Qualitative analysis of 1st- and 2nd-order nonlinear networks

The paper presents several circuit-theory approaches for analysing the qualitative behaviour of nonlinear networks containing one or two energy-storage elements. The main concept consists in the transformation of a dynamic-network problem into an equivalent resistive-network problem. In particular, it is shown that any 1st-order nonlinear network can be analysed by obtaining the solution waveforms of an associated resistive constant-slope network. For 2nd-order autonomous nonlinear networks, it is shown that their isoclines are identical to the transfer-characteristic plots of an associated resistive isocline network. Many qualitative properties are shown to be derivable from this network. The classical approach for finding singular points, separatrices, and limit cycles is shown to have simple circuit-theory interpretations. The paper concludes with the presentation of three symmetry theorems useful for analysing 2nd-order nonlinear networks.