Try using Latin Hypercube sampling from a reasonable range for each season length. In pseudocode:
springRange = [some ball around 91.25] e.g. [81.25,101.25]
summerRange = [some ball around 91.25] e.g. [81.25,101.25]
fallRange = [some ball around 91.25] e.g. [81.25,101.25]
winterRange = [some ball around 91.25] e.g. [81.25,101.25]
ranges = [springRange(1), summerRange(1),fallRange(1), winterRange(1); ...
springRange(2), summerRange(2), fallRange(2), winterRange(2)];
ourHyperCube = lhsdesign(number_of_runs,4); %Makes a Latin Hypercube
for i = 1:number of runs
SeasonLengths_run = ourHyperCube(i,:) * (ranges(2,:) - ranges(1,:)) + ranges(1,:);
% SeasonLengths_run = something of the form [springLength, summerLength, fallLength, winterLength];
sum season lengths to get t_final
simulate ODE over [t_0 t_final]
pass season values to ODE
save run
end
%%%%%%%%%%%%%%
Then, in your ODE file, incorporate time-varying parameters. You can do this in a trivial way by telling it (
if t<startOfSummer
use SpringParams
end
and likewise for the other seasons.
This is a really rough sketch, obviously, but the concept might work. And I'd be interested to see your solution, so let us know if it works!
