Mode Analysis of a Tubular Structure of Coupled Fifth-Power Non-Linear Oscillators for Large-Intestinal Modelling

A tubular structure of coupled-non-linear oscillators provides a natural extension of hypothesized models for the electrical slow-wave activity of the mammalian intestines. In this paper, fifth-power van der Pol dynamics are used for the oscillator units providing a zero stable state, which may be important in terms of the human large-intestine where periods of electrical silence may occur. The matrix Krylov-Bogolioubov linearisation method is used to provide mode analysis of this structure. Although more extended than for the conventional third-power case the theoretical analysis reveals a rich mode behaviour. After development of the mxn general cases, two particular examples of 3x4 and 4x4 structures are given. The theoretical results for the 3x4 case compare favourably with the experimental investigation using electronic implementation of van der Pol type oscillators.