Monday, November 24, 2014 03:15 PM
Title: The effect of moderate noise on a limit cycle oscillator: counterrotation and bistability
Speakers: Mike Schwemmer & Jay Newby,
Mathematical Biosciences Institute, The Ohio State University
Abstract: The effects of noise on the dynamics of nonlinear systems is known to lead to many counterintuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different dynamics. In particular, the system can rotate in the opposite direction of the deterministic limit cycle, cease oscillating altogether, or even display bistable switching. Utilizing standard techniques from stochastic calculus and recently developed stochastic phase reduction methods, we elucidate the mechanisms underlying the different dynamics and verify our analysis with the use of numerical simulations. Lastly, we discuss how different vector fields surrounding the limit cycle can lead to different types of bistable switching behaviors.