Hi Rob,

Thanks for your response! I didn't realize I had one here, until today. Since I wrote that question, I have been done two important things:

1) learn more math: last semester was numerical methods, this semester is dynamical systems

2) learned how to use Cython -- already, this has helped me speed up my simulations to the point where making things like bifurcation diagrams is a bigger deal for me (another thing I know PyDSTool can do too)

This semester, in my dynamical systems course, we are going to be using lots of XPPAUT, but I plan on using PyDSTool. I have already had a look at tutorials like: http://www.ni.gsu.edu/~rclewley/PyDSTool/Tutorial/Tutorial_VdP.html

I am excited! Again, sorry for not seeing this message earlier, and thanks for offering to help! I will post on the discussion board if I find something specific I could use some help with.

Kind regards,

Brian

On Wed, Oct 8, 2014 at 8:26 AM, Rob Clewley <rob.clewley@gmail.com> wrote:

Hi Brian,

I know we've talked about this before, but here are some more general
suggestions about your problem.
>
> So, I changed the implementation so that everything was done in "one-shot"
> (luckily the only non-DE rule I had so far was easily converted to a DE
> rule, although there is one coming up which I don't see any easy conversion
> for...[that is the subject of this
> question](http://scicomp.stackexchange.com/questions/14765/scipy-integrate-odeint-how-can-odeint-access-a-parameter-set-that-is-evolving-i)).
>

Having looked at that, your problem is not so bad. You will need to
solve a piecewise (a.k.a. "hybrid") system, but you shouldn't be
discretizing it based on time but based on events -- i.e. when your
particle crosses into a new discrete area you are calling p. You then
have a discrete state update for your parameters and then you can
restart your smooth integrator until the next transition. This is a
well-studied problem in this form and is numerically soluble with a
hybrid solver such as that provided by PyDSTool. Between positional
transitions, your dynamical system is smooth and can be solved with a
regular ODE solver. The Jacobian within each domain should be simple
enough to pre-calculate (as a function of p or <p>). There are a few
hybrid model examples with PyDSTool on the tutorial and I am willing
to help a bit with the setup once you've given a new script for your
problem a shot. Take a copy of a helpful example (e.g. the SLIP pogo
stick dynamics) and adapt it to set up what you can. Put in some
comments etc. of what you need to happen.

PyDSTool will be able to convert the ODEs to C code automatically but
not the transition rules, which will still happen in python. This will
not be the *fastest* way to solve it but, more importantly, this way
will give you an accurate solution in a form that you can understand
and manipulate, and you can worry about optimizing speed later, IMO.

-Rob
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