YANG Yingzhong,WANG Kuancheng.Stability of the boundary equilibrium of amensalism system with feedback controls[J].Journal of Yanbian University,2017,43(04):308-310.
具有反馈控制的偏害模型边界平衡点的稳定性
- Title:
- Stability of the boundary equilibrium of amensalism system with feedback controls
- 关键词:
- 反馈控制; 绝灭; 偏害模型; Lyapunov函数; 稳定性
- Keywords:
- feedback controls; extinction; amensalism system; Lyapunov function; stability
- 分类号:
- O175.14
- 文献标志码:
- A
- 摘要:
- 研究具有反馈控制变量的两种群偏害模型边界平衡点的稳定性.通过构造适当的Lyapunov绝灭函数获得了保证某个种群绝灭的充分性条件,并证明了边界平衡点的稳定性.最后,通过数值模拟对所得结论进行了验证.本文研究结果补充了文献[7]的相关结果.
- Abstract:
- The stability of the boundary equilibrium of amensalism system with feedback controls is studied. By constructing a suitable extinction function and Lyapunov function, some sufficient conditions which ensure the attractivity of the boundary equilibrium are obtained. The stability of the boundary equilibrium is proved by constructing the Lyapunov function. Finally, the relevant conclusions are verified by numerical simulation.The research results supplement the related results of the literature [7].
参考文献/References:
[1] Niyaz T, Muhammadhaji A. Positive periodic solution of cooperative systems with delays and feedback controls[J]. International Journal of Differential Equations, 2013,2013(24):93-101.
[2] Li Z, Han M, Chen F. Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays[J]. Nonlinear Analysis: Real World Applications, 2013,14(1):402-413.
[3] 赵亮,陈凤德.具有反馈控制的竞争系统边界平衡点的稳定性[J].北华大学学报(自然科学版),2013,14(5):516-519.
[4] 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.
[5] 杨坤,王海娜,陈凤德.反馈控制Lotka-Volterra合作系统稳定性研究[J].应用数学,2014(2):243-247.
[6] 陈凤德,龚晓杰,普丽琼,等.具有反馈控制的Lotka-Volterra捕食-食饵系统研究[J].生物数学学报,2015,30(2):328-332.
[7] 黄宏韬,林锦贤.具有反馈控制变量的偏害模型稳定性研究[J].福州大学学报(自然科学版),2017,45(1):69-73.
相似文献/References:
[1]陈江彬.具反馈控制和Holling-III类功能反应的修正Leslie-Gower捕食系统研究[J].延边大学学报(自然科学版),2017,43(03):189.
CHEN Jiangbin.Dynamics of a modified Leslie-Gower predator-prey system withHolling-type III response function and feedback controls[J].Journal of Yanbian University,2017,43(04):189.
[2]张杰华.具毒素影响的两种群离散竞争模型的绝灭性[J].延边大学学报(自然科学版),2018,44(03):208.
ZHANG Jiehua.Extinction of a two species discrete competitive systemwith the effects of toxic substances[J].Journal of Yanbian University,2018,44(04):208.
备注/Memo
收稿日期: 2017-10-22 基金项目: 福建省中青年教师教育科研项目(JAT170739)作者简介: 杨英钟(1982—),男,副教授,研究方向为微分方程定性理论.