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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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