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)
a Department of Physics, Yunnan University, Kunming 650091, China; b Nonlinear Research Institute, Baoji University Of Sciences And Arts, Baoji 721007, China
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 $\tau_1$.
Received: 30 May 2007
Revised: 05 July 2007
Accepted manuscript online:
Fund: 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).
Cite this article:
Wang Can-Jun(王参军) and Mei Dong-Cheng(梅冬成) Transitions in a genotype selection model driven by coloured noises 2008 Chin. Phys. B 17 479
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