色噪声和周期激励下肿瘤细胞增长系统的随机共振
Stochastic Resonance in a Tumor Cell Growth System Driven by a Colored Noise and Periodic Excitation
作者: 李行 , 刘子铭 , 李胜宏 :江苏科技大学数理学院,江苏 镇江;
关键词: 肿瘤细胞增长系统; 色噪声; 随机共振; 信噪比; Tumor Cell Growth System; Colored Noise; Stochastic Resonance; Signal-to-Noise Rate
摘要:Abstract: In this paper, stochastic resonance in a tumor cell growth system driven by a colored noise and periodic excitation is investigated. According to Novikov theorem and unified colored noise theory, the related Fokker-Plank equation and the stable probability density function are obtained. Based on theory, we present the explicit expression of signal-to-noise ratio. Conclusions are that: stochastic resonance produced as noise strength is little and its strength is increased as tumor cell growth rate and amplitude of periodic effect are increased respectively. But the carrying capacity has no obvious impact on the strength of stochastic resonance, however, the more carrying capacity is, the more the required noise strength to attain stochastic resonance is.
文章引用: 李行 , 刘子铭 , 李胜宏 (2015) 色噪声和周期激励下肿瘤细胞增长系统的随机共振。 应用物理, 5, 147-153. doi: 10.12677/APP.2015.511020
参考文献
[1]
Benzi, R., Sutera, A. and Vulpiani, A. (1981) Stochastic Resonance in Climatic Change. Journal of Physics A: Mathematical and Theoretical, 14, L453-L457.
http://dx.doi.org/10.1088/0305-4470/14/11/006
[2]
Nicolis, C. and Nicolis, G. (1981) Stochastic Aspect of Climatic Transitions Additive Fluctuations. Tellus, 33, 225-234.
http://dx.doi.org/10.1111/j.2153-3490.1981.tb01746.x
[3]
Fauve, S. and Helslot, F. (1983) Stochastic Resonance in a Bistable System. Physics Letters A, 97, 5-7.
http://dx.doi.org/10.1016/0375-9601(83)90086-5
[4]
McNamara, B. and Wiesenfeld, K. (1989) Theory of Stochastic Resonance. Physics Review A, 39, 4854-4869.
http://dx.doi.org/10.1103/PhysRevA.39.4854
[5]
Liao, H.Y., Ai, B.Q. and Hu, L. (2008) A New Logistic Model for Bacterial Growth in the Presence of a Gaussian Colored Moise. Brazilian Journal of Physical, 37, 1125.
http://dx.doi.org/10.1590/S0103-97332007000700009
[6]
Zeng, C.H., Zhou, X.F., et al. (2009) Stochastic Resonance in a Bacterium Growth System Subjected to Colored Noises. Communications in Theoretical Physics, 52, 615-618.
http://dx.doi.org/10.1088/0253-6102/52/4/12
[7]
Panetta, J.C. (1995) A Logistic Model of Periodic Excitation. Applied Mathematics Letters, 8, 83-86.
http://dx.doi.org/10.1016/0893-9659(95)00053-S
[8] Novikov, E.A. (1965) Functional and Random-Force Method in Turbulence Theory. Soviet Physics—JETP, 20, 1290.
[9]
Jung, P. and Haanggi, P. (1987) Dynamical Systems: A Unified Colored-Noise Approximation. Physical Review A, 35, 4464-4466.
http://dx.doi.org/10.1103/PhysRevA.35.4464