I'm looking for datasets for biological systems that have been modeled by systems of ODEs (or more generally biological time series data). I can't even find a simple predator-prey dataset (from a legit source). Where can I find biological data (ecological, protein concentrations, etc vs. time)? Thanks.
You can find data related to the Canadian lynx and snowshoe hare pelt-trading records of the Hudson Bay Company, starting in 1845. It seems to be a standard dataset, described for instance in Predator-Prey Models.
I didn't get it: are you looking for synthtic datasets only, or are you looking for real time series data for validating your own ODE models?
In any case, try perhaps The Long Term Ecological Research Repository
" The Long Term Ecological Research (LTER) program concentrates on studies of ecological processes that play out at time scales spanning decades to centuries. Long-term data sets from the LTER program provide a context to evaluate the nature and pace of ecological change, to interpret its effects, and to forecast the range of future biological responses to change."
I don't know what exactly you would qualify as 'biological' data, but I would classify predator/prey relationships as 'ecological' ... and therefore I'd look in one of two places:
DataONE (Data Observation Network for Earth). Searches about 30 archives of environmental & ecological data.
Dryad, a repository for evolutionary & environmental data. Some journals in the field require data be deposited here if you publish papers through them.
DataONE searches Dryad, but Dryad also allows browsing, or searching by the journal in which the data was used, which might help you to find data of interest.
I'm personally not aware of any search engines in the ecological & environmental sciences that allow for searching by the dimensionality of the data. You tend to see that sort of restriction when there are many different types of instruments observing the same regions ... like in astronomy and solar physics.