Effects Of Noise And Time Delay On Phase Transformation Of Gene Selection Model

The role of random forces in nonlinear systems has been growing attention recently.Noise is generally associated with something, which is irregular and cannot be perfectly controlled, disturbing the movement of the system. However, further study found that, the noise under certain conditions will have an important impact on the system, a series of phenomenon which is impossible in the deterministic equation become possible under the effect of noise. System in general we consider are the default system in which interaction is instantaneous, without considering the time-delay,but many practical problems are not so. Based on these two aspects factors, the effects of global and local time-delay on a genotype selection model driven by different noises and the roles of time-delay and noises in Logistic model are investigated in this paper. The main contents and conclusions are as follows:1.The effects of global and local time-delay on a genotype selection model driv-en by multiplicative and additive noises are investigated. The stationary probability distributions are derived using the small delay approximation and numerical simula-tions respectively. The influence of different time-delays on the stationary probabili-ty distribution is discussed. It is found that both global and local time-delay can in-duce phase transitions, but the changes are totally different. Moreover,multiplicative and additive noise can induce phase transition whether the time-delay is global or not.2.The effects of global and local time-delay on a genotype selection model driv-en by colored or sine-Wiener noise are investigated. The stationary probability distributions are derived by directly simulating the Langevin Equation. It is shown that the bounded noise can enhance transitions, regardless of time-delay, though the colored noise and bounded sine-Wiener noise with the same mean and stationary correlation. In the system with local time-delay, time-delay plays different roles with different noises. When time-delay is global, the colored noise and the sine-Wiener noise can’t induce phase transition.3.The effects of time-delay and noises on the stationary probability distribu- tions and the mean first-passage time in a Logistic system are investigated. The stationary probability distributions is derived by using the small delay approxima-tion and unified colored-noise approximation. On the other hand, the expression of mean first-passage time is derived by using the steepest-descent approximation. The results indicate that the noise and the correlation between two noises enhance the stability of stable state, the correlation times and time-delay inverses.