Shil´nikov´s theorem-a tutorial

The phenomenon of chaos has been observed in many nonlinear deterministic systems in both experimental and computer-simulation contexts. Given the nature of this phenomenon, however, an analytical tool is needed to ensure that what is observed is not an artifact of the device used to measure or simulate the given system. This paper provides a tutorial look at one of the few and most useful of such tools: Shil´nikov´s theorem and its various extensions. This exposition presents the basic terminology and concepts related to Shil´nikov´s results, a formal statement and subsequent discussion of its two basic versions for 3D systems, as well as two example applications of Shil´nikov´s method to a piecewise-linear system