# 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! #### DEFINE YOUR MAP HERE!! ################### f(x)=a*x*(1-x) par a=3.95 # Ricker map # f(x)=x*exp(a*(1-x)) # par a=2.4 ############################## # 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