水-植物随机模型正解全局存在性与持久性  

Persistence and Global Existence of Positive Solutions for Water-plant Stochastic Model

作　　者：王晶囡 陈辉 杨德中 陆超轶 谭雨丽 WANG Jingnan;CHEN Hui;YANG Dezhong;LU Chaoyi;TAN Yuli(School of Science,Harbin University of Science and Technology,Harbin 150080)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《工程数学学报》2021年第5期653-661,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11801122);黑龙江省自然科学基金(A2018008);哈尔滨理工大学生创新项目(201810214280).

摘　　要：人类对大自然的过度开发和破坏所造成的土地荒漠化已经成为我国内陆盆地严重的生态环境问题之一.为了了解荒漠化地区植物可持续生长的情况,本文建立了一个新的水-植物随机效应模型来研究水补给的随机性对植物增长的影响.利用相图分析法和Ito公式证明了水-植物随机模型正解的全局存在性.利用平均积分法、Ito公式和局部鞅的强大数定律研究并得到了植物强平均持久生存的充分条件.数值模拟展示了水补给的随机性对植物增长的变化情况.理论和数值模拟的结果为治理土地荒漠化提供了理论依据.Land desertification caused by human over-exploitation and destruction of nature has become one of the severest ecological problems of China inland basin.In order to learn about the situation of the sustainable growth of plants in desertification areas,we establish a new water-plant model with stochastic effects to study the effect of the random water supply on plant growth in this paper.Through phase diagram analysis and Ito formula,we prove the global existence of the positive solution for water-plant stochastic model.By the average integral method,Ito formula and the strong large numbers law of local martingales,we obtain the sufficient conditions for the strong persistence in the mean of plants.The numerical simulations show the effect of the random water supply on plant growth.The results of theoretical and numerical simulations provide the theoretical basis for the control over the desertification problem.

关 键 词：随机过程 高斯白噪声 水-植物随机模型 

分 类 号：O211.63[理学—概率论与数理统计]