Multimode oscillations in mutually coupled van der Pol type oscillators with fifth-power nonlinear characteristics

Coupled van der Pol oscillators containing a fifth-order conductance characteristic are analyzed using a method due to Endo and Mori. This structure has been proposed for modeling the myoelectrical activity of the human large intestine since it produces stable conditions of zero, two single-mode frequencies, and also a double-mode condition. The paper first considers the case of oscilators having equal frequencies and it is shown that for a certain range of parameters double modes are possible for two oscillators, which is in contrast to the case of conventional van der Pol dynamics. The theoretical results have been experimentally verified using both analog simulations and electronic circuitry. In digestive tract modeling, the coupled oscillators must often have unequal intrinsic frequencies and this case is also considered and shown to give similar but more complex parameter conditions for the establishment of double modes.