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Re: Re: Re: directionfields from StreamPlot

To clarify one point: when one updates Gorni's PoincareMaps.nb so as to 
work with Mathematica 7, one then replaces Park's DrawGraphics with 
Park's Presentations package.

Murray Eisenberg wrote:
> 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:
> 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:
> 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 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 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
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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