Applications of Bifurcation: Nonautonomous Periodically-Excited Systems

This paper reviews some examples of bifurcation in low-order, periodically driven dynamical systems. The generic loss of stability is a key component in dynamical systems theory, and provides a central pillar in assessing qualitative changes in system dynamics. Although bifurcation tends to be thought of in rather abstract, theoretical terms, we show that it also provides a compelling framework to guide laboratory-based experiments. Both local and global stability transitions and their connection are illustrated in this accessible, review-like pictorial overview of simple mechanical/structural systems driven toward instability.