Study On Steady State Distribution And Numerical Methods Of Stochastic Plant-Soil Organic Matter Model

Land desertification is a major global environmental problem,which not only reduces the living space of human beings,but also worsens the development environment,exacerbates poverty,and endangers social stability Land desertification and its resulting desertification have seriously restricted the current survival and development of mankind,as well as the sustainable development of China’s economy and society.In order to demonstrate the authenticity and effectiveness of the ecological model,a large number of researchers have added complex natural environmental factors to the ecological model.In this article,we take plants and soil organic matter as research objects,establish a plant soil organic matter model with random terms,and carry out the following two aspects of research:1.It is difficult to obtain analytical solutions for the plant soil organic matter model.In order to predict the changes in the density of vegetation and soil organic matter over a certain period of time,it is necessary to construct an effective numerical algorithm.The existing methods cannot maintain the positive nature of the numerical solution.In order to obtain the computational results of random plant models,we extended the traditional Euler Maruyama Method and established an equilibrium implicit numerical method for plant soil organic matter models with random interference.Finally,numerical experiments verify the effectiveness of the BIM method.2.By constructing a suitable Lyapunov function,the positivity,existence and uniqueness of the solution of a random plant soil organic matter model are studied.Sufficient conditions for the existence of a stable distribution are given and it is proved that the system has a unique ergodic stable distribution.Finally,the theoretical results are verified by numerical simulation.