  This paper deals with the analysis of nonlinear circuits that interconnect
passive elements (capacitors, inductors, and resistors) with nonlinear
resistors exhibiting a range of $\it{negative}$ resistance. Such active
elements are necessary to design circuits that switch and oscillate. We
generalize the classical passivity theory of circuit analysis to account for
such non-equilibrium behaviors. The approach closely mimics the classical
methodology of (incremental) dissipativity theory, but with dissipation
inequalities that combine $\it{signed}$ storage functions and $\it{signed}$
supply rates to account for the mixture of passive and active elements.
