[1]吴丽萍.一类具反馈控制的偏利模型平衡点的稳定性[J].延边大学学报(自然科学版),2022,(01):30-36.
　WU Liping.Stability of the equilibrium for a commensal symbiosis model with feedback controls[J].Journal of Yanbian University,2022,(01):30-36.
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一类具反馈控制的偏利模型平衡点的稳定性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 期数: 2022年01期 页码: 30-36 栏目: 基础科学研究 出版日期: 2022-04-20
Title:
Stability of the equilibrium for a commensal symbiosis model with feedback controls
文章编号:
1004-4353(2022)01-0030-07
作者:
吴丽萍
(闽江学院 数学与数据科学学院(软件学院), 福州 350108)
Author(s):
WU Liping
(College of Mathematics and Data Science(Software College), Minjiang University, Fuzhou 350108, China)
关键词:
偏利模型;  反馈控制;  出生率密度制约;  全局稳定
Keywords:
commensal symbiosis model;  feedback controls;  density dependent birth rate;  global stability
分类号:
O175.14
文献标志码:
A
摘要:
研究一类具有反馈控制变量和出生率具有密度制约的偏利共生模型的平衡点稳定性.首先通过分析系统的平衡点,得到系统正平衡点和边界平衡点存在的条件; 其次通过构造适当的Lyapunov函数,得到在一定条件下系统的正平衡点和边界平衡点是全局稳定的; 最后利用数值模拟验证了所得结果的正确性.
Abstract:
Stability of the equilibrium for a commensal symbiosis model with density dependent birth rate and feedback controls is investigated.Firstly, the equilibrium of the system is analyzed, and the conditions for the existence of positive equilibrium and the boundary equilibrium are obtained.Secondly, by constructing some suitable Lyapunov functions, the global stability of the positive equilibrium and the boundary equilibrium is showed under some suitable assumptions.Finally, the conclusions are verified by data simulation.

参考文献/References:

[1] 孙广才,孙欢.两种群共生关系的模型分析[J].渭南师范学院学报,2013,28(9):5 - 8.
[2] HAN R Y, CHEN F D.Global stability of a commensal symbiosis model with feedback controls[J].Communications in Mathematical Biology and Neuroscience, 2015(2015):1 - 10.[2021- 05-20].http://scik.org/index.php/cmbn/article/view/2125.
[3] CHEN F D.Permanence of a discrete N - species cooperation system with time delays and feedback controls[J].Applied Mathematics and Computation, 2007,186:23 - 29.
[4] CHEN J H, WU R X.A commensal symbiosis model with non - monotonic functional response[J].Communications in Mathematical Biology and Neuroscience, 2017(2017):1 - 8.[2021-04-21].http://scik.org/index.php/cmbn/article/view/2839.
[5] TANG S Y, CHEN L S.Density - dependent birth rate, birth pulses and their population dynamic consequences[J].Journal of Mathematical Biology, 2002,44(2):185 - 199.
[6] CHEN F D, XUE Y L, LIN Q F, et al.Dynamic behaviors of a Lotka - Volterra commensal symbiosis model with density dependent birth rate[J].Advances in Difference Equations, 2018,2018(1):296.
[7] 陈兰荪,宋新宇,陆征一.数学生态学模型与研究方法[M].成都:四川科学技术出版社,2003:92 - 99.

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备注/Memo

收稿日期: 2021-12-17
基金项目: 福建省自然科学基金(2021J011032)
作者简介: 吴丽萍(1972—),女,硕士,副教授,研究方向为生物数学.

更新日期/Last Update: 2022-04-20