Non-Linear Circuit Mode Analysis

An exposition is given of recent advances in the theoretical analysis of circuits comprising sets of intercoupled non-linear oscillators. Motivation for this work has come from mathematical modelling of biomedical systems, particularly for the electrical activity of the gastro-intestinal digestive tract. Over the past few years a matrix linearisation method has been developed and applied to a wide range of structures comprising chains, arrays, rings and tubes. Also, different coupling components including pur time delay and two types of van der Pol oscillator dynamics have neeb investigated. Numerous mode patterns have been predicted and experimentally observed and stability criteria established for a wide range of conditions. The multi-oscillator mode analysis entails a two-stage process comprising matrix mode decoupling followed by equivalent linearisation similar to the Krylov-Bogolioubov approach.