Mode analysis of a two-dimensional low-pass multimode oscillator

The multimode oscillator properties of a square array of van der Pol oscillators coupled by inductances are analyzed in the quasiharmonic approximation. The criteria for discriminating the stability of single, nonresonant double, and degenerate modes are shown. Two fundamental techniques are employed in the analysis. One is the equivalent-linearization technique developed by Kryloff and Bogoliuboff. The other is mode analysis. The analytical and experimental results for a (3 x 4)-section array are discussed as an example of the method.