Chaning the "spacing" when continuing a limit cycle
Numerical Bifurcation Analysis Toolbox in Matlab
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I'm trying to produce a limit cycle as in "Advances in numerical continuation software: MatCont" tutorial C, and I am able to continue a limit cycle of interest in my system. My problem comes with trying to control how the limit cycle is continue, specifically I seem to have no control over when a limit cycle is graphed with a given parameter value. Attached is two images, one of my solution (which is a blob) and the other is the solution given in the paper. I would like to edit mine such that the spacing of the limit cycles makes it obvious how the limit cycle changes with the parameter, is there a way to do this without extracting the data manually?
In addition, I don't seem to have control over how far the continuer will go as it changes the parameter. I would like to have the full range of epsilon between 0 and my hopf bifurcation, visible in the image, but since the limit cycle ends when epsilon is 0, i think the continuer starts to slow down as epsilon gets smaller and thus never gets to 0. I need to extend the calculation many times to get to where my graph is now, but it would be nice to not have to start the simulation, wait for it to finish, extend, wait to finish, extend, etc.... Any insight to this problem would be appreciated. Thank you.
to edit mine such that the spacing of the limit cycles makes it obvious how the limit cycle change
Not really, but you could try to adjust "MaxStepSize" in the Continuer window to a larger value. The problem is that the closer you get to epsilon=0, the smaller the step in the parameter and the larger in phase space, and the period too, and this is not independent. So at some point the cycles will appear to not vary a lot as the parameter does not change a lot (while the period does).
to not have to start the simulation-->Continuation, wait for it to finish, extend, wait to finish, extend, etc
Increase the number of steps from 300 (standard) to 20000 (for example). There is no general rule we could implement for this.