On the Equations of Nonlinear Networks

Abstract

A systematic method of selecting state variables and formulating the normal form differential equations of general classes of nonlinear networks is presented. It is shown that the key problem in the formulation of the differential equations is the calculation of certain functions which appear in these equations. Iterative procedures for the calculation of these functions are given for certain classes of networks, and it is shown that the conditions for convergence of these procedures are closely related to certain physical properties of the network. These procedures are readily adaptable to machime computation and can be made an integral part of any numerical method used for the solution of the differential equations of the network.