Acta Mathematica Sinica

, Volume 19, Issue 4, pp 801–822

Periodicity and Stability in Periodic n-Species Lotka-Volterra Competition System with Feedback Controls and Deviating Arguments

  • Meng Fan
  • Ke Wang
  • Patricia J. Y. Wong
  • Ravi P. Agarwal
ORIGINAL ARTICLES

DOI: 10.1007/s10114-003-0311-1

Cite this article as:
Fan, M., Wang, K., Wong, P.J.Y. et al. Acta Math Sinica (2003) 19: 801. doi:10.1007/s10114-003-0311-1

Abstract

By using the method of coincidence degree and Lyapunov functional, a set of easily applicable criteria are established for the global existence and global asymptotic stability of strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterra competition system with feedback controls and several deviating arguments. The problem considered in this paper is in many aspects more general and incorporate as special cases various problems which have been studied extensively in the literature. Moreover, our new criteria, which improve and generalize some well known results, can be easily checked.

Keywords

Strictly positive periodic solutionsGlobally asymptotic stabilityLotka-Volterra competition systemFeedback controlsDeviating argumentsCoincidence degreeLyapunov functional

MR (2000) Subject Classification

34K1534K2034C2534D20

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Meng Fan
    • 1
  • Ke Wang
    • 1
  • Patricia J. Y. Wong
    • 2
  • Ravi P. Agarwal
    • 3
  1. 1.Department of Mathematics, Key Laboratory for Vegetation Ecology of the Education Ministry of P. R. ChinaNortheast Normal UniversityChangchunP. R. China
  2. 2.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA