There are different frameworks for various categories of simulation, though a decent general platform for prototyping is MatLab, or to a lesser extent Octave (a free MatLab compatible language). It's fairly good at expressing matrix and cellular data and differential equations, which should cover the examples you listed. As you get to more specific categories, it would be worthwhile to pose the question for suggested frameworks to more specialised groups (for example, for tree-graph based simulations, you want an L-system engine).
Spread sheets can also be handy for crunching through data sets and building up quick & dirty analyses.
It's also useful to keep a good plotting tool handy. I personally like gnuplot, but there are many options available, such as Grapher (comes with OS X), or the graphing tools in spread sheets.