Positivity-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model

doi:10.1007/s10543-021-00891-y

	Positivity-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model
	Hong, Jialin 2,4; Ji, Lihai 1; Wang, Xu 2,4; Zhang, Jingjing 3
刊名	BIT NUMERICAL MATHEMATICS
	2021-09-06
页码	28
关键词	Stochastic Lotka-Volterra predator-prey model Positivity Stochastic symplecticity Structure-preserving methods Convergence order conditions
ISSN号	0006-3835
DOI	10.1007/s10543-021-00891-y
英文摘要	In this paper, positivity-preserving symplectic numerical approximations are investigated for the 2d-dimensional stochastic Lotka-Volterra predator-preymodel driven by multiplicative noises, which plays an important role in ecosystem. The model is shown to possess both a unique positive solution and a stochastic symplectic geometric structure, and hence can be interpreted as a stochastic Hamiltonian system. To inherit the intrinsic biological characteristic of the original system, a class of stochastic Runge-Kutta methods is presented, which is proved to preserve positivity of the numerical solution and possess the discrete stochastic symplectic geometric structure as well. Uniform boundedness of both the exact solution and the numerical one are obtained, which are crucial to derive the conditions for convergence order one in the L-1(Omega)-norm. Numerical examples illustrate the stability and structure-preserving property of the proposed methods over long time.
资助项目	National Natural Science Foundation of China[11601032] ; National Natural Science Foundation of China[11971458] ; National Natural Science Foundation of China[12171047]
WOS研究方向	Computer Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000692962500001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59245]
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Xu
作者单位	1.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.East China Jiaotong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hong, Jialin,Ji, Lihai,Wang, Xu,et al. Positivity-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model[J]. BIT NUMERICAL MATHEMATICS,2021:28.
APA	Hong, Jialin,Ji, Lihai,Wang, Xu,&Zhang, Jingjing.(2021).Positivity-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model.BIT NUMERICAL MATHEMATICS,28.
MLA	Hong, Jialin,et al."Positivity-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model".BIT NUMERICAL MATHEMATICS (2021):28.