Nonlinear dynamics and chaos theory in electrical systems and circuits Is there a possible application of the field of chaos theory and nonlinear dynamics to electrical systems such as circuits and power?
If so, are they based on conventional nonlinear dynamics or are they more based on electromagnetic theory?
 A: Whenever you have a system that is nonlinear, the methods and results from dynamical systems theory apply, so the range of applications is very broad and, yes, includes electronic circuits, of which the Chua's circuit is the most well known. It should be said, tough, that it probably counts more as a constructed example of a simple circuit that displays chaos, rather than an effective application of the theory.
A more recent application of the complex systems theory (which includes chaos theory) to electrical systems is the power distribution network dynamics, especially their stability with respect to failure or attacks (for example). The usual approach in this case falls under the concept of complex networks, sometimes in conjunction with agent-based models, besides more "conventional" nonlinear dynamics theory (qualitative nature of transients and asymptotic states, stability, etc.).

are they more based on electromagnetic theory?

When you restrict yourself to electrical systems and circuits, a description at this level is often all you need, and it's not necessary to reach to the fundamentals. But there are examples of chaos in electromagnetism, such as the space-temporal chaos of three wave interactions (e-print) in plasmas and, more fundamentally, the Hamiltonian description of magnetic field lines.
