       Re: Graphing the Separatix

• To: mathgroup at smc.vnet.net
• Subject: [mg81998] Re: Graphing the Separatix
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 9 Oct 2007 05:34:17 -0400 (EDT)
• Organization: Uni Leipzig
• References: <fea9pk\$k80\$1@smc.vnet.net>

```Hi,

the curvature of the field lines has a zero along the separatrix
in this case.

To get curved lines you have to compute the field lines by
integrating the equations for the vector field.

Regards
Jens

DBK wrote:
> I am plotting the vector fields for the two equation system below
> using version 6. I have two questions.
> 1. How do I plot the separatix (i.e. stable manifold) separating the
> two basins of attraction?
> 2. How do I show the dynamics of the system with curved rather than
> straight vectors?
>
> Needs["VectorFieldPlots`"];
> p1 = 0.28;
> p2 = 0.7;
> p3 = 0.8;
> p4 = 0.15;
> p5 = 0.7;
> p6 = 0.6;
> p7 = 6.5;
> p8 = 0.3;
> aah = 0.00003333;
> fields = (VectorFieldPlot[{(p1 a  (p2 - a - p3 c))/p2, (
>     p4 c (p5 - c - (p6 a^p7)/(a^p7 + p8^p7)))/p5}, {a, 0, 1}, {c, 0,
>     1}, PlotPoints -> 10, ScaleFactor -> None, Axes -> Automatic,
>    MaxArrowLength -> 1, VectorHeads -> True])
>
>

```

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