# cobweb.ode
# way to fool XPP into cobwebbing
# first I define a function that every other step evaluates
# the map -- in the alternate steps, it just keeps the same
# value so that it alternates between horizontal and vertical
# jumps
g(x,y)=if(mod(t,2)<.5)then(f(x))else(y)
# note that 't' is the iteration number 0,1,2,...
# if t is even evaluate f otherwise keep the old y
y(t+1)=g(x,y)
x(t+1)=if(t==0)then(x)else(y)
# note that x(t+2)=f(x(t)) so every other point is the map!
f(x)=a*x*(1-x)
par a=3.1
# these are just useful for plotting f(x),x
par xlo=0,xhi=1,nit=25
# 
init y=0,x=.25
# always start y=0
#
# here I create scaled x-values to plot f(x)
xx=xlo+(xhi-xlo)*t/nit
aux map=f(xx)
aux st=xx
# some convenient settings for the graphics
@ xlo=0,ylo=0,xhi=1.001,yhi=1.001
@ xp=x,yp=y
@ nplot=3
# add the plots y=x and y=f(x)
@ xp2=st,yp2=st
@ xp3=st,yp3=map
# tell xpp that it is discrete and iterate 100 times
@ meth=discrete,total=25
done