Graphing the Separatix

*To*: mathgroup at smc.vnet.net*Subject*: [mg81945] Graphing the Separatix*From*: DBK <boydkramer at gmail.com>*Date*: Sun, 7 Oct 2007 05:34:24 -0400 (EDT)

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])