Mixed-mode oscillations: From neural phenomena to mechanical modelling

Abstract

This paper offers new results from a study of mixed-mode oscillations, with application to both neural and mechanical systems. It is initially shown that the Fitzhugh-Nagumo model, which is itself a simplification of the previous electrophysiological model of Hodgkin and Huxley, has a direct analogue in the form of the model for a bistable spring mass system. This system is then shown to exhibit three qualitatively different motions and the design parameter space for the oscillator is examined in order to define conditions for these and for mixed-mode oscillations. The paper concludes with a conjecture that an autonomous system of this form can display some of the dynamic characteristics of the autonomous van der Pol oscillator, and one example of this equivalence is examined numerically.