maple_day2.html

455 DAY 2 MAPLE EXERCISE

> restart:
seq(r^t,t=0..10);

> r:=1.1;
seq(r^t,t=0..10);

> r:=1.1;
seq([t,r^t],t=0..10);

> r:=1.1;
pts:=[seq([t,r^t],t=0..30)];
plot(pts,style=point,labels=[time,N]);

Define a procedure that creates a cobweb diagram for the map f(r,x), where
r is a parameter,
x0 is the starting value,
rang is the plotting range, and
n is the number of iterates to be done:

> restart:
cobweb:=proc(f,r,x0,rang,n)
x:=x0;
count:=0;
pt[count]:=[x,0]; count:=count+1;
for i from 1 to n do
    xnew:=f(r,x);
    pt[count]:=[x,xnew]; count:=count+1;
    pt[count]:=[xnew,xnew]; count:=count+1;
    x:=xnew;
end do; unassign('i'):
p1:=plot([seq(pt[i],i=0..count-1)],color=magenta):
p2:=plot(z,z=rang,color=orange):
p3:=plot(f(r,z),z=rang,color=blue,thickness=2):
my_title:=convert(r,string);
return plots[display](p1,p3,p2,view=[rang,rang],title=my_title);
end proc:

Warning, `x` is implicitly declared local to procedure `cobweb`

Warning, `count` is implicitly declared local to procedure `cobweb`

Warning, `pt` is implicitly declared local to procedure `cobweb`

Warning, `i` is implicitly declared local to procedure `cobweb`

Warning, `xnew` is implicitly declared local to procedure `cobweb`

Warning, `p1` is implicitly declared local to procedure `cobweb`

Warning, `p2` is implicitly declared local to procedure `cobweb`

Warning, `p3` is implicitly declared local to procedure `cobweb`

Warning, `my_title` is implicitly declared local to procedure `cobweb`

Use the cobweb procedure for the logistic map and r=3.2:

> f:=(r,x)->r*x*(1-x);
cobweb(f,3.2,0.1,0..1,20);

Make an animation for the logistic map in which r increases from 1 to 4:

> r_values:=[seq(1.0+i/40,i=1..120)]:
plots[display](seq(cobweb(f,r_values[i],0.1,0..1,40),i=1..120),insequence=true);