Investigation of stochastic synchronization in bursting oscillators

Abstract

Stochastic Synchronisation in uncoupled oscillators is a well studied phenomenon for many naturally occurring oscillators. The idea of this phenomenon is quite counter-intuitive since in this process, introduction of noise in a dynamical system brings about order and synchrony. The basic idea is that when two uncoupled oscillators are undergoing their cycles and are subjected to some noises coming from common sources and thus having a correlation, they can tend to synchronise due to the perturbations of the correlated noises. The theory of stochastic synchronisation is based on the concept of Phase Response Curve (PRC) which is the characteristic of a given oscillator. It has been studied many times through numerical and experimental methods in simple oscillators but has not been much explored for the bursting oscillators. In this study, I have tried to investigate the phenomenon of stochastic synchronisation in Hindmarsh Rose (HR) oscillator which is a basic model type of neuronal bursting oscillators. This class of oscillators, called bursters, is a complicated one as the system alternates between oscillations and stable fixed points. The aim of this project was to compute an accurate Phase Response Curve of HR using different methods and then to use it to simulate the noise perturbed HR oscillations and finally trying to determine whether the stochastic synchronisation is exhibited in HR or not and if not, what could be the possible reasons.