【作者】 王莉；

【导师】 王波；

【作者基本信息】 河南大学 ， 计算数学， 2017， 硕士

【摘要】 在现实生活中,植被生态系统受人类活动的影响而严重退化,导致了生态平衡的破坏、气候的恶化等一系列问题,这直接威胁着人类的生命财产安全.为了更真实直观的描述草原生态系统的稳定性,本文运用随机动力学理论,基于生态系统中具有典型意义下的Shnerb植被动态模型和曾庆存等人提出的简化两变量草原生态动力学模型,提出相应的草原随机生态动力学模型,并对其研究,主要工作如下:(1)针对Shnerb草原植被动态模型,添加随机扰动项,利用FPK方法研究噪声对草原生态模型的影响.数值结果表明:在引入随机噪声后,草原生态系统的稳定性发生变化,并且在一定的噪声强度下会使系统发生稳态之间的转换,使模型的分岔点发生改变.(2)针对曾庆存等人提出简化的草原生态系统动力学模型,建立随机模型,并采用随机微分方程Runge-Kutta格式对该模型进行数值模拟.结果表明:在分岔区间上,噪声强度足够大的随机噪声会使系统发生稳态的转换,且使系统的分岔值发生改变.通过本文的研究分析可知,系统控制参数的改变和噪声强度的变化都能使生态系统稳态发生改变.更多还原

【Abstract】 In real life,vegetation ecosystem is affected by human activities and serious degradation,led to the destruction of ecological balance,the deterioration of climate and a series of problems,which directly threatens human life and property security.In order to describe the stability of the grassland ecosystem truly and intuitively,this paper uses stochastic dynamics theory,based on the ecological system possessing typical significance Shnerb vegetation dynamic model and proposed by Ceng Qing cun et al in grassland ecosystem dynamics model,establishing the corresponding stochastic dynamic model,the main work is as follows:(1)We take advantages of FPK method and add some disturbances to study the impact of noise for the model of grassland ecological system.The result shows that after the introduction of random noise,the stability of the grassland ecosystem changes,and in a certain intensity of noise will make the system steady state transformation,so that the bifurcation point of the model changes.(2)For the simplified grassland ecosystem,we firstly set up a stochastic model and use stochastic Runge-Kutta scheme to simulate the grassland ecological dynamics.The result of our study demonstrated in the bifurcation interval,the random noise of the noise intensity is large enough to make the system stable,and the bifurcation value of the system is changed.Through the research analysis,control system parameters and noise intensity can make the ecological system steady changed.更多还原