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Topic: phase portraits
Replies: 6   Last Post: Feb 5, 2011 5:45 AM

 Messages: [ Previous | Next ]
 Daniel Lichtblau Posts: 1,761 Registered: 12/7/04
Re: phase portraits
Posted: Feb 4, 2011 1:38 AM

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

Date Subject Author
2/3/11 noslowski
2/4/11 Daniel Lichtblau
2/4/11 Sergio Miguel Terrazas Porras
2/4/11 James
2/4/11 sjoerd.c.devries@gmail.com
2/4/11 Virgil Stokes
2/5/11 Murray Eisenberg