【摘要】：隨機微分方程理論現(xiàn)已被廣泛地應(yīng)用于物理學、生物數(shù)學、經(jīng)濟數(shù)學、自動控制、通信理論等眾多領(lǐng)域.在現(xiàn)實生活中任何系統(tǒng),都存在著各種隨機因素的干擾,并且系統(tǒng)的應(yīng)用都依賴于動力學行為.本文分別考慮了在Brown運動、分數(shù)Brown運動、Poisson過程和模糊產(chǎn)生擾動情況下的隨機微分系統(tǒng)的動力學行為-散逸性和穩(wěn)定性.其研究內(nèi)容主要有以下幾個方面:(1)利用Ito公式和Bellman-Gronwall-type估計,在一定的條件下研究了分數(shù)Brown運動時變隨機種群收獲系統(tǒng)的均方散逸性.并分別利用補償?shù)瓜駿uler方法和分步倒向Euler方法在Hurst參數(shù)H的限制下,證明了該系統(tǒng)數(shù)值方法的均方散逸性,保留了原系統(tǒng)的散逸特征.最后通過數(shù)值算例對所給出的結(jié)論進行了驗證.(2)利用Ito公式、Cauchy-Schwarz不等式和隨機分析的一些理論,給出了帶跳年齡相關(guān)隨機時滯種群系統(tǒng)的均方穩(wěn)定性.再利用補償隨機θ方法在步長△t和參數(shù)θ限制下,證明了此系統(tǒng)數(shù)值方法的均方穩(wěn)定性.最后通過數(shù)值例子結(jié)合MATLAB軟件驗證了結(jié)果的正確性.(3)通過建立恰當?shù)腖yapunov-Krasovskii泛函,利用Ito公式、Bellman-Gronwall-type估計和模糊集理論,給出了在環(huán)境污染下年齡相關(guān)模糊隨機種群系統(tǒng)均方散逸性條件,最后通過數(shù)值例子結(jié)合MATLAB軟件驗證了結(jié)果的正確性和有效性.
[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.
【學位授予單位】：北方民族大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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