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I was wondering if there is any available continuation and bifurcation analysis package for Mathematica. I'm looking for something like AUTO. I've seen there is already a Matlab version of the software.

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http://library.wolfram.com/infocenter/Demos/149/ This looks like a solution. Its called dynpac4.

An updated version is available at http://www2.me.rochester.edu/~clark/dynpac.html

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    $\begingroup$ Interesting find! That version is quite old, from the year 2000 when Mathematica $VersionNumber==4.0. There's an updated version of the package available here. I'll have a look and see what continuation and bifurcation functions it has. $\endgroup$ – Chris K Feb 12 at 18:34
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    $\begingroup$ The package is a product of its time ("it often looks like the FORTRAN I wrote for 30 years" as per the introduction :-), but there are many great pedagogical examples of dynamical systems in there. Something like this needs to be updated! Unfortunately it doesn't look like there are functions for continuing an equilibrium or detecting bifurcations like AUTO or CONTENT can. $\endgroup$ – Chris K Feb 12 at 20:03
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    $\begingroup$ @ChrisK I tried a few examples and they all worked, which is somewhat unusual for such an old package. Ironically, this is very likely because the author went against convention and used all lowercase names. These days the biggest menace to package compatibility is that new versions of Mathematica indiscriminately add lots of new names into the system namespace, which pretty much guarantees that some packages will break. $\endgroup$ – Szabolcs Apr 1 at 10:26

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