YU Shengbin.Extinction and stability in a continuous competitive system with the effect of toxic substances[J].Journal of Yanbian University,2016,42(03):196-202.
具毒素影响的连续型竞争系统的绝灭性和稳定性
- Title:
- Extinction and stability in a continuous competitive system with the effect of toxic substances
- Keywords:
- continuous system; extinction; competitive; toxicology; stability
- 分类号:
- O175.14
- 文献标志码:
- A
- 摘要:
- 研究具有非线性相互抑制项和毒素影响的连续型非自治竞争系统的绝灭性和稳定性问题.通过构造适当的绝灭函数,得到了保证系统一个种群绝灭、另外一个种群全局吸引的充分性条件,所得结果补充了文献[1]和[8]的工作.数值模拟结果表明,本文结果具有可靠性.
- Abstract:
- We consider the extinction and stability of a nonautonomous continuous competitive system with nonlinear inter-inhibition terms and one toxin-producing species. By constructing some suitable Lyapunov type extinction functions, sufficient conditions which guarantee the extinction of species and the stability property of another species are obtained. The results supplement the literature [1] and [8]. The numerical simulations show that the results are reliable.
参考文献/References:
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[4] 陈凤德,赵亮.一类非自治两种群浮游生物相克模型的绝灭性[J].沈阳大学学报(自然科学版),2014,26(1):1-3.
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[6] LI Zhong, CHEN Fengde. Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances[J]. Applied Mathematics and Computation, 2006,182(1):684-690.
[7] CHEN Fengde, XIE Xiangdong, MIAO Zhanshuai, et al. Extinction in two species nonautonomous nonlinear competitive system[J]. Applied Mathematics and Computation, 2016,274(1):119-124.
[8] WANG Qinglong, LIU Zhijun, LI Zuxiong, et al. Existence and global asymptotic stability of positive almost periodic solutions of a two-species competitive system[J]. International Journal of Biomathematics, 2014,7(4):1450040(18 pages).
[9] YU Shengbin. Permanence for a discrete competitive system with feedback controls[J]. Commun Math Biol Neurosci, 2015(2015), Article ID 16.
[10] 余胜斌.一类离散非自治竞争系统的绝灭性和稳定性[J].延边大学学报(自然科学版),2015,41(4):279-284.
[11] CHEN F, GONG X, CHEN W. Extinction in two dimensional discrete Lotka-Volterra competitive system with the effect of toxic substances(II)[J]. Dyn Contin Discrete Impuls Syst, Ser B, Appl Algorithms, 2013,20:449-461.
[12] De Oca F M, Vivas M. Extinction in two dimensional Lotka-Volterra system with infinite delay[J]. Nonlinear Anal, Real World Appl, 2006,7(5):1042-1047.
[13] CHEN Fengde, LI Zhong, HUANG Yunjin. Note on the permanence of a competitive system with infinite delay and feedback controls[J]. Nonlinear Anal, Real World Appl, 2006,8(2):680-687.
相似文献/References:
[1]余胜斌.一类离散非自治竞争系统的绝灭性和稳定性[J].延边大学学报(自然科学版),2015,41(04):279.
YU Shengbin.Extinction and stability in a class of discrete non-autonomous competition system[J].Journal of Yanbian University,2015,41(03):279.
[2]张志敏.一类非自治差分竞争系统的绝灭性和稳定性[J].延边大学学报(自然科学版),2017,43(02):104.
ZHANG Zhimin.Extinction and stability in a nonautonomous difference competitive system[J].Journal of Yanbian University,2017,43(03):104.
备注/Memo
收稿日期: 2016-08-15 作者简介: 余胜斌(1984—),男,讲师,研究方向为生物数学.基金项目: 福建省高校杰出青年科研人才培育计划项目(2016); 福建省自然科学基金资助项目(2015J01012, 2015J01019)