This work presents a unified theory of nonlinear RLC networks using an entirely new approach--the parametric approach. The class of networks considered includes any arbitrary time-invariant, nonlinear RLC network whose elements can be characterized by a unicursal curve. In particular, curves which are multiple-valued functions of both terminal variables such as the hysteresis curves are admissible. Through the use of Stieltjes integrals, a generalization of the concepts of 'content' and 'co-content' as well as 'energy' and 'co-energy' is made which leads directly to a generalization of the Legendre transformation. It is then shown that the equilibrium equations of such networks can always be formulated mathematically as a system of algebraic-differential equations. The Schauder fixed point theorem and the principle of contraction mapping are then used to formulate a number of existence theorems on the solutions of nonlinear resistive networks. The concept of equivalent nonlinear networks as well as the principle of duality in nonlinear networks is introduced and a number of useful theorems on equivalent nonlinear networks are presented. (Author)
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