The 1980s were the decade which drew the attention of scientists to nonlinear and chaotic phenomena. Scientists had to lay the groundwork by integrating geometric and topological concepts (phase space, embedding, Lyapunov exponents, dimensions). The 1990s were the decade of refinement and application. From an engineer's point of view, there are at least three outstanding books worth mentioning which summarize the state of the art. Each book is supplemented by software for -line analysis, implementing the ideas presented in the respective books.
- Abarbanel was among the first to speak of a new applied discipline (Nonlinear Signal Processing) and outline it. You can find his book at http://www.zweb.com/apnonlin/. The software is called cspX TOOLS FOR DYNAMICS. It is commercial software and can be found at http://www.zweb.com/apnonlin/csp.html.
- Kantz & Schreiber name the discipline and their book Nonlinear Time Series Analysis. Their software is called TISEAN. It is free and can be found at http://www.mpipks-dresden.mpg.de/~tisean/. TISEAN 2.0 is also available for the MS Win32 platforms, because they compiled it with the Cygwin Toolset, the free UNIX emulation layer on top of Win32.
- Nusse & Yorke distribute their software (called Dynamics2) with their book (called Dynamics 2nd Ed.). It is a hands-on approach to learning the concepts and computing relevant quantities: http://keck2.umd.edu/dynamics/general_info/smalldyn_download.html.
In the list of FAQs of sci.nonlinear, you will find even more books, links and software (see Resources).