基因選擇模型中有界噪聲和時間延遲誘導的相變
發(fā)布時間：2019-06-22 13:29
【摘要】：近幾十年來,噪聲對非線性系統(tǒng)的影響引起了人們高度的重視.眾所周知,在任何真實的動態(tài)系統(tǒng)中隨機漲落都是無處不在的.因此隨機系統(tǒng)也就包含了比確定性系統(tǒng)豐富的多的信息.傳統(tǒng)的觀點認為,噪聲總是對宏觀秩序起消極破壞的作用.然而,大量實驗事實已經(jīng)證明,噪聲也有一些積極的作用,比如：噪聲加強穩(wěn)定性、噪聲誘導相變、噪聲維持同步和隨機共振等等.在這些現(xiàn)象中,隨機相變是噪聲積極性作用中最為有意思的例子之一,系統(tǒng)的穩(wěn)態(tài)概率分布函數(shù)通常被用于定性分析這一現(xiàn)象.然而,在以前的大多數(shù)研究中,人們通常忽略了噪聲的有界性,大多數(shù)時候都用高斯噪聲表示隨機漲落,這與真實的物理量是有界的這一事實矛盾.所以,把有界噪聲引入到非線性系統(tǒng)中非常有必要.另外,在自然界中時間延遲也是不可避免的.那么包含有時間延遲的物理系統(tǒng)才更加符合實際.因此,對有界噪聲驅(qū)使下的隨機延遲系統(tǒng)值得深入的研究.基因選擇作為21世紀科學界中最為熱門的話題之一,它有著廣泛的應用價值.文章中,我們根據(jù)實際的物理背景,將單倍體基因選擇的過程用數(shù)學模型描述出來.再結(jié)合隨機非線性動力學知識,引入內(nèi)外噪聲和時間延遲,建立隨機的基因選擇模型,為我們進一步探索基因選擇系統(tǒng)的動態(tài)行為打好基礎.本文研究了有界噪聲激勵下的基因選擇系統(tǒng)中的相變現(xiàn)象.利用數(shù)值模擬的方法,我們獲得了系統(tǒng)的穩(wěn)態(tài)概率分布函數(shù).結(jié)果表明：加性和乘性的有界噪聲都可以誘導系統(tǒng)發(fā)生相變現(xiàn)象.乘性的有界噪聲能促進基因的分離,在基因選擇過程中扮演著積極的作用；而加性的有界噪聲抑制基因的分離.內(nèi)外噪聲的關(guān)聯(lián)強度也可誘導系統(tǒng)發(fā)生相變,關(guān)聯(lián)的強度越大越有利于某一類基因的單倍體從種群中勝出.一個更有意思的結(jié)論是：內(nèi)外噪聲間的互關(guān)聯(lián)時間可以誘導系統(tǒng)發(fā)生一種類似重入相變的現(xiàn)象,即：系統(tǒng)的穩(wěn)態(tài)概率分布函數(shù)曲線隨著噪聲間互關(guān)聯(lián)時間的增大從單峰變成雙峰接著變成四峰結(jié)構(gòu).另外,時間延遲在基因選擇過程中也扮演著不可忽視的作用.本文用數(shù)值模擬的方法研究了不同類型的時間延遲對基因選擇系統(tǒng)的影響.結(jié)果顯示：局部時間延遲可以誘導系統(tǒng)發(fā)生相變現(xiàn)象,而全局時間延遲并不改變系統(tǒng)的動力學行為.研究發(fā)現(xiàn)分別出現(xiàn)在基因變異重組和基因繼承再生過程中的時間延遲,在基因選擇過程中起著恰恰相反的作用.本文的研究目的是探索隨機漲落和時間延遲對基因選擇系統(tǒng)的作用,以此更深入的了解基因選擇表達的機制.
[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.
【學位授予單位】：陜西師范大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：TB53
本文編號：2504626
[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.
【學位授予單位】：陜西師范大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：TB53
【參考文獻】
相關(guān)期刊論文 前4條
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2 楊林靜;;Logistic系統(tǒng)躍遷率的時間延遲效應[J];物理學報;2011年05期
3 林靈;閆勇;梅冬成;;時間延遲增強雙穩(wěn)系統(tǒng)的共振抑制[J];物理學報;2010年04期
4 王參軍;梅冬成;;Transitions in a genotype selection model driven by coloured noises[J];Chinese Physics B;2008年02期
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