Special considerations in forced nonlinear systems

Several techniques for the analysis of nonlinear systems are examined. In particular, an iterative method of determining the response of a nonlinear network is presented. The approach, shown to be termwise equivalent to the Volterra-series solution, provides a significant reduction in the amount of computation necessary to determine the complete system response. The class of circuits discussed consists of a single nonlinear element in an arbitrary linear, time-invariant circuit. For this class, a general verification of stability scheme is proposed. Special emphasis is placed on systems with cubic nonlinear characteristics because they demonstrate the interesting jump-resonance phenomenon. Analysis of such systems provides the basis for insight into operation of much more complicated physical systems. In this analysis, initial conditions are always set to zeros, and the switching angle of the forcing function is instead used as the deciding initial state in the attainment of all harmonic-system solutions. Computer simulation results, applying to a specific system, show the regions of initial conditions which lead to two different steady-state oscillations