Validation of the Mathematica model
I will verify the e-mail address of the responsible people at The Harvard Museum of Zoology, and I will send to that person an email requesting access to the collection.
- I concluded succesfully the validation of the model. The model reproduce now perfectly the Matlab model provided by David Miguez. Moreover, I tried to characterize the equilibrium point using Phaser and Mathematica (I obtained phase plane images in order to have a vector of initial conditions close to the unstable equilibrium pint associated to the observed oscillatory behavior), unfortunately the Newton algorithm of Phaser is very sensitive to the step, and in consequnce I am not sure if this software is really useful for the purpose here established.
- It seems that for the given system the unstable equilibrium point is associated to a robust attractive limit cycle. It would be be convenient to analyze the behavior of this cycle characterizing the ranges of the initial conditions robustness of the system the equilibrium point.
- Concerning the robustness of the system when affected by changes in the parameters, it seems that phaser offers a nice tool (the chosen parameter can be increased by a fixed delta and then the corresponding behavior is recorded in a sequence which, something like a video -this only work for the licenced version-).
- I must now to see if the Madalane Chaves approach is useful to establis bistability of this kind of systems.
- The updated version of the files are Media:david.zip:
New version of the LaTeX file
Asking for a visit to see the collection of ants