Coexisting Dynamical Phenomena with Different Time Scales in Autonomous Systems: How Their Generation and Combination Can Occur

This chapter describes a dynamical scenario in which an autonomous system can incorporate many oscillation modes of different frequencies, and where the oscillations can intermittently combine with each other to produce extremely complex self-sustained behaviors with multiple time scales. The complex oscillations are illustrated by means of the experimental devices with which they were discovered, which are simple enough to offer a comprehensive view of what is happening at the physical level. At the same time, we consider what remains to be understood in order to explain the observed behavior and how the qualitative methods of nonlinear dynamics can be used to provide such an understanding. Although a proper mathematical theory for the oscillatory mixing mechanism has yet to be developed, its features suggest significant possibilities for scalability, making it potentially relevant for the study of systems exhibiting rich oscillatory dynamics.