A random dynamical systems perspective on stochastic resonance. (7th June 2017)

• Record Type: Journal Article
• Authors: Maria Cherubini, Anna; Lamb, Jeroen S W; Rasmussen, Martin; Sato, Yuzuru
• Is Part Of: Nonlinearity. Volume 30:Number 7(2017:Jul.)
• Page Start: 2835
• Page End: 2853
• Publication Date: 2017-06-07
• Subjects: nonautonomous random dynamical systems -- stochastic resonance -- Markov measures -- random attractors; 37H10 -- 37H99 -- 60H10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa72bd
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a nonautonomous forcing. We prove the existence of a unique global attracting random periodic orbit and a stationary periodic measure. We use the stationary periodic measure to define an indicator for the stochastic resonance.