当前位置:主页 > 科技论文 > 基因论文 >

基因选择模型中有界噪声和时间延迟诱导的相变

发布时间:2019-06-22 13:29
【摘要】:近几十年来,噪声对非线性系统的影响引起了人们高度的重视.众所周知,在任何真实的动态系统中随机涨落都是无处不在的.因此随机系统也就包含了比确定性系统丰富的多的信息.传统的观点认为,噪声总是对宏观秩序起消极破坏的作用.然而,大量实验事实已经证明,噪声也有一些积极的作用,比如:噪声加强稳定性、噪声诱导相变、噪声维持同步和随机共振等等.在这些现象中,随机相变是噪声积极性作用中最为有意思的例子之一,系统的稳态概率分布函数通常被用于定性分析这一现象.然而,在以前的大多数研究中,人们通常忽略了噪声的有界性,大多数时候都用高斯噪声表示随机涨落,这与真实的物理量是有界的这一事实矛盾.所以,把有界噪声引入到非线性系统中非常有必要.另外,在自然界中时间延迟也是不可避免的.那么包含有时间延迟的物理系统才更加符合实际.因此,对有界噪声驱使下的随机延迟系统值得深入的研究.基因选择作为21世纪科学界中最为热门的话题之一,它有着广泛的应用价值.文章中,我们根据实际的物理背景,将单倍体基因选择的过程用数学模型描述出来.再结合随机非线性动力学知识,引入内外噪声和时间延迟,建立随机的基因选择模型,为我们进一步探索基因选择系统的动态行为打好基础.本文研究了有界噪声激励下的基因选择系统中的相变现象.利用数值模拟的方法,我们获得了系统的稳态概率分布函数.结果表明:加性和乘性的有界噪声都可以诱导系统发生相变现象.乘性的有界噪声能促进基因的分离,在基因选择过程中扮演着积极的作用;而加性的有界噪声抑制基因的分离.内外噪声的关联强度也可诱导系统发生相变,关联的强度越大越有利于某一类基因的单倍体从种群中胜出.一个更有意思的结论是:内外噪声间的互关联时间可以诱导系统发生一种类似重入相变的现象,即:系统的稳态概率分布函数曲线随着噪声间互关联时间的增大从单峰变成双峰接着变成四峰结构.另外,时间延迟在基因选择过程中也扮演着不可忽视的作用.本文用数值模拟的方法研究了不同类型的时间延迟对基因选择系统的影响.结果显示:局部时间延迟可以诱导系统发生相变现象,而全局时间延迟并不改变系统的动力学行为.研究发现分别出现在基因变异重组和基因继承再生过程中的时间延迟,在基因选择过程中起着恰恰相反的作用.本文的研究目的是探索随机涨落和时间延迟对基因选择系统的作用,以此更深入的了解基因选择表达的机制.
[Abstract]:In recent decades, the influence of noise on nonlinear systems has attracted great attention. As we all know, random fluctuations are ubiquitous in any real dynamic system. Therefore, stochastic systems contain more abundant information than deterministic systems. According to the traditional view, noise always plays a negative role in destroying the macro order. However, a large number of experimental facts have proved that noise also has some positive effects, such as noise enhancement stability, noise induced phase transition, noise maintenance synchronization and stochastic resonance and so on. Among these phenomena, random phase transition is one of the most interesting examples of noise enthusiasm. The steady-state probability distribution function of the system is usually used for qualitative analysis. However, in most previous studies, people usually ignore the bounded nature of noise, and most of the time use Gaussian noise to represent random fluctuations, which contradicts the fact that the real physical quantity is bounded. Therefore, it is necessary to introduce bounded noise into nonlinear systems. In addition, time delay is inevitable in nature. Then the physical system with time delay is more realistic. Therefore, the stochastic delay system driven by bounded noise is worthy of further study. Gene selection, as one of the hottest topics in the scientific community in the 21 st century, has a wide range of application value. In this paper, according to the actual physical background, the process of haploid gene selection is described by mathematical model. Combined with the knowledge of random nonlinear dynamics, the internal and external noise and time delay are introduced to establish a random gene selection model, which lays a good foundation for us to further explore the dynamic behavior of gene selection system. In this paper, the phase transition in gene selection system excited by bounded noise is studied. By using the method of numerical simulation, we obtain the steady-state probability distribution function of the system. The results show that both additive and multiplier bounded noise can induce the phase transition of the system. Multiplicative bounded noise can promote gene isolation and play an active role in gene selection, while additive bounded noise suppresses gene isolation. The correlation intensity of internal and external noise can also induce systematic phase transition, and the greater the intensity of association, the more favorable the haploid of a certain kind of gene is to win from the population. A more interesting conclusion is that the intercorrelation time between internal and external noise can induce a similar phenomenon of reentrant phase transition, that is, the steady-state probability distribution function curve of the system changes from single peak to double peak and then to four peak structure with the increase of intercorrelation time between noise. In addition, time delay also plays an important role in gene selection. In this paper, the effects of different types of time delays on gene selection system were studied by numerical simulation. The results show that the local time delay can induce the phase transition of the system, while the global time delay does not change the dynamic behavior of the system. It was found that the time delay occurred in the process of gene mutation and recombination and gene inheritance and regeneration respectively, which played the opposite role in the process of gene selection. The purpose of this study is to explore the effect of random fluctuations and time delays on gene selection system, so as to better understand the mechanism of gene selection expression.
【学位授予单位】:陕西师范大学
【学位级别】:硕士
【学位授予年份】:2016
【分类号】:TB53

【参考文献】

相关期刊论文 前4条

1 王参军;;随机基因选择模型中的延迟效应[J];物理学报;2012年05期

2 杨林静;;Logistic系统跃迁率的时间延迟效应[J];物理学报;2011年05期

3 林灵;闫勇;梅冬成;;时间延迟增强双稳系统的共振抑制[J];物理学报;2010年04期

4 王参军;梅冬成;;Transitions in a genotype selection model driven by coloured noises[J];Chinese Physics B;2008年02期



本文编号:2504626

资料下载
论文发表

本文链接:https://www.wllwen.com/kejilunwen/jiyingongcheng/2504626.html


Copyright(c)文论论文网All Rights Reserved | 网站地图 |

版权申明:资料由用户69c79***提供,本站仅收录摘要或目录,作者需要删除请E-mail邮箱bigeng88@qq.com