中国物理B ›› 2008, Vol. 17 ›› Issue (2): 479-485.doi: 10.1088/1674-1056/17/2/023

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Transitions in a genotype selection model driven by coloured noises

梅冬成1, 王参军2   

  1. (1)Department of Physics, Yunnan University, Kunming 650091, China; (2)Department of Physics, Yunnan University, Kunming 650091, China;Nonlinear Research Institute, Baoji University Of Sciences And Arts, Baoji 721007, China
  • 收稿日期:2007-05-30 修回日期:2007-07-05 出版日期:2008-02-20 发布日期:2008-02-20
  • 基金资助:
    Project supported by the Natural Science Foundation of Yunnan province of China (Grant No 2006A0002M) and the Science Foundation of Baoji University of Science and Arts of China (Grant No Zk0697).

Transitions in a genotype selection model driven by coloured noises

Wang Can-Jun(王参军)a)b)† and Mei Dong-Cheng(梅冬成)a)   

  1. a Department of Physics, Yunnan University, Kunming 650091, China; b Nonlinear Research Institute, Baoji University Of Sciences And Arts, Baoji 721007, China
  • Received:2007-05-30 Revised:2007-07-05 Online:2008-02-20 Published:2008-02-20
  • Supported by:
    Project supported by the Natural Science Foundation of Yunnan province of China (Grant No 2006A0002M) and the Science Foundation of Baoji University of Science and Arts of China (Grant No Zk0697).

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摘要： This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time $\tau_{1}$ and $\tau_{2}$ by means of the numerical technique. By directly simulating the Langevin Equation, the following results are obtained. (1) The multiplicative coloured noise dominates, however, the effect of the additive coloured noise is not neglected in the practical gene selection process. The selection rate $\mu$ decides that the selection is propitious to gene $A$ haploid or gene $B$ haploid. (2) The additive coloured noise intensity $\alpha$ and the correlation time $\tau_2$ play opposite roles. It is noted that $\alpha$ and $\tau_2$ can not separate the single peak, while $\alpha$ can make the peak disappear and $\tau_2$ can make the peak be sharp. (3) The multiplicative coloured noise intensity $D$ and the correlation time $\tau_1$ can induce phase transition, at the same time they play opposite roles and the reentrance phenomenon appears. In this case, it is easy to select one type haploid from the group with increasing $D$ and decreasing $\tau_1$.

关键词: genotype selection model, coloured noise, stationary probability distribution

Abstract: This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time $\tau_{1}$ and $\tau_{2}$ by means of the numerical technique. By directly simulating the Langevin Equation, the following results are obtained. (1) The multiplicative coloured noise dominates, however, the effect of the additive coloured noise is not neglected in the practical gene selection process. The selection rate $\mu$ decides that the selection is propitious to gene $A$ haploid or gene $B$ haploid. (2) The additive coloured noise intensity $\alpha$ and the correlation time $\tau_2$ play opposite roles. It is noted that $\alpha$ and $\tau_2$ can not separate the single peak, while $\alpha$ can make the peak disappear and $\tau_2$ can make the peak be sharp. (3) The multiplicative coloured noise intensity $D$ and the correlation time $\tau_1$ can induce phase transition, at the same time they play opposite roles and the reentrance phenomenon appears. In this case, it is easy to select one type haploid from the group with increasing $D$ and decreasing $\tau_1$.

Key words: genotype selection model, coloured noise, stationary probability distribution

中图分类号:  (Noise)

  • 05.40.Ca
87.10.-e (General theory and mathematical aspects) 02.50.Cw (Probability theory)