (0,1)
% and the time interval over which to run the 
% simulation.
!c:
s=1;
while s>0;
r=input('input growth rate r:    ')
x0=input('input initial population x0:     ')
z0=input('input second initial population z0:     ')
n=input('end of time interval b:     ')
x=zeros(n+1,1);
z=zeros(n+1,1);
t=zeros(n+1,1);
x(1)=x0;
z(1)=z0;
tt(1)=0;
for i=1:n
t(i)=i-1;
x(i+1)=r*x(i)*(1-x(i));
z(i+1)=r*z(i)*(1-z(i));
end
t(n+1)=n;
nn=100;
del=1./nn;
xstart=0;
yy=zeros(nn+1,1);
lin=zeros(nn+1,1);
xx=zeros(nn+1,1);
for i=1:nn+1
xx(i)=xstart+(i-1)*del;
lin(i)=xx(i);
yy(i)=r*xx(i)*(1-xx(i));
end
plot(xx,lin,xx,yy),pause
xc=zeros(24,1);
yc=zeros(24,1);
xc(1)=x0;
yc(1)=0;
xc(2)=x0;
yc(2)=r*x0*(1-x0);
yc(3)=yc(2);
xc(3)=yc(2);
zc=zeros(24,1);
zyc=zeros(24,1);
zc(1)=z0;
zyc(1)=0;
zc(2)=z0;
zyc(2)=r*z0*(1-z0);
zyc(3)=zyc(2);
zc(3)=zyc(2);
plot(xx,lin,xx,yy,xc,yc,zc,zyc),pause
for j=4:12;
jj=2*j-4;
xc(jj)=xc(jj-1);
yc(jj)=r*xc(jj)*(1-xc(jj));
xc(jj+1)=yc(jj);
yc(jj+1)=yc(jj);
zc(jj)=zc(jj-1);
zyc(jj)=r*zc(jj)*(1-zc(jj));
zc(jj+1)=zyc(jj);
zyc(jj+1)=zyc(jj);
plot(xx,lin,xx,yy,xc,yc,zc,zyc),pause
end
plot(t,x,t,x,'o',t,z,t,z,'+'),pause
s=input('Do you want to stop - if so enter 0')
end