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