this doesn't answer your question, I'm pretty sure I've seen something like this before in Maple but I don't have the means to access my notes at this moment, so just off the top of my head, in the meantime, something with arrows:

ode1 := diff(x(t),t)=-x(t)*(1-x(t)^2-y(t)^2)^2-y(t);
ode2 := diff(y(t),t)=-y(t)*(1-x(t)^2-y(t)^2)^2+x(t);

ic1:= [x(0)=0.68,y(0)=0.68]:
ic2:= [x(0)=-0.68,y(0)=-0.68]:
ic3:= [x(0)=1.5,y(0)=1.5]:
ic4:= [x(0)=-1.5,y(0)=1.5]:
ic5:= [x(0)=1.5,y(0)=-1.5]:
ic6:= [x(0)=-1.5,y(0)=-1.5]:

DEtools[DEplot](
  {ode1,ode2},
  {x(t),y(t)},
  t=0..20,
  [ic1,ic2,ic3,ic4,ic5,ic6],
  scene=[x(t),y(t)],
  x=-1.5..1.5, y=-1.5..1.5,
  arrows=smalltwo,
  dirfield=400,
  size=magnitude,
  color=magnitude,
  linecolor=black,
  thickness=6,
  numpoints=1000
);
 

I'm afraid I am not a regular visitor of this blog (mine), so I'm noticing your question rather late. Thanks for dropping by!

The point is to keep track of trajectories that start close together and to see how fast they diverge from the stable manifold for small differences in the initial conditions. DEplot shows trajectories that start from initial conditions distributed about the whole plane (this can be randomized or controlled on a point by point basis). To get an idea of the speed of divergence I sample a small number of trajectories that originate from a common neighborhood at fixed time intervals. My previous blog posts explain the basic idea. Keywords: "salvo of arrows".

what I meant to say but forgot to emphasize is that if you use shorthand notation for some of the recurrent expressions in your big formula, you may THEN be able to spot a pattern that would lead to a simplification. However, as Axel notes, there may not be a more compact form.

I have no idea why you would disagree with the shorthand idea, as you don't say why; it is a very common way of making big formulae look small.

what I meant to say but forgot to emphasize is that if you use shorthand notation for some of the recurrent expressions in your big formula, you may THEN be able to spot a pattern that would lead to a simplification. However, as Axel notes, there may not be a more compact form.

I have no idea why you would disagree with the shorthand idea, as you don't say why; it is a very common way of making big formulae look small.

please do leave feedback about your solution, as these threads may be visited at a later time by Maple users in search of answers for problems similar to yours.

and someone may find a more efficient way than the one you found.

please do leave feedback about your solution, as these threads may be visited at a later time by Maple users in search of answers for problems similar to yours.

and someone may find a more efficient way than the one you found.

I am reminded of this exchange:

http://www.mapleprimes.com/forum/whatmapleequivalentmatlabsaxisinfinfinfinf

Robert's pointplot3d looks much better in Standard than in Classic, so if you're going to use Classic, you may perhaps wish to have some control over the size of the printed symbols this way:

plots[pointplot3d]([seq([V[i],V[i-1],i],i=1..100)], 
colour=black,axes=box,symbol=diamond,symbolsize=10);

Details may be found here ?plot3d,options

Robert's pointplot3d looks much better in Standard than in Classic, so if you're going to use Classic, you may perhaps wish to have some control over the size of the printed symbols this way:

plots[pointplot3d]([seq([V[i],V[i-1],i],i=1..100)], 
colour=black,axes=box,symbol=diamond,symbolsize=10);

Details may be found here ?plot3d,options

your method is indeed easier Doug, I will try it, thanks for sharing.

Remark. It can indeed be annoying to see the placeholder instead of the image because you do want to make sure you are inserting the correct image.

Hi Christopher,

yes, it can be frustrating to learn how to post pictures, you're not alone, I used to dread it. I have now worked out a routine, let's see if it'll work for you.

First, upload the picture in "My files", as you have done. Note that there is a limit to file size, so uploading too big a picture could cause problems. Make sure your picture is not huge, if it is then reduce its size before uploading. Just to be sure, click on the url link to see if the picture correctly uploaded and can be seen in the browser. Then copy the url link to it (CTRL+C or whatever works for you).

Secondly, in the main body of your post, select the "insert/edit image" icon, the yellow one that looks like an envelope/mountain-top/something. Enlarge the window if you can't see everything (in my case the pop-up window is tiny and useless, need to drag it bigger with the mouse, waste of time).

Thirdly, in the "URL" blank, copy the url.

Fourthly, in "Width", select anything between 300 and 600, I usually go for 400. I don't bother filling in anything else.

Fifth, Click on the "Link" tab. There copy the "URL" again and select the "Target" as "New Window". I'm merely telling you what I do, other options would probably work too.

Then, in Sixth, click on "OK" and this will return you to the body of your post.

I find that I can copy multiple images and insert text in between, but I wouldn't recommend it because there's always something that, you know, that word you nearly used earlier. And you don't want one of those automatic window refresh or involuntary double-click on whathaveyou mess up with a painfully crafted post. So my advice is to have one post per image even if it looks like you're cheaply trying to raise your "Maple Leaf" count by multiple-posting.

Hope this helps!

> So this problem is with using the subscript [0] ? Have you encountered this before ?

the problem comes up now and again, I have seen it half a dozen times in the past year, at least. I have no idea why Maple doesn't always handle subscripts well. It is generally recommended to avoid subscripts and write things like xi instead of x[i].

> So this problem is with using the subscript [0] ? Have you encountered this before ?

the problem comes up now and again, I have seen it half a dozen times in the past year, at least. I have no idea why Maple doesn't always handle subscripts well. It is generally recommended to avoid subscripts and write things like xi instead of x[i].

Thanks Scott, okay I was assuming that the animation would play automatically, but instead I had to trigger it by selecting "play" in the context menu (I don't usually do mouse clicks so it didn't occur to me to try it).

Even better, I found that by selecting the following:

Tools -> Options -> Display -> Plot Display -> Window

I get a very intuitive "play" button at the bottom of the pop-up window. Then it doesn't take a genius to figure out that pressing play will trigger the animation. Even I was able to work it out. And this one time I overcame a certain reluctance and touched a mouse.

Cheers Scott,

Patrick.

Giorgios, the animation doesn't work here (Maple13.01, standard), I haven't looked into it, is a change in the parameters required or something?.