Thermal Fluctuation of a Self-Oscillating Reaction System under a Periodic External Force. II: Quasi-Periodic Region

Abstract

A reductive perturbation scheme is proposed for describing the quasi-periodic behavior exhibited by a self-oscillating reaction system under a weak periodic force. Using this scheme and the system size expansion the behavior of thermal fluctuation is investigated. As a result it is found that variance of thermal fluctuation has a component making a secular increase with time. This phenomenon, similar to the ensemble dephasing or phase diffusion of a free limit cycle, is interpreted as ensemble dephasing in a stroboscopic phase space, i.e., stroboscopic ensemble dephasing.