Transitions in a genotype selection model driven by coloured noises

This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time τ1 and τ2 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 μ decides that the selection is propitious to gene A haploid or gene B haploid. （2） The additive coloured noise intensity and the correlation time τ2 play opposite roles. It is noted that α and τ2 can not separate the single peak, while can make the peak disappear and ~-2 can make the peak be sharp. （3） The multiplicative coloured noise intensity D and the correlation time τ1 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 τ1.

Transitions in a genotype selection model driven by coloured noises

This paper investigates a genotype selection model subjected to botha multiplicative coloured noise and an additive coloured noise withdifferent correlation time $tau_{1}$ and $tau_{2}$ by means of thenumerical technique. By directly simulating the Langevin Equation,the following results are obtained. (1) The multiplicative colourednoise dominates, however, the effect of the additive coloured noiseis not neglected in the practical gene selection process. Theselection rate $mu$ decides that the selection is propitious to gene$A$ haploid or gene $B$ haploid. (2) The additive coloured noiseintensity $alpha$ and the correlation time $tau_2$ play oppositeroles. It is noted that $alpha$ and $tau_2$ can not separate thesingle peak, while $alpha$ can make the peak disappear and $tau_2$can make the peak be sharp. (3) The multiplicative coloured noiseintensity $D$ and the correlation time $tau_1$ can induce phasetransition, at the same time they play opposite roles and thereentrance phenomenon appears. In this case, it is easy to select onetype haploid from the group with increasing $D$ and decreasing$tau_1$.