年龄结构模糊随机种群模型解的存在唯一性和指数稳定性

发布时间：2018-06-27 05:21

本文选题：随机种群扩散模型 + 模糊　；参考：《宁夏大学》2015年硕士论文

【摘要】：本论文主要以具有年龄结构的随机种群扩散模型为研究对象,在此模型基础上分别引入随机项分数Brown运动和Poisson过程以及环境污染,从而建立了三种年龄结构随机种群扩散模型.同时将模糊这种不确定性因素考虑到以上几种不同的种群系统中,得到几类具有年龄结构的模糊随机种群扩散模型.分别讨论系统的存在唯一性并给出了各模型近似解的误差估计式.最后通过数值算例验证了各模型的指数稳定性.本文主要的研究内容有如下几方面：(1)以随机的年龄结构种群扩散模型为基础,把突发性的灾难(例如,火灾、水灾、地震和飓风等)考虑到年龄结构种群扩散模型中,同时引入模糊不确定性,建立带Poisson跳的年龄结构模糊随机种群扩散模型.在方程系数满足有界条件(弱于线性增长条件)和：Lipschitz条件下,运用逐次逼近法,通过构造Picard迭代序列,讨论了该模型的强解的存在性和唯一性.利用Gronwall引理、模糊理论的性质、Ito公式和三角不等式,讨论了方程强解存在的充分条件和近似解误差的估计式及均方意义下的稳定性,并给出了稳定的充分条件.通过一个具体的例子对得到的结论进行了验证.(2)研究了带分数Brown运动和Poisson跳的年龄结构模糊随机种群扩散模型.基于Gronwall引理、分数Brown运动的Ito公式、模糊理论的性质等对模型的强解的存在唯一性和指数稳定性进行了探讨.根据数值例子进行了计算模拟,验证了理论结果的正确性.(3)将模糊性和随机性这两种不确定性因素同时考虑到环境污染当中,构建了一类基于环境污染的模糊随机种群扩散模型.在方程系数满足有界条件(弱于线性增长条件)和Lipschitz条件下,运用逐次逼近法,通过构造Picard迭代序列,讨论了该模型的强解的存在性和唯一性.利用Gronwall引理、模糊理论的性质、Ito积分和三角不等式,给出了方程强解存在的充分条件和近似解误差的估计式及均方意义下的稳定性,并给出了稳定的充分条件.
[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.
【学位授予单位】：宁夏大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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