Stochastic Synchrony and Phase Resetting Curves: Theory and Applications

STOCHASTIC SYNCHRONY AND PHASE RESETTING CURVES: THEORY AND APPLICATIONS Sashi K. Marella, PhD University of Pittsburgh, 2012 We investigate the relationship between the shape of the phase-resetting curve (PRC) and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated Poisson inputs. Using perturbation methods, we derive an expression relating the shape of the PRC to the probability density function (PDF) of the phase difference between the oscillators. Using various measures of synchrony and crosscorrelation we demonstrate that the degree of stochastic synchronization is dependent on the firing rate of the neuron and the membership of the PRC (Type I or Type II). We apply our theory to the olfactory bulb to investigate whether the correlated output of the olfactory bulb granule cells can synchronize uncoupled mitral cells via a positive feedback loop in correlation. We demonstrate the emergence and temporal evolution of input correlation in recurrent networks with feedback. We also investigate the rate of convergence to the steady-state PDF using an analytical approach. Our investigation explores several theoretical models ranging from spiking models to abstract analytically tractable models.