Bounded Noise And Time Delay Induced Phase Transitions In The Gene Selection Model

The influence of noise on nonlinear systems has proved to be of considerable interest in recent years. It well-known that stochastic fluctuation are ubiquitous in any real dynamical system. The fluctuating systems can contain more abundant action than deterministic ones. From traditional point, people may think that noise plays a disruptive role in nature, leading to irregular or random behavior. Neverthe-less, many experimental facts have exploited noise in different beneficial ways, such as noise enhanced stability, noise induced transition, noise sustained synchronization and stochastic resonance and so on. Among these appealing phenomena, stochastic transition, as one of the most interesting examples of the constructive role of noise, and is generally characterized with a qualitative change of the Stationary probability distribution. However, in most of the previous works, the fluctuation was assumed to be Gaussian process, which is unbounded and can reach large values. This fact contradicts the very nature of a real physical quantity which is always bounded. Therefore, a bounded random interference is more practicable in natural world, and bounded noise is a suitable model to describe this bounded fluctuation. In addition, time delay is unavoidable in nature, and the inclusion of time delay term is more reasonable in realistic systems. Therefore, the synergistic effect of bounded noise with time delay on nonlinear systems should be further researched.Genetic selection is one of the most popular topic in 21 century, which have extensive application. According to the actual physical background, the process of haploid genetic selection is described by The quantitative model. Combined with the knowledge of nonlinear dynamics, delay time and stochastic fluctuations are introduced in this system. A stochastic genotype selection model have been established for us to further researched.In this paper, the phenomenon of transition in genotype selection system is in-vestigated, which is subjected to bounded noise. Stationary probability distribution function is obtained by numerical simulations. It is found that:the additive and multiplicative both can induce transitions showing in genotype selection system.The multiplicative bounded noise can facilitate the gene separation and it plays a constructive role in the genetic selection progress, while the additive bounded noise suppresses the gene separation. The correlation parameter between noises can induce transitions showing in genotype selection system. The strong correlation be-tween noises gives a big chance to one type haploid out of the group. Besides, what's more interesting is that the correlation time can induce a new transitions(i.e.,the curve of the stationary probability distribution function changes from unimodal to bimodal, and then to four peaks as the correlation time increases).In addition, time delay play an non-ignorable role in the genetic selection progress. We present a numerical investigation of occurrence of transitions in a genotype selection model with different time delay. Results show that:local time delays and, being in gene transformation and gene heredity progress respectively, play an opposite roles in the gene selection process. What's more interesting is that there is no transition during the process of gene select when the system is subjected to global time delay.In this paper, we aim to explore random dynamical behaviors of a genotype selection model with time delay in the present of bounded noises, which is expected to be a more powerful tool to demonstrate the interactions between the genotype selection system and its surrounding.