一类集合生态系统的一致持久性
The Uniform Persistence of a Meta-Ecosystem
DOI: 10.12677/PM.2020.1011126, PDF,   
作者: 刘 菁, 杨喜陶:湖南科技大学数学与计算科学学院,湖南 湘潭
关键词: 集合生态系统一致持久性时滞比较原理Meta-Ecosystem Uniform Persistence Delay Comparison Theorem
摘要: 本文研究了一类集合生态系统内部双向资源交换的动力学行为,利用比较原理研究它的一致持久性,得到了该系统一致持久性的充分条件。
Abstract: In this paper we study the dynamic behavior of bi-directional resource exchange within a meta-ecosystem. By using the comparison principle, some sufficient conditions are determined that guarantee the uniform persistence of the model.
文章引用:刘菁, 杨喜陶. 一类集合生态系统的一致持久性[J]. 理论数学, 2020, 10(11): 1061-1069. https://doi.org/10.12677/PM.2020.1011126

参考文献

[1] Freedman, H.I. and Waltman, P. (1977) Mathematical Analysis of Some Three-Species Food-Chain Models. Mathe-matical Biosciences, 33, 257-276. [Google Scholar] [CrossRef
[2] Gard, T.C. (1980) Persis-tence in Food-Chains with General Interactions. Mathematical Biosciences, 51, 165-174. [Google Scholar] [CrossRef
[3] Garay, B.M. and Hofbauer, J. (2003) Robust Permanence for Ecological Differential Equations, Minimax, and Discretizations. SIAM Journal on Mathematical Analysis, 34, 1007-1039. [Google Scholar] [CrossRef
[4] Ashwin, P., Buescu, J. and Stewart, I. (1996) From Attractor to Chaotic Saddle: A Tale of Transverse Instability. Nonlinearity, 9, 703-737. [Google Scholar] [CrossRef
[5] Schreiber, S. (2000) Criteria for Cr Robust Permanence. Journal of Differential Equations, 162, 400-426. [Google Scholar] [CrossRef
[6] Hirsch, M.W., Smith, H.L. and Zhao, X.-Q. (2001) Chain Transitivity, Attractivity and Strong Repellors for Semidynamical Systems. Journal of Dynamics and Differential Equations, 13, 107-131. [Google Scholar] [CrossRef
[7] Hofbauer, J. and Schreiber, S.J. (2010) Robust Permanence for Structured Populations. Journal of Differential Equations, 248, 1955-1971. [Google Scholar] [CrossRef
[8] Smith, H.L. and Zhao, X.-Q. (2001) Robust Persistence for Semidynamical Systems. Nonlinear Analysis, 47, 6169-6179. [Google Scholar] [CrossRef
[9] Thieme, H.R. (1993) Persistence under Relaxed Point-Dissipativity (with Application to an Endemic Model). SIAM Journal on Mathematical Analysis, 24, 407-435. [Google Scholar] [CrossRef
[10] Thieme, H.R. (2000) Uniform Persistence and Permanence for Non-Autonomous Semiflows in Population Biology. Mathematician Bios, 166, 173-201. [Google Scholar] [CrossRef
[11] Messan, M.R., Kopp, D., Allen, D.C. and Kang, Y. (2018) Dynamics Implications of Bi-Directional Exchange within a Meta-Ecosystem. Mathematical Biosciences, 301, 167-184. [Google Scholar] [CrossRef] [PubMed]
[12] Hale, J.K. (1977) Theory of Functional Differential Equations. Springer-Verlag, Berlin. [Google Scholar] [CrossRef
[13] Kuang, Y. (1993) Delay Differential Equations with Applications in Population Dynamics. Academic, New York.
[14] Yang, X.T. (2006) Uniform Persistence for a Predator-Prey System with Delays. Applied Mathematics and Computation, 173, 523-534. [Google Scholar] [CrossRef
[15] 蒋燕, 杨喜陶. 一类非自治密度依赖的时滞捕食者–食饵系统的一致持久性[J]. 湖南文理学院学报(自然科学版), 2017(29): 9-12.