Power electronics circuits are rich in nonlinear dynamics. Their operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of nonlinear behavior. This paper provides an overview of the chaotic dynamics and bifurcation scenarios observed in power converter circuits, emphasizing the salient features of the circuit operation and the modeling strategies. In particular, this paper surveys the key publications in this field, reviews the main modeling approaches, and discusses the salient bifurcation behaviors of power converters with particular emphasis on the disruption of standard bifurcation patterns by border collisions.

We study the problem of controlling a general complex network toward an assigned synchronous evolution by means of a pinning control strategy. We define the pinning controllability of the network in terms of the spectral properties of an extended network topology. The roles of the control and coupling gains, as well as of the number of pinned nodes, are also discussed.

This paper addresses the problem of providing mathematical conditions that allow one to ensure that biological networks, such as transcriptional systems, can be globally entrained to external periodic inputs. Despite appearing obvious at first, this is by no means a generic property of nonlinear dynamical systems. Through the use of contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all their solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific cases of models of transcriptional systems as well as constructs of interest in synthetic biology. A self-contained exposition of all needed results is given in the paper.