Long-time dynamics of a reaction–diffusion system with negative feedback and inhibition. (September 2020)

• Record Type: Journal Article
• Authors: Lei, Chengxia; Zhou, Jialin
• Is Part Of: Applied mathematics letters. Volume 107(2020)
• Publication Date: 2020-09
• Subjects: Reaction–diffusion system with negative feedback and inhibition -- A priori estimate -- Equilibrium -- Global attractivity; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106475
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper concerns the long-time dynamics of a reaction–diffusion system with negative feedback and inhibition. We first derive a priori L ∞ -norm estimates for the solution. Then, by constructing two different types of Lyapunov functions, we prove that the positive equilibrium is globally attractive when the basic reproduction number R 0 > 1, while the microorganisms-free equilibrium is globally attractive when R 0 ≤ 1 .