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  本文選題：隨機捕食模型 + 全局漸近穩(wěn)定性　； 參考：《南昌大學(xué)》2017年碩士論文

【摘要】：本文利用Lyapunov泛函方法和隨機分析理論,研究了兩類隨機時滯系統(tǒng)的動力學(xué)行為,主要工作如下:第一章介紹了隨機時滯系統(tǒng)的研究背景、研究進展以及現(xiàn)實意義,同時給出了下文將要用到的相關(guān)定義和引理.第二章研究了一類帶有兩種不同功能函數(shù)的隨機時滯一個捕食者兩個競爭食餌模型,通過構(gòu)造合適的Lyapunov-Krasovskii泛函,證明了系統(tǒng)的全局正解是存在惟一的和隨機最終有界性的,進而給出了系統(tǒng)的隨機持久性和滅絕性的充分條件,然后通過控制環(huán)境噪聲強度和參數(shù)給出了模型全局漸近穩(wěn)定性的充分條件,最后給出了一些數(shù)值例子進一步說明所得結(jié)論的有效性.第三章討論了一類帶有混合時滯的隨機中立型憶阻神經(jīng)網(wǎng)絡(luò)模型的輸入-狀態(tài)穩(wěn)定性問題,在模型中同時考慮了中立項和混合時滯,使得模型更具有新穎性,并且利用Lyapunov穩(wěn)定性理論和隨機分析理論得出了系統(tǒng)均方指數(shù)輸入-狀態(tài)穩(wěn)定性的條件,最后給出一些數(shù)值例子佐證了所得結(jié)論的正確性.第四章給出了本文的結(jié)論以及對后續(xù)工作的展望.
[Abstract]:In this paper, the dynamic behavior of two kinds of stochastic time-delay systems is studied by using Lyapunov functional method and stochastic analysis theory. The main work is as follows: in Chapter 1, the background, research progress and practical significance of stochastic time-delay systems are introduced. At the same time, the relevant definitions and Lemma used in this paper are given. In chapter 2, we study a class of stochastic predator and two competitive prey models with two different function functions. By constructing appropriate Lyapunov-Krasovskii functional, we prove that the global positive solution of the system is unique and stochastic ultimate boundedness. Furthermore, the sufficient conditions for stochastic persistence and extinction of the system are given, and the sufficient conditions for the global asymptotic stability of the model are obtained by controlling the environmental noise intensity and parameters. Finally, some numerical examples are given to illustrate the validity of the conclusion. In chapter 3, we discuss the input-state stability of a class of stochastic neutral amnesia neural networks with mixed delays. We consider both neutral terms and mixed delays in the model, which makes the model more novel. By using Lyapunov stability theory and stochastic analysis theory, the conditions for the input-state stability of the mean square exponent are obtained. Finally, some numerical examples are given to prove the correctness of the conclusions. The fourth chapter gives the conclusion of this paper and the future work.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【參考文獻】

相關(guān)期刊論文 前1條

1 馮光輝;王玲書;;一類具有時滯和階段結(jié)構(gòu)的捕食模型及其Hopf分支[J];北華大學(xué)學(xué)報(自然科學(xué)版);2010年01期

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本文編號：2099513