基于年龄结构随机种群系统的渐近行为
发布时间：2018-11-08 11:37
【摘要】：随机微分方程理论现已被广泛地应用于物理学、生物数学、经济数学、自动控制、通信理论等众多领域.在现实生活中任何系统,都存在着各种随机因素的干扰,并且系统的应用都依赖于动力学行为.本文分别考虑了在Brown运动、分数Brown运动、Poisson过程和模糊产生扰动情况下的随机微分系统的动力学行为-散逸性和稳定性.其研究内容主要有以下几个方面:(1)利用Ito公式和Bellman-Gronwall-type估计,在一定的条件下研究了分数Brown运动时变随机种群收获系统的均方散逸性.并分别利用补偿倒向Euler方法和分步倒向Euler方法在Hurst参数H的限制下,证明了该系统数值方法的均方散逸性,保留了原系统的散逸特征.最后通过数值算例对所给出的结论进行了验证.(2)利用Ito公式、Cauchy-Schwarz不等式和随机分析的一些理论,给出了带跳年龄相关随机时滞种群系统的均方稳定性.再利用补偿随机θ方法在步长△t和参数θ限制下,证明了此系统数值方法的均方稳定性.最后通过数值例子结合MATLAB软件验证了结果的正确性.(3)通过建立恰当的Lyapunov-Krasovskii泛函,利用Ito公式、Bellman-Gronwall-type估计和模糊集理论,给出了在环境污染下年龄相关模糊随机种群系统均方散逸性条件,最后通过数值例子结合MATLAB软件验证了结果的正确性和有效性.
[Abstract]:Stochastic differential equation theory has been widely used in many fields such as physics, biological mathematics, economic mathematics, automatic control, communication theory and so on. In real life, there are all kinds of random interference in any system, and the application of the system depends on the dynamic behavior. In this paper, the dynamical behavior of stochastic differential systems with Brown motion, fractional Brown motion, Poisson process and fuzzy disturbance are considered respectively. The main research contents are as follows: (1) by using Ito formula and Bellman-Gronwall-type estimation, the mean-square escape of fractional Brown motion time-varying random population harvesting system is studied under certain conditions. By using the compensation backward Euler method and the step backward Euler method under the limit of the Hurst parameter H, the mean square escape of the numerical method is proved, and the escape characteristic of the original system is preserved. Finally, the results are verified by numerical examples. (2) by using Ito formula, Cauchy-Schwarz inequality and some theories of stochastic analysis, the mean square stability of stochastic time-delay systems with jump age is given. Furthermore, the mean square stability of the numerical method is proved by using the compensated stochastic 胃 method under the limit of step size t and parameter 胃. Finally, numerical examples combined with MATLAB software are used to verify the correctness of the results. (3) by establishing appropriate Lyapunov-Krasovskii functional, using Ito formula, Bellman-Gronwall-type estimation and fuzzy set theory, The mean square escape condition of age-dependent fuzzy stochastic population system under environmental pollution is given. Finally, the validity and validity of the results are verified by a numerical example and MATLAB software.
【学位授予单位】：北方民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2318391
[Abstract]:Stochastic differential equation theory has been widely used in many fields such as physics, biological mathematics, economic mathematics, automatic control, communication theory and so on. In real life, there are all kinds of random interference in any system, and the application of the system depends on the dynamic behavior. In this paper, the dynamical behavior of stochastic differential systems with Brown motion, fractional Brown motion, Poisson process and fuzzy disturbance are considered respectively. The main research contents are as follows: (1) by using Ito formula and Bellman-Gronwall-type estimation, the mean-square escape of fractional Brown motion time-varying random population harvesting system is studied under certain conditions. By using the compensation backward Euler method and the step backward Euler method under the limit of the Hurst parameter H, the mean square escape of the numerical method is proved, and the escape characteristic of the original system is preserved. Finally, the results are verified by numerical examples. (2) by using Ito formula, Cauchy-Schwarz inequality and some theories of stochastic analysis, the mean square stability of stochastic time-delay systems with jump age is given. Furthermore, the mean square stability of the numerical method is proved by using the compensated stochastic 胃 method under the limit of step size t and parameter 胃. Finally, numerical examples combined with MATLAB software are used to verify the correctness of the results. (3) by establishing appropriate Lyapunov-Krasovskii functional, using Ito formula, Bellman-Gronwall-type estimation and fuzzy set theory, The mean square escape condition of age-dependent fuzzy stochastic population system under environmental pollution is given. Finally, the validity and validity of the results are verified by a numerical example and MATLAB software.
【学位授予单位】：北方民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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