Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model
HAN Li-Bo 1,2, GONG Xiao-Long1, CAO Li2, WU Da-Jin3
1School of Physics Science and Technology, Yangtze University, Jingzhou 4340232State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 4300743Department of Physics, Huazhong University of Science and Technology, Wuhan 430074
Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model
HAN Li-Bo 1,2;GONG Xiao-Long1;CAO Li2;WU Da-Jin3
1School of Physics Science and Technology, Yangtze University, Jingzhou 4340232State Key Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 4300743Department of Physics, Huazhong University of Science and Technology, Wuhan 430074
摘要An approximate Fokker--Planck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution (SPD) and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ, is in -1<λ≤ 0 and can be the double extrema in 0<λ<1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, <x>, versus λ. The position and the value of the minimum are controlled by the noise-correlated times.
Abstract：An approximate Fokker--Planck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution (SPD) and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ, is in -1<λ≤ 0 and can be the double extrema in 0<λ<1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, <x>, versus λ. The position and the value of the minimum are controlled by the noise-correlated times.
HAN Li-Bo;GONG Xiao-Long;CAO Li;WU Da-Jin. Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model[J]. 中国物理快报, 2007, 24(3): 632-635.
HAN Li-Bo, GONG Xiao-Long, CAO Li, WU Da-Jin. Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model. Chin. Phys. Lett., 2007, 24(3): 632-635.
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2007, Vol. 24 
