两类随机三种群捕食者—食模型的渐近性质
发布时间：2018-07-29 17:50
【摘要】：在生态学系统中,捕食者和被捕食者之间的关系一直存在,深入研究它们对生态环境保护有非常重要的意义。为了研究外界噪声扰动对捕食者-食模型的影响,研究者将外界随机干扰项引入到确定性微分方程中。研究具有噪声扰动的种群模型对生物种群的发展十分重要,这样得到的结论更符合实际意义也更具有研究价值。本文研究了在白噪声扰动下的两类随机三种群捕食者-食模型的渐近性质。主要结果如下:针对具有白噪声扰动的第一类非线性随机模型,本文选取合适的Lyapunov函数,运用Chebyshev不等式和It?公式及其它理论知识,研究了该捕食者-食模型解的全局存在唯一性、随机最终有界性。另外,在一定的假设条件下,该模型解是随机持久的。在不同的条件下研究了模型解的持久性,得出随机种群模型与相应确定型模型性质类似。针对具有白噪声扰动的第二类随机模型,基于Chebyshev不等式和It?公式,本文选取合适的Lyapunov函数,证明了该模型解的全局存在唯一性。在一定的假设条件下,运用Hesse矩阵,证明了第二类随机模型的正平衡解是全局渐近稳定的。为了说明结论的有效性,本文给出了数值模拟。
[Abstract]:In the ecological system, the relationship between predator and prey exists all the time, and it is very important to study them deeply for the protection of ecological environment. In order to study the effect of external noise disturbance on predator-food model, the external random disturbance term is introduced into deterministic differential equations. It is very important to study the population model with noise disturbance for the development of biological population. In this paper, we study the asymptotic behavior of two classes of stochastic three-species predator-food model under white noise disturbance. The main results are as follows: for the first kind of nonlinear stochastic model with white noise disturbance, this paper selects the appropriate Lyapunov function, applies Chebyshev inequality and ITT? The formula and other theoretical knowledge are used to study the global existence and uniqueness of the solution of the predator-feeding model and the stochastic ultimate boundedness. In addition, under certain assumptions, the solution of the model is stochastic and persistent. The persistence of the model solution is studied under different conditions, and the properties of the stochastic population model and the corresponding deterministic model are similar. For the second kind of stochastic model with white noise disturbance, based on Chebyshev inequality and ITT? In this paper, the global existence and uniqueness of the solution of the model are proved by selecting the appropriate Lyapunov function. Under certain assumptions and by using Hesse matrix, it is proved that the positive equilibrium solution of the second kind of stochastic model is globally asymptotically stable. In order to illustrate the validity of the conclusion, a numerical simulation is presented in this paper.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2153518
[Abstract]:In the ecological system, the relationship between predator and prey exists all the time, and it is very important to study them deeply for the protection of ecological environment. In order to study the effect of external noise disturbance on predator-food model, the external random disturbance term is introduced into deterministic differential equations. It is very important to study the population model with noise disturbance for the development of biological population. In this paper, we study the asymptotic behavior of two classes of stochastic three-species predator-food model under white noise disturbance. The main results are as follows: for the first kind of nonlinear stochastic model with white noise disturbance, this paper selects the appropriate Lyapunov function, applies Chebyshev inequality and ITT? The formula and other theoretical knowledge are used to study the global existence and uniqueness of the solution of the predator-feeding model and the stochastic ultimate boundedness. In addition, under certain assumptions, the solution of the model is stochastic and persistent. The persistence of the model solution is studied under different conditions, and the properties of the stochastic population model and the corresponding deterministic model are similar. For the second kind of stochastic model with white noise disturbance, based on Chebyshev inequality and ITT? In this paper, the global existence and uniqueness of the solution of the model are proved by selecting the appropriate Lyapunov function. Under certain assumptions and by using Hesse matrix, it is proved that the positive equilibrium solution of the second kind of stochastic model is globally asymptotically stable. In order to illustrate the validity of the conclusion, a numerical simulation is presented in this paper.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前1条
1 Shan-Shan Pan;Wei-Qiu Zhu;;Dynamics of a prey-predator system under Poisson white noise excitation[J];Acta Mechanica Sinica;2014年05期
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