PERIODIC SOLUTION OF A HIGHER DIMENSIONAL ECOLOGICAL SYSTEM

Yonghui Xia; Huicheng Wang; Kit Ian Kou; Zhaoping Hu

doi:10.11948/2016058

2016 Volume 6 Issue 3

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Yonghui Xia, Huicheng Wang, Kit Ian Kou, Zhaoping Hu. PERIODIC SOLUTION OF A HIGHER DIMENSIONAL ECOLOGICAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 893-906. doi: 10.11948/2016058

Citation:

Yonghui Xia, Huicheng Wang, Kit Ian Kou, Zhaoping Hu. PERIODIC SOLUTION OF A HIGHER DIMENSIONAL ECOLOGICAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 893-906. doi: 10.11948/2016058

PERIODIC SOLUTION OF A HIGHER DIMENSIONAL ECOLOGICAL SYSTEM

1 School of Mathematical Sciences, Huaqiao University, 362021, Quanzhou, Fujian, China;
2 Department of Mathematics, Zhejiang Normal University, Jinhua, 310004, China;
3 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau;
4 Department of Mathematics, Shanghai University, Shanghai 200444, China

Abstract

Abstract

The main purpose of this article is to study the periodicity of a Lotka-Volterra's competition system with feedback controls. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions. Our method is base on combining matrix's spectral theory and inequality |x(t)| ≤ x(t₀) + ∫₀^ω |ẋ(t)|dt. Some examples and their simulations show the feasibility of our main result.
- Periodic solutions /
- asymptotic stability /
- feedback controls /
- Lyapunov function
MSC: 34C25;93D20;93B52;37B25

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