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Re: phase portraits

• To: mathgroup at smc.vnet.net
• Subject: [mg116173] Re: phase portraits
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Fri, 4 Feb 2011 01:38:24 -0500 (EST)

J and B wrote:
> I am trying to find examples where Mathematica is used to study dynamic
> equations through the use of phase portraits, including their respective
> points: equilibrium, stability, attractors, bifurcations and so on.
>  
> Does any one have any work on this subject that he/she would mind sharing?
> I had many courses in this field in graduate school in the early 70's, and
> now I am trying to get a handle on them again.  Back then I was using
> Fortran.   Things have changed a lot.
>  
> Thanks

There are Demonstrations that cover some of this. I give URLs to some of 
the more relevant ones below.

http://demonstrations.wolfram.com/PhasePortraitAndFieldDirectionsOfTwoDimensionalLinearSystems/
http://demonstrations.wolfram.com/EigenvaluesAndLinearPhasePortraits/
http://demonstrations.wolfram.com/VisualizingTheSolutionOfTwoLinearDifferentialEquations/
http://demonstrations.wolfram.com/ATourOfSecondOrderOrdinaryDifferentialEquations/
http://demonstrations.wolfram.com/UsingEigenvaluesToSolveAFirstOrderSystemOfTwoCoupledDifferen/
http://demonstrations.wolfram.com/BifurcationsInFirstOrderODEs/

Also might want to check
http://library.wolfram.com/search/?query=phase+portrait&collection=library&x=0&y=0

Daniel Lichtblau
Wolfram Research