Theoretical Analysis of Subthreshold Oscillatory Behaviors in Nonlinear Autonomous Systems

We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict quantitatively the subthreshold oscillatory activities, including the damping coefficients and the oscillatory frequencies which are in good agreement with those observed in experiments. Then we generalize the linearization method to an arbitrary autonomous nonlinear system. The detailed extension of this theoretical approach is also presented and further discussed.