Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

doi:10.1088/1674-1056/19/2/020504

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20504-020504.doi: 10.1088/1674-1056/19/2/020504

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

贾正林

Department of Physics, Yuxi Normal University, Yuxi 653100, Yunnan Province, China

收稿日期:2009-01-04 修回日期:2009-03-04 出版日期:2010-02-15 发布日期:2010-02-15
基金资助:
Project supported by the Natural Science Foundation of Yunnan Province of China (Grant No.~2008CD214).

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

Jia Zheng-Lin(贾正林)^†

Department of Physics, Yuxi Normal University, Yuxi 653100, Yunnan Province, China

Received:2009-01-04 Revised:2009-03-04 Online:2010-02-15 Published:2010-02-15
Supported by:
Project supported by the Natural Science Foundation of Yunnan Province of China (Grant No.~2008CD214).

摘要/Abstract

摘要： This paper investigates the stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal in a cancer growth system with the cross-correlated noises and time delay. To describe the periodic change of the birth rate due to the periodic treatment, a multiplicative periodic signal is added to the system. Under the condition of small delay time, the analytical expression of the signal-to-noise ratio R_{\rm SNR} is derived in the adiabatic limit. By numerical calculation, the effects of the cross-correlation strength \lambda and the delay time \tau on R_{\rm SNR} are respectively discussed. The existence of a peak in the curves of R_{\rm SNR} as a function of the noise intensities indicates the occurrence of the SR phenomenon. It is found that \lambda and \tau play opposite role on the SR phenomenon, i.e., the SR is suppressed by increasing \lambda whereas it is enhanced with the increase of \tau, which is different from the case where the periodic signal is additive.

Abstract: This paper investigates the stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal in a cancer growth system with the cross-correlated noises and time delay. To describe the periodic change of the birth rate due to the periodic treatment, a multiplicative periodic signal is added to the system. Under the condition of small delay time, the analytical expression of the signal-to-noise ratio $R_{\rm SNR}$ is derived in the adiabatic limit. By numerical calculation, the effects of the cross-correlation strength $\lambda$ and the delay time $\tau$ on $R_{\rm SNR}$ are respectively discussed. The existence of a peak in the curves of $R_{\rm SNR}$ as a function of the noise intensities indicates the occurrence of the SR phenomenon. It is found that $\lambda$ and $\tau$ play opposite role on the SR phenomenon, i.e., the SR is suppressed by increasing $\lambda$ whereas it is enhanced with the increase of $\tau$, which is different from the case where the periodic signal is additive.

Key words: time delay, cross-correlated noise, stochastic resonance, cancer growth system

中图分类号: (Diseases)

87.19.X-

87.17.Ee (Growth and division) 87.10.-e (General theory and mathematical aspects) 02.50.Ey (Stochastic processes) 05.40.Ca (Noise)

贾正林. Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system[J]. 中国物理B, 2010, 19(2): 20504-020504.

Jia Zheng-Lin(贾正林). Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system[J]. Chin. Phys. B, 2010, 19(2): 20504-020504.

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Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

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