【摘要】：在生態(tài)學(xué)系統(tǒng)中,捕食者和被捕食者之間的關(guān)系一直存在,深入研究它們對(duì)生態(tài)環(huán)境保護(hù)有非常重要的意義。為了研究外界噪聲擾動(dòng)對(duì)捕食者-食模型的影響,研究者將外界隨機(jī)干擾項(xiàng)引入到確定性微分方程中。研究具有噪聲擾動(dòng)的種群模型對(duì)生物種群的發(fā)展十分重要,這樣得到的結(jié)論更符合實(shí)際意義也更具有研究?jī)r(jià)值。本文研究了在白噪聲擾動(dòng)下的兩類隨機(jī)三種群捕食者-食模型的漸近性質(zhì)。主要結(jié)果如下:針對(duì)具有白噪聲擾動(dòng)的第一類非線性隨機(jī)模型,本文選取合適的Lyapunov函數(shù),運(yùn)用Chebyshev不等式和It?公式及其它理論知識(shí),研究了該捕食者-食模型解的全局存在唯一性、隨機(jī)最終有界性。另外,在一定的假設(shè)條件下,該模型解是隨機(jī)持久的。在不同的條件下研究了模型解的持久性,得出隨機(jī)種群模型與相應(yīng)確定型模型性質(zhì)類似。針對(duì)具有白噪聲擾動(dòng)的第二類隨機(jī)模型,基于Chebyshev不等式和It?公式,本文選取合適的Lyapunov函數(shù),證明了該模型解的全局存在唯一性。在一定的假設(shè)條件下,運(yùn)用Hesse矩陣,證明了第二類隨機(jī)模型的正平衡解是全局漸近穩(wěn)定的。為了說明結(jié)論的有效性,本文給出了數(shù)值模擬。
[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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

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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本文編號(hào)：2153518