On the Properties of Nonlinear Integral Equations That Arise in the Theory of Dynamical Systems

Abstract

This paper reports on some results concerning the properties of integral equations that govern the behavior of a large class of control systems or electrical networks containing linear time-invariant elements and an arbitrary finite number of nonlinear time-varying elements. In particular, for networks containing linear time-invariant elements and an arbitrary finite number of positive-slope nonlinear resistors, it is proved, under reasonable conditions, that the response to a periodic excitation applied at t = 0 is ultimately periodic with the same period as the excitation, regardless of the initial state of the network.