Anomalies in nonlinear device models

Circuit models of many nonlinear devices and systems have given rise to anomalous and paradoxical phenomena which have defined any logical explanation using classical circuit and system theory. The difficulty is due largely to our tendency to apply linear circuit and system theory to explain grossly nonlinear phenomena. These anomalies can only be resolved by developing a new foundation for "nonlinear device modeling", where unconventional circuit elements and modern mathematical tools (e.g., singular perturbation, topological dynamics, etc.) play leading roles [1-3]. The purpose of this lecture is to sample some recent advances in this exciting area of research.