On positive periodic solutions of Lotka-Volterra competition systems with deviating arguments

By Xianhua Tang, Xingfu Zou. 2006

57 citations recorded by the source corpus.

By using Krasnoselskii's fixed point theorem, we prove that the following periodic n-species Lotka-Volterra competition system with multiple deviating arguments (*) x i (t)=x i (t) r i (t) - Σa ij (t)x j )t - x ij (t))], i = 1,2,...,n, has at least one positive ω-periodic solution provided that the corresponding system of linear equations n (**) a ij x j = r i , i=1,2,...,n, has a positive solution, where r i ,a ij ∈ C(R,[0,oo)) and τ ij ∈ C(R,R) are ω-periodic functions with r i = 1/ω ∫ ω 0 r i (s)ds > 0; a ij = 1/ω ∫ ω 0 a ij (s)ds ≥ 0, i,j=1,2,...,n. Furthermore, when a ij (t) = a ij and τ ij (t) ≡ τ ij , i,j = 1,... n, are constants but r i (t), i = 1,..., n, remain ω-periodic, we show that the condition on (**) is also necessary for (*) to have at least one positive 01- periodic solution.

Subfields: Applied Mathematics, Public Health, Environmental and Occupational Health, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9b4fc89b894c305ca9e6517553af38e5d03b4512

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In Applied Mathematics

  1. Daomin Cao
  2. Xianhua Tang
  3. Xingfu Zou
  4. Sitong Chen
  5. Chang-Lin Xiang
  6. Shusen Yan
  7. Shuangjie Peng
  8. Shiwang Ma

In Public Health, Environmental and Occupational Health

  1. Daomin Cao
  2. Xianhua Tang
  3. Xingfu Zou
  4. Wan-Tong Li
  5. Guo Lin
  6. Shiwang Ma
  7. Shigui Ruan
  8. Jianhong Wu

In Statistical and Nonlinear Physics

  1. Xianhua Tang
  2. Xingfu Zou

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