title: Robust entrainment phenomena of oscillations by delay time in the photosensitive Oregonator model.
abstract: The influences of delayed feedback on the oscillating behaviors are numerically investigated by using the photosensitive Oregonator model with a Hopf point. We find that the time delay in the robust entrainment phenomena determines the time scale of the system, that is, T_{m}=(tau+delta)N (N=1,2,cdots, three dots, centered) , where T_{m} is the mean period of the oscillation and delta is a small constant compared with the delay time tau . Further, our numerical simulation shows that, when the system has a characteristic period T0 under the feedback with time delay, there exists an asymptotical line delta=delta_{0}T_{0} ( delta_{0} independent of any parameters) in the entrainment region with increasing strength of the feedback control c ; when the system has no characteristic period, the above linear relation is also kept, and delta decreases with increasing c .
authors.affiliation: State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Bao
authors.forename: Zan
authors.initials: Z
authors.lastname: Li
authors.forename: Lu-Qun
authors.initials: LQ
authors.lastname: Zhou
authors.forename: Zhuo
authors.initials: Z
authors.lastname: Gao