Thermal Fluctuation of a Self-Oscillating Reaction System Entrained by a Periodic External Force

Abstract

The thermal fluctuation of a self-oscillating system entrained by a periodic external force is studied by means of the system size expansion method with the aid of the reductive perturbation approach. Three main results are obtained, i.e., (i) the suppression of the ensemble dephasing or phase diffusion of a free limit cycle by a periodic force (ii) the critical anomaly of the fluctuations at the instability points of the entrained system (iii) the existence of the stroboscopic circulation of fluctuation which is defined analogously to the irreversible circulation of fluctuation and plays the central role in characterizing the instabilities of the entrained system. These results do not depend on particular models although the Sel'kov-Higgins model for the glycolytic reaction is used in the present work.