Theoretical Analysis of Subthreshold Oscillatory Behaviors in Nonlinear Autonomous Systems.pdf

Theoretical Analysis of Subthreshold Oscillatory Behaviors in Nonlinear Autonomous Systems Shenbing Kuang, Jiafu Wang,∗ Ting Zeng, and Aiyin Cao Department of Physical Science and Technology, Wuhan University of Technology, Wuhan 430070 China 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 7 autonomous nonlinear system. The detailed extension of this theoretical approach is also presented 0 and further discussed. 0 2 PACS numbers: 87.10.+e, 05.45.-a y a Oscillatory behaviors are one of the most important iors in autonomous neuronal system, we consider the M features for the nonlinear systems and have attracted Hindmarsh-Rose (HR) neural model, as an example, un- much attention in recent years [1, 2, 3]. Oscillation phe- der a subthreshold constant stimulus. The dynamics of 8 nomena have been discovered in many areas of the chem- HR neuron system could be described by the following ] ical and biological sciences, such as chemical oscillation equations[20]: M