本文選題：隨機(jī)種群擴(kuò)散模型 + 模糊��； 參考：《寧夏大學(xué)》2015年碩士論文

【摘要】：本論文主要以具有年齡結(jié)構(gòu)的隨機(jī)種群擴(kuò)散模型為研究對象,在此模型基礎(chǔ)上分別引入隨機(jī)項(xiàng)分?jǐn)?shù)Brown運(yùn)動(dòng)和Poisson過程以及環(huán)境污染,從而建立了三種年齡結(jié)構(gòu)隨機(jī)種群擴(kuò)散模型.同時(shí)將模糊這種不確定性因素考慮到以上幾種不同的種群系統(tǒng)中,得到幾類具有年齡結(jié)構(gòu)的模糊隨機(jī)種群擴(kuò)散模型.分別討論系統(tǒng)的存在唯一性并給出了各模型近似解的誤差估計(jì)式.最后通過數(shù)值算例驗(yàn)證了各模型的指數(shù)穩(wěn)定性.本文主要的研究內(nèi)容有如下幾方面：(1)以隨機(jī)的年齡結(jié)構(gòu)種群擴(kuò)散模型為基礎(chǔ),把突發(fā)性的災(zāi)難(例如,火災(zāi)、水災(zāi)、地震和颶風(fēng)等)考慮到年齡結(jié)構(gòu)種群擴(kuò)散模型中,同時(shí)引入模糊不確定性,建立帶Poisson跳的年齡結(jié)構(gòu)模糊隨機(jī)種群擴(kuò)散模型.在方程系數(shù)滿足有界條件(弱于線性增長條件)和：Lipschitz條件下,運(yùn)用逐次逼近法,通過構(gòu)造Picard迭代序列,討論了該模型的強(qiáng)解的存在性和唯一性.利用Gronwall引理、模糊理論的性質(zhì)、Ito公式和三角不等式,討論了方程強(qiáng)解存在的充分條件和近似解誤差的估計(jì)式及均方意義下的穩(wěn)定性,并給出了穩(wěn)定的充分條件.通過一個(gè)具體的例子對得到的結(jié)論進(jìn)行了驗(yàn)證.(2)研究了帶分?jǐn)?shù)Brown運(yùn)動(dòng)和Poisson跳的年齡結(jié)構(gòu)模糊隨機(jī)種群擴(kuò)散模型.基于Gronwall引理、分?jǐn)?shù)Brown運(yùn)動(dòng)的Ito公式、模糊理論的性質(zhì)等對模型的強(qiáng)解的存在唯一性和指數(shù)穩(wěn)定性進(jìn)行了探討.根據(jù)數(shù)值例子進(jìn)行了計(jì)算模擬,驗(yàn)證了理論結(jié)果的正確性.(3)將模糊性和隨機(jī)性這兩種不確定性因素同時(shí)考慮到環(huán)境污染當(dāng)中,構(gòu)建了一類基于環(huán)境污染的模糊隨機(jī)種群擴(kuò)散模型.在方程系數(shù)滿足有界條件(弱于線性增長條件)和Lipschitz條件下,運(yùn)用逐次逼近法,通過構(gòu)造Picard迭代序列,討論了該模型的強(qiáng)解的存在性和唯一性.利用Gronwall引理、模糊理論的性質(zhì)、Ito積分和三角不等式,給出了方程強(qiáng)解存在的充分條件和近似解誤差的估計(jì)式及均方意義下的穩(wěn)定性,并給出了穩(wěn)定的充分條件.
[Abstract]:In this paper, the stochastic population diffusion model with age structure is taken as the research object. Based on this model, three age structure stochastic population diffusion models are established by introducing stochastic term fractional Brownian motion and Poisson process and environmental pollution, respectively. At the same time, some fuzzy stochastic population diffusion models with age structure are obtained by taking fuzzy uncertainty into account of the different population systems mentioned above. The existence and uniqueness of the system are discussed, and the error estimates of the approximate solutions of each model are given. Finally, the exponential stability of each model is verified by numerical examples. The main contents of this paper are as follows: (1) based on the random age structure population diffusion model, the sudden disasters (such as fire, flood, earthquake and hurricane) are taken into account in the age structure population diffusion model. At the same time, a fuzzy stochastic population diffusion model with Poisson jump is established by introducing fuzzy uncertainty. In this paper, the existence and uniqueness of the strong solution of the model are discussed by constructing Picard iterative sequence by the successive approximation method under the bounded condition (weaker than the linear growth condition) and the one-step Lipschitz condition for the coefficients of the equation. By using Gronwall Lemma, the properties of fuzzy theory, Ito formula and trigonometric inequality, the sufficient conditions for the existence of strong solutions of the equation, the estimation of approximate solution errors and the stability in the sense of mean square are discussed, and the sufficient conditions for stability are given. The results are verified by a concrete example. (2) A fuzzy stochastic population diffusion model with fractional Brownian motion and Poisson jump is studied. Based on the Gronwall Lemma, the Ito formula of fractional Brownian motion and the properties of fuzzy theory, the existence and uniqueness of strong solutions and the exponential stability of the model are discussed. A numerical simulation is carried out to verify the correctness of the theoretical results. (3) the fuzzy and randomness uncertainties are taken into account in the environmental pollution at the same time. A fuzzy stochastic population diffusion model based on environmental pollution is constructed. In this paper, the existence and uniqueness of the strong solution of the model are discussed by constructing Picard iterative sequence by means of successive approximation under the bounded condition (weaker than the linear growth condition) and Lipschitz condition for the coefficients of the equation. By using the Gronwall Lemma, the properties of fuzzy theory such as Ito integral and trigonometric inequality, the sufficient conditions for the existence of the strong solution of the equation and the estimation of the approximate solution error and the stability in the mean square sense are given, and the sufficient conditions for stability are given.
【學(xué)位授予單位】：寧夏大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O175

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本文編號：2072811