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一类推广的Gilpin-Ayala竞争系统的绝灭性 被引量：2

Extintion in a generalized Gilpin-Ayala competition system
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摘要 研究一类具有无穷时滞的二维Gilpin-Ayala竞争系统,利用比较原理和振荡性原理,证明在一定条件下,系统中一种物种将绝灭,而另一物种趋于稳定. In this paper, a two dimensinal Gilpin - Ayala competition system with infinite delay is studied. By applying the standard comparison theorem and fluctuation theorem. We prove that one of species of the system will be driven to extinction while the other will stabilize at a certain solution.
作者 王丹红 许君雁 王海娜
机构地区 闽江学院数学系 福州大学数学与计算机科学学院
出处 《福州大学学报（自然科学版）》 CAS CSCD 北大核心 2013年第6期967-971,共5页 Journal of Fuzhou University(Natural Science Edition)
基金 福建省自然科学基金资助项目(2012J05007) 福建省教育厅科研资助项目(JB12160)
关键词 Gilpin—Ayala竞争系统 无穷时滞 绝灭性 Gilpin- Ayala competition system infinite delay extinction
分类号 O175.1 [理学—基础数学]
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参考文献9

  • 1Fan Meng, Wang Ke. Global periodic solutions of a generalized n - species Gilpin - Ayala competition model [ J ]. Computer and Mathematics with Applications, 2000, 40 (10/11): 1 141 -1 151.
  • 2Goh B S, Agnew T T. Stability in Gilpin and Ayala' s models of competition[J]. Math Biology, 1977, 4(3) : 275 -279.
  • 3周孔容,雷镜朝.Gilpin-Ayala竞争模型全局稳定性分析[J].四川大学学报,1987,24(4):361-366.
  • 4Liao Xiao -xin, Li Jia. Stability in Gilpin -Ayala competition models with diffusion[ J ]. Nonlinear Analysis: Theory, Methods & Applications, 1997, 28(10) : 1 751 -1 758.
  • 5Chen Feng - de, Yu Ming -chen, Guo Shang - jiang, et al. Global atrativitity of a generalized Lotka - Volterra competi - tion model[J]. Differ Equ Dyn Syst, 2010, 18(3) : 303 -315.
  • 6Chen Feng - de. Average conditions for permanence and extinction in nonantonomous Gilpin - Ayala competition model [ J ]. Non- linear Analysis: Real World Applications, 2006, 7(4) : 895 -915.
  • 7Chen Feng - de. Some new results on the permanence and extinction of nonantonomous Gilpin - Ayala type competition model with delays [ J ]. Nonlinear Analysis : Real World Applications, 2006, 7 (5) : 1 205 - 1 222.
  • 8Chen Feng - de, Li Zhong, Huang Yun - jin. Note on the permanence of a competitive system with infinite delay and feedback controls [ J ]. Nonlinear Analysis : Real World Applications, 2007, 8 (3) : 680 - 687.
  • 9de Oca F M, Vivas M. Extinction in a two dimensional Lotka - Voherra system with infinite delay [ J ]. Nonlinear Analysis : Real World Applications, 2006, 7 (5) : 1 042 - 1 047.

同被引文献20

  • 1ChenFengde.PERSISTENCE AND PERIODIC ORBITS FOR TWO-SPECIES NON-AUTONOMOUS DIFFUSION LOTKA-VOLTERRA MODELS[J].Applied Mathematics(A Journal of Chinese Universities),2004,19(4):359-366. 被引量：5
  • 2Goh B S, Agnew T T. Stability in Gilpin and Ayala' s models of competition[ J]. Math Biology, 1977, 4 (3) : 275 -279.
  • 3Liao Xiaoxin, Li Jia. Stability in Gilpin-Ayala competition models with diffusion[ J]. Nonlinear Analysis:Theory, Methods & Applications, 1997,28 (10) : 1751 - 1758.
  • 4Chen Fengde. Average conditions for permanence and extinction in nonautonomous Gilpin-Ayala competition model[ J ]. Non- linear Analysis : Real World Applications, 2006,7 (4) : 895 - 915.
  • 5Chen Fengde, Yu Mingchen, Guo Shangjiang, Li Zhong. Global Atrativitity of a Generalized Lotka-Volterra Competition Model [J]. Differ Equ Dyn Syst,2010, 18(3) : 303 -315.
  • 6Chen Fengde. Some new results on the permanence and extinction of nonautonomous Gilpin-Ayala type competition model with delays[ J ]. Nonlinear Analysis : Real World Applications, 2006, 7 (5) : 1205 - 1222.
  • 7Chen Fengde, Li Zhong, Huang YunJin. Note on the permanence of a competitive system with infinite delay and feedback controls [ J ]. Nonlinear Analysis : Real World Applications, 2007, 8 ( 3 ) :680 - 687.
  • 8Zhong Li,Fengde Chen.Extinction in two dimensional nonautonomous Lotka–Volterra systems with the effect of toxic substances[J]. Applied Mathematics and Computation . 2006 (1)
  • 9Francisco Montes de Oca,Miguel Vivas.Extinction in a two dimensional Lotka–Volterra system with infinite delay[J]. Nonlinear Analysis: Real World Applications . 2005 (5)
  • 10Fengde Chen.Average conditions for permanence and extinction in nonautonomous Gilpin–Ayala competition model[J]. Nonlinear Analysis: Real World Applications . 2005 (4)

引证文献2

福州大学学报（自然科学版）
2013年 第6期

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