一个种群与环境资源相互作用模型的有限差分逼近  

Finite Difference Approximation for a Model of Interaction Between Population and Environmental Resources

作　　者：王文静 靳欢欢 黄启华 WANG Wenjing;JIN Huanhuan;HUANG Qihua(Department of Computer, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2022年第5期22-30,共9页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(No.11871060).

摘　　要：本文建立并研究了一个种群与资源相互作用的数学模型.该模型由一个一阶双曲偏微分方程和一个微分-积分方程耦合而成,其中双曲方程描述了受资源影响的大小结构、种群的生长和死亡过程;微分-积分方程描述了资源的输入、衰减以及种群对资源的消耗过程.通过对模型进行离散化,建立了模型的隐式有限差分逼近格式,证明了有限差分逼近的收敛性及模型弱解的存在唯一性.In this paper,a mathematical model for the interaction between a population and a resource has been established and studied.The model is composed of a first order hyperbolic partial differential equation coupled with an integral differential equation.The hyperbolic equation describes the growth and death processes of the size-structured population under the influence of the resources.By discretizing the model,an implicit finite-difference approximation scheme of the model has been established,the convergence of the finite-difference approximation and the existence and uniqueness of the weak solution of the model been proved.

关 键 词：种群 资源 有限差分 存在唯一性 

分 类 号：O175[理学—数学]