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MathGroup Archive 2011

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2 parameter bifurcation diagrams

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121547] 2 parameter bifurcation diagrams
  • From: Robert Reynolds <milver at mathstat.yorku.ca>
  • Date: Mon, 19 Sep 2011 07:05:49 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello, I am trying to plot a 2-parameter bifurcation diagram for a time dependent ode system using mathematica. I have attached a pdf version for the work I am trying to achieve. Do you have any mathematica code that will plot the attached bifurcation plots?

Bifurcation diagrams are usually drawn in the phase space
or augmented phase space. I see now the definition of that Neimark-Sacker bifurcation diagram. The curves show where Floquet exponents have a zero real part. In a time periodic system you need to locate the periodic point depending on the parameters numerically compute the matrix of the linearization of the return map and compute the
eigenvalues. Once you have this, then a simple "ContourPlot" in mathematica gives you the picture you see on page 451. IN the situation you have in the book, I guess that the equilibrium points are known (0,0) is certainly one but not intersting for the model.
So, yes mathematica could do this very well, but would require a bit more effort to find the Jacobean of the return map.




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