随机基因选择模型中的延迟效应

Time-delay effect of a stochastic genotype selection model

研究了噪声驱动的基因选择模型中的延迟效应.据小延迟方法和随机等价法则得到相应的延迟Fokker-Planck方程,给出稳态概率分布函数的近似表达式.分析了在噪声驱动下,延迟时间对系统稳态性质的影响.结果表明:延迟时间可以诱导系统从单稳态向双稳态转化,发生相变;在基因选择过程中,延迟时间有利于从基因群体中选择出某一单倍体基因.数值模拟结果与理论预测基本符合.

The time-delay effect of a genotype selection model driven by noise is investigated. The approximate delay Fokker-Planck equation is obtained based on the small time delay method and the stochastic equivalent rule. The explicit expression of the steady state probability distribution is derived, and the effect of the time delay on the steady sate properties of the genotype selection model driven by noise is discussed. It is found that the time delay can induce the transition from monostable state to bistable state. The time delay is helpful to select one type of genes from another type of mixing genes. The theoretical predictions are found to be in basic agreement with numerical results.