Components for the toolbox
There is no universal program that would solve all kinds of problems for you. Almost always it is necessary to code something by yourself. Each reseacher has his own set of subprograms, code snippets, favourite algorithms and methods which is collected by years and serves as an initial material for everyday work.
At first glance, the matter this page is devoted to has no immediate concern with nonlinear dynamics. However, your precious intentions, methods, algorithms should be implemented in a stuff any programm is made of - some kind of programming languages your computer is aware of. And presumably you need a toolbox of reusable standard building blocks to make your life easier. By simplest estimations, minimal set of tools should include the following:
Statistical problems are not mentioned here, and spectral ones, and ..., and ... - would be happy myself to read about all this somewhere else.
Obviously, there are packages of subprograms "all-in-one" or "batteries included" - libraries where you can find all the necessary, except for, perhaps, last item of our list. If you are working under MATLAB or MATHEMATICA, well, I am wasting your time here. Or, for example, if you are the happy owner of the COMPAQ FORTRAN compiler, you have all you might need with IMSL library, precompiled and ready to use. Absolutely convenient thing.
However, often and often it would be desirable to have at hand something
Probably, it means that you need open source libraries.
First of all there are
General purpose libraries
Very often such a universal solution is not a flexible enough one. Necessity to fix up the problems of interdependency, compatibility and cross-references leads to a bootstrap and excessive formalization of interfaces.
To make a long story short, I want to say that sometimes the preferable way is to collect yourself a library from the pieces, taken from different reliable sources, for your own purposes. Therefore, I am going to give here alternative solutions concerning the aforementioned list of components for programming the nonlinear dynamics problems. They should not be considered as the best and strongly recommended for usage, but only as a probable choice and a point just to begin with.