Existence and stability of periodic solutions for parabolic competition systems

Xianlin Huang, Hongyang Zhang, Hang Yin, Xiao-zhi Gao

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


We consider a nonlinear reaction-diffusion competition model with Neumann boundary condition. The main goal of this article is to research the existence and uniqueness of positive periodic solution when most of parameters are functions of time t and space x. We apply the lower and upper solutions method to present existence conditions of positive periodic solution. We obtain uniqueness conditions of positive periodic solution from priori estimates of the system. Moreover, Numerical simulation is carried out to illustrate feasibility of our main results.

Original languageEnglish
Title of host publicationProceedings of the 35th Chinese Control Conference, CCC 2016
EditorsJ. Chen , Q. Zhao
Number of pages6
ISBN (Electronic)9789881563910
Publication statusPublished - 26 Aug 2016
MoE publication typeA4 Article in a conference publication
EventChinese Control Conference - Chengdu, China
Duration: 27 Jul 201629 Jul 2016
Conference number: 35

Publication series

NameChinese Control Conference
ISSN (Electronic)2161-2927


ConferenceChinese Control Conference
Abbreviated titleccc2016
Internet address


  • Holling-Tanner competing model
  • Lower and upper solutions method
  • Periodic solution
  • Priori estimate
  • Reaction-diffusion

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