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Re: Re: directionfields from StreamPlot looks

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100567] Re: [mg100531] Re: directionfields from StreamPlot looks
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 8 Jun 2009 02:06:52 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200906050703.DAA25606@smc.vnet.net> <h0d72j$srt$1@smc.vnet.net> <200906061026.GAA04631@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

At the end of your message (below), you ask about visualizing Poincare 
maps. I recommend you look at Gianluca Gorni's notebook PoincareMaps.nb 
(which includes the code for a corresponding package). There's a version 
for old versions of Mathematica at Gorni's web site:

   http://sole.dimi.uniud.it/~gianluca.gorni/

I've done much of the revision of that notebook so that it will work 
with Mathematica 7, but there's still some work to do about which I've 
written directly to Prof. Gorni. If you're interested, I can send you a 
copy of what I have so far.

However, to run Gorni's functions, you'll also need a copy of David 
Park's non-free but marvelous and useful Presentations package, which 
handles much of the underlying graphics.  You can obtain the package 
from Park's site:

   http://home.comcast.net/~djmpark/DrawGraphicsPage.html

The posted copy of Gorni's package uses Park's older DrawGraphics 
package, which like Presentations is not free and is available from the 
same site of David's.

sean_incali at yahoo.com wrote:
> 
> k1 and k2 are pseudo first order reaction rate constants. It can range
> from 10^-3 to 10^7 or so. (for diffusion limited process)  h range
> from 0 to 1.
> 
> The [original] system ...is kinda simplified... The system below behaves a bit
> more interestingly.  (Let's say...k1=3, k2=7, t=50 and then...)
> 
> Manipulate[
>  StreamPlot[{va - k1 (t^-h) a - k2 ( t^-h ) b,  k1 (t^-h ) a - db},
> {a, -10, 10}, {b, -10, 10}], {k1, 0.01,10}, {k2, 0.01, 10}, {t, 0.1,
> 50}, {h, 0, 1}, {va, 0.1, 10}, {db, 0.1, 10}]
> 
> 
> As you vary va, db, and h, you will see the center of stable attractor
> shifts.
> 
> This is entirely a different post, but if I wanted to see a poincare
> section of that system, will that be doable in mathematica?  Seems
> Like Stephen Lynch's book uses 3 different CAs to generate the
> figures. And Mathematica version doesn't have the codes for poincare
> section shown in fig 8.11 b....

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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