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

• To: mathgroup at smc.vnet.net
• Subject: [mg99642] Re: a' vs a and a vs a' looks different in streamplot
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Sun, 10 May 2009 05:14:58 -0400 (EDT)
• References: <gu3bgr\$fd\$1@smc.vnet.net>

```sean_incali at yahoo.com wrote:
> Consider the following.
>
> a'[t]= -a[t] -kr -b[t]

This is legal input, but I guess you meant a'[t] == -a[t] -kr -b[t], right?

>
> 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?
>

This is because you did not switch the axes, but the components of the
vectors.  The result is that the vectors were mirrored with respect to
the first bisector (not simply rotated), without the positions at which
they're drawn being changed.

Compare this version, where the axes are exchanged as well.

StreamPlot[{-a - kr b, a}, {b, -10, 10}, {a, -10, 10}]

Now the full plot is mirrored, not just the vectors themselves.

```

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