一类非自治随机互惠系统的渐近性态
Asymptotic Behavior of a Non-Autonomous Stochastic Mutualism System
DOI: 10.12677/PM.2019.94068, PDF,    国家自然科学基金支持
作者: 郭 奥, 丁孝全*：河南科技大学数学与统计学院，河南 洛阳
关键词: 随机互惠系统；全局吸引性；持续性；灭绝性；周期解；Stochastic Mutualism System； Global Attractivity； Permanence； Extinction； Periodic Solution
摘要: 本文讨论一类非自治随机互惠系统的渐近性态。首先，对任意正初值，建立了系统全局正解的存在唯一性。接着，利用随机微分方程比较定理和Lyapunov函数，得到了系统的持续性、灭绝性、全局吸引性和周期解的存在性。最后，数值模拟验证了理论结果的合理性。
Abstract: This paper is devoted to the asymptotic behavior of a non-autonomous stochastic mutualism system. Firstly, the existence and uniqueness of global positive solution to the system is established for any positive initial value. Then by using the comparison theorem for stochastic differential equations and Lyapunov functions, the sufficient conditions for the permanence, extinction, global attractivity, and existence of periodic solutions to the system are derived respectively. Finally, some numerical simulations are given to illustrate our theoretical results.
文章引用：郭奥, 丁孝全. 一类非自治随机互惠系统的渐近性态[J]. 理论数学, 2019, 9(4): 514-526. https://doi.org/10.12677/PM.2019.94068

参考文献

[1] Boucher, D.H. (1985) The Biology of Mutualism: Ecology and Evolution. Oxford University Press, New York.
[2] 陈凤德, 谢向东. 合作种群模型动力学研究[M]. 北京: 科学出版社, 2014.
[3] Graves, W.G., Peckham, B. and Pastor, J. (2006) A Bifurcation Analysis of a Differential Equations Model for Mutualism. Bulletin of Mathematical Biology, 68, 1851-1872.
[Google Scholar] [CrossRef] [PubMed]
[4] 向红, 张小兵, 孟新友. 一类互惠模型的持续生存与周期解[J]. 兰州交通大学学报, 2009, 28(4): 156-158.
[5] Gard, T.C. (1986) Stability for Multispecies Population Models in Random Environments. Nonlinear Analysis, 10, 1411-1419.
[Google Scholar] [CrossRef] 
[6] Mao, X., Renshaw, E. and Marion, G. (2002) Environmental Brownian Noise Suppresses Explosions in Population Dynamics. Stochastic Processes and Their Applications, 97, 95-110.
[Google Scholar] [CrossRef] 
[7] Rudnicki, R. and Pichór, K. (2007) Influence of Stochastic Per-turbation on Prey-Predator Systems. Mathematical Biosciences, 206, 108-119.
[Google Scholar] [CrossRef] [PubMed]
[8] Liu, M. and Wang, K. (2011) Persistence and Extinction in Stochastic Non-Autonomous Logistic Systems. Journal of Mathematical Analysis and Applications, 375, 443-457.
[Google Scholar] [CrossRef] 
[9] Mandal, P.S. and Banerjee, M. (2012) Stochastic Persistence and Sta-tionary Distribution in a Holling-Tanner Type Prey-Predator Model. Physica A, 391, 1216-1233.
[Google Scholar] [CrossRef] 
[10] 王克. 随机生物数学模型[M]. 北京: 科学出版社, 2010.
[11] 吕敬亮. 几类随机生物种群模型性质的研究[D]: [博士学位论文] . 哈尔滨: 哈尔滨工业大学, 2011.
[12] Ji, C. and Jiang, D. (2012) Persistence and Non-Persistence of a Mutualism System with Stochastic Perturbation. Discrete and Continuous Dynamical Systems, 32, 867-889.
[Google Scholar] [CrossRef] 
[13] Liu, M. and Wang, K. (2013) Popula-tion Dynamical Behavior of Lotka-Volterra Cooperative Systems with Random Perturbations. Discrete and Continuous Dy-namical Systems, 33, 2495-2522.
[Google Scholar] [CrossRef] 
[14] Liu, M. and Wang, K. (2013) Analy-sis of a Stochastic Autonomous Mutualism Model. Journal of Mathematical Analysis and Applications, 402, 392-403.
[Google Scholar] [CrossRef] 
[15] Qiu, H., Lv, J. and Wang, K. (2013) Two Types of Permanence of a Stochastic Mutualism Model. Advances in Difference Equations, 2013, 37.
[Google Scholar] [CrossRef] 
[16] Li, M., Gao, H., Sun, C. and Gong, Y. (2015) Analysis of a Mutualism Model with Stochastic Perturbations. International Journal of Biomathematics, 8, Article ID: 1550072.
[Google Scholar] [CrossRef] 
[17] Guo, S. and Hu, Y. (2017) Asymptotic Behavior and Numerical Simulations of a Lotka-Volterra Mutualism System with White Noises. Advances in Difference Equations, 2017, 125.
[Google Scholar] [CrossRef] 
[18] Gao, H. and Wang, Y. (2019) Stochastic Mutualism Model under Re-gime Switching with Lévy Jumps. Physica A, 515, 355-375.
[Google Scholar] [CrossRef] 
[19] Han, Q. and Jiang, D. (2015) Periodic Solution for Stochastic Non-Autonomous Multispecies Lotka-Volterra Mutualism Type Eco-system. Applied Mathematics and Computation, 262, 204-217.
[Google Scholar] [CrossRef] 
[20] Zhang, X., Jiang, D., Alsaedi, A. and Hayat, T. (2016) Periodic Solutions and Stationary Distribution of Mutualism Models in Ran-dom Environments. Physica A, 460, 270-282.
[Google Scholar] [CrossRef] 
[21] Wang, B., Gao, H. and Li, M. (2017) Analysis of a Non-Autonomous Mutualism Model Driven by Lévy Jumps. Discrete and Continuous Dy-namical Systems: Series B, 21, 1189-1202.
[Google Scholar] [CrossRef] 
[22] Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus. 2nd Edition, Springer, Berlin.
[23] Mao, X. (2007) Stochastic Differential Equations and Applications. 2nd Edition, Horwood Publishing, Chichester.
[24] Khasminskii, R. (2012) Stochastic Stability of Differential Equations. 2nd Edition, Springer, Berlin.
[Google Scholar] [CrossRef] 
[25] Higham, D.J. (2001) An Algorithmic Introduction to Numerical Sim-ulation of Stochastic Differential Equations. SIAM Review, 43, 525-546.
[Google Scholar] [CrossRef] 
[26] Barbălat, I. (1959) Systèmes D’équations Différentielles D’oscillations Nonlinéaires. Revue Roumaine de Mathématique Pures et Appliquées, 4, 267-270.

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