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Re: a' vs a and a vs a' looks different in streamplot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99658] Re: [mg99627] a' vs a and a vs a' looks different in streamplot
  • From: sean k <sean_incali at yahoo.com>
  • Date: Sun, 10 May 2009 05:17:56 -0400 (EDT)
  • Reply-to: sean_incali at yahoo.com

I recognize I only gave one equation with 2 unknowns. That's not the issue though.  Let's say the system was... 

a'[t]== -a[t] -kr -b[t]
b'[t]== -a[t]

And we want to look at the vectorfields. When I plot the a' vs a or a vs a' I get two entirely different plots. (not just 90 rotation of each other)



--- On Sat, 5/9/09, sean_incali at yahoo.com <sean_incali at yahoo.com> wrote:

> From: sean_incali at yahoo.com <sean_incali at yahoo.com>
> Subject: [mg99627] a' vs a and a vs a' looks different in streamplot
> To: mathgroup at smc.vnet.net
> Date: Saturday, May 9, 2009, 12:31 AM
> Consider the following.
> 
> a'[t]= -a[t] -kr -b[t]
> 
> Let us plot the vectorfields of a' vs a. (or a vs
> a' for that matter)
> as follows.
> 
> Manipulate[{StreamPlot[{a, -a - kr b}, {a, -10, 10}, {b,
> -10, 10},
>    FrameLabel -> {a, a'}],
>   StreamPlot[{-a - kr b, a}, {a, -10, 10}, {b, -10, 10},
>    FrameLabel -> {a', a}]}, {kr, 0, 10}]
> 
> Why do the plots of " a vs. a' " and "
> a' vs. a " look so different?
> They aren't just 90' rotation of each other.
> 
> Shouldn't they be?
> 
> Thanks for any insight.
> 
> Sean


      


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