KMS Of Academy of mathematics and systems sciences, CAS
| Positivity-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model | |
| Hong, Jialin1,2; Ji, Lihai3; Wang, Xu1,2; Zhang, Jingjing4 | |
| 2021-09-06 | |
| Source Publication | BIT NUMERICAL MATHEMATICS
 |
| ISSN | 0006-3835 |
| Pages | 28 |
| Abstract | 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. |
| Keyword | Stochastic Lotka-Volterra predator-prey model Positivity Stochastic symplecticity Structure-preserving methods Convergence order conditions |
| DOI | 10.1007/s10543-021-00891-y |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11601032] ; National Natural Science Foundation of China[11971458] ; National Natural Science Foundation of China[12171047] |
| WOS Research Area | Computer Science ; Mathematics |
| WOS Subject | Computer Science, Software Engineering ; Mathematics, Applied |
| WOS ID | WOS:000692962500001 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59246 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wang, Xu |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China 4.East China Jiaotong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China |
| Recommended Citation 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. |
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