本文選題：時(shí)滯 + 脈沖效應(yīng)��； 參考：《電子科技大學(xué)》2015年博士論文

【摘要】：自然界中許多系統(tǒng)狀態(tài)變量的變化率不僅依賴(lài)系統(tǒng)的當(dāng)前狀態(tài),而且與過(guò)去某個(gè)時(shí)刻或過(guò)去一段時(shí)間的狀態(tài)有關(guān),對(duì)這類(lèi)系統(tǒng)進(jìn)行建模時(shí)用時(shí)滯微分方程或泛函微分方程來(lái)代替原來(lái)的常微分方程更為合適。另一方面,現(xiàn)實(shí)世界中還有許多自然或人為因素會(huì)對(duì)系統(tǒng)的內(nèi)在規(guī)律帶來(lái)突然的變化,這些作用時(shí)間往往非常短暫,在建模時(shí)可視為在某個(gè)固定時(shí)刻發(fā)生,但系統(tǒng)狀態(tài)在這些時(shí)刻卻不再連續(xù),因此在對(duì)這類(lèi)系統(tǒng)建模時(shí)用半連續(xù)的脈沖微分方程來(lái)代替連續(xù)的動(dòng)力系統(tǒng)更為合理。此外,現(xiàn)實(shí)自然界中許多系統(tǒng)狀態(tài)變量的變化還會(huì)受到環(huán)境噪聲的影響,這時(shí)再用確定的常微分方程來(lái)刻畫(huà)相應(yīng)的系統(tǒng)也不再合適,而應(yīng)該用隨機(jī)微分方程來(lái)描述相關(guān)問(wèn)題更為合理。因此,本文正是基于上述背景,分別就四類(lèi)具有時(shí)滯、脈沖效應(yīng)以及隨機(jī)擾動(dòng)的混雜生物動(dòng)力系統(tǒng)進(jìn)行研究和討論：1.對(duì)一類(lèi)脈沖輸入營(yíng)養(yǎng)基和具有分布時(shí)滯的營(yíng)養(yǎng)基再生的恒化器模型進(jìn)行研究,利用脈沖比較定理、Floquet定理以及微小參數(shù)擾動(dòng)法等技巧得到了系統(tǒng)微生物滅絕周期解全局漸近穩(wěn)定性的充分判據(jù),另外通過(guò)構(gòu)造合適的Liapunov函數(shù)得到了系統(tǒng)的有界性,并在此基礎(chǔ)上充分運(yùn)用分析技巧得到了恒化器中微生物能夠連續(xù)培養(yǎng)的充分條件。最后對(duì)相關(guān)理論結(jié)果進(jìn)行數(shù)值模擬,并進(jìn)一步分析了參數(shù)變化對(duì)微生物滅絕或持久生存的影響。2.對(duì)一類(lèi)具有消化時(shí)滯和周期脈沖捕獲的食物鏈系統(tǒng)進(jìn)行研究,利用脈沖比較定理、微小參數(shù)擾動(dòng)以及微分不等式的技巧等,得到系統(tǒng)具有全局漸近穩(wěn)定的捕食者滅絕周期解及系統(tǒng)持久生存性的充分條件,并通過(guò)數(shù)值例子及數(shù)值模擬進(jìn)一步驗(yàn)證了理論結(jié)果的正確性和可行性,同時(shí)還通過(guò)分析及數(shù)值實(shí)驗(yàn)驗(yàn)證得到了能將害蟲(chóng)數(shù)量控制在更低的經(jīng)濟(jì)閡值水平之下的控制策略。3.對(duì)一類(lèi)具有多時(shí)滯和脈沖效應(yīng)的非自治概周期捕食系統(tǒng)進(jìn)行研究,利用多元函數(shù)微分中值定理、微分不等式、積分不等式等數(shù)學(xué)分析技巧,得到了系統(tǒng)持久生存的充分條件。同時(shí),通過(guò)構(gòu)造一系列Liapunov泛函,證明了系統(tǒng)在一定條件下存在唯一的、一致漸近穩(wěn)定的概周期解。最后通過(guò)數(shù)值例子及其仿真進(jìn)一步證實(shí)了理論結(jié)果的正確性和有效性,并分析了不同脈沖效應(yīng)和不同時(shí)滯對(duì)系統(tǒng)動(dòng)力學(xué)行為的影響。4.對(duì)一類(lèi)具有脈沖效應(yīng)和隨機(jī)擾動(dòng)的非自治食物鏈系統(tǒng)進(jìn)行研究,利用Ito積分公式、指數(shù)鞅不等式、微分不等式等分析技巧得到了系統(tǒng)的滅絕性、非持久生存、均方意義上持久生存、隨機(jī)持久生存等漸近性質(zhì)。最后通過(guò)一系列數(shù)值實(shí)驗(yàn)來(lái)佐證相關(guān)理論結(jié)果、觀察相關(guān)生態(tài)學(xué)現(xiàn)象,同時(shí)還通過(guò)數(shù)值實(shí)驗(yàn)分析討論了不同強(qiáng)度的脈沖效應(yīng)和環(huán)境噪聲對(duì)系統(tǒng)的影響。
[Abstract]:The rate of change of many system state variables in nature depends not only on the current state of the system, but also on the state of a past moment or period of time.It is more appropriate to replace the original ordinary differential equation with delay differential equation or functional differential equation when modeling this kind of system.On the other hand, there are also many natural or man-made factors in the real world that can cause sudden changes in the internal laws of the system, which are often very short and can be modeled as occurring at a fixed moment.However, the state of the system is not continuous at these times, so it is more reasonable to use semi-continuous impulsive differential equations instead of continuous dynamical systems in modeling such systems.In addition, many changes of system state variables in real nature will also be affected by environmental noise, and it is no longer appropriate to describe the corresponding system with a definite ordinary differential equation.It is more reasonable to describe the related problems with stochastic differential equations.Therefore, based on the above background, four kinds of hybrid biodynamic systems with time delay, impulsive effect and stochastic disturbance are studied and discussed respectively in this paper.The models of a kind of pulse input nutrient base and nutrient base regeneration with distributed delay are studied.The sufficient criteria for the global asymptotic stability of the periodic solution of microbial extinction are obtained by using the impulsive comparison theorem and the perturbation method of small parameters. In addition, the boundedness of the system is obtained by constructing appropriate Liapunov functions.On the basis of this, the sufficient conditions for the continuous culture of microbes in the chemostat were obtained by using the analytical techniques.Finally, the related theoretical results are numerically simulated, and the effects of parameter changes on the extinction or sustainable survival of microorganisms are further analyzed.In this paper, a class of food chain systems with digestive delay and periodic pulse capture is studied. The comparison theorem of impulses, the perturbation of small parameters and the technique of differential inequality are used.Sufficient conditions for the system to have globally asymptotically stable predator extinction periodic solutions and the persistence of the system are obtained, and the correctness and feasibility of the theoretical results are further verified by numerical examples and numerical simulations.At the same time, through the analysis and numerical experiments, the control strategy. 3. 3, which can keep the pest population under the lower economic threshold level, is obtained.In this paper, a class of nonautonomous almost periodic predator-prey systems with multiple delays and impulsive effects is studied. By using the differential mean value theorem of multivariate functions, differential inequalities, integral inequalities and other mathematical analytical techniques, sufficient conditions for the persistence of the system are obtained.At the same time, by constructing a series of Liapunov Functionals, it is proved that there exists a unique uniformly asymptotically stable almost periodic solution for the system under certain conditions.Finally, the correctness and validity of the theoretical results are further verified by numerical examples and simulations, and the effects of different impulsive effects and different delays on the dynamic behavior of the system are analyzed.In this paper, a class of nonautonomous food chain systems with impulsive effects and stochastic perturbations is studied. By using Ito integral formula, exponential martingale inequality, differential inequality and other analytical techniques, the extinction and non-persistence of the system are obtained.In the sense of mean square persistence, stochastic persistence and other asymptotic properties.Finally, a series of numerical experiments are used to support the related theoretical results and observe the related ecological phenomena. At the same time, the effects of pulse effect and ambient noise on the system are analyzed and discussed by numerical experiments.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O175
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本文編號(hào)：1771168