Equivalent dynamics in different neural oscillator models

This paper introduces a method of model transformation for neural oscillators defined by a set of ordinary differential equations and a nonlinearity and gives an example for two popular neural oscillator models. The method finds the parameters of one oscillator model such that its dynamics are equivalent to that of another oscillator model. Although this equivalence is obtained using the assumption of harmonic oscillations, it can be shown in simulations that these transformed neural oscillators not only behave equivalently in the state of harmonic balance, but also mainly equivalent in stationary and chaotic activation states. Moreover, even networks consisting of those oscillators show equivalent dynamics under very different dynamic regimes.