Open AccessThe study of global stability of a diffusive Michaelis-Menten and tanner predator-prey model
Author(s) -
Demou Luo
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1917651l
Subject(s) - mathematics , bounded function , predation , stability (learning theory) , domain (mathematical analysis) , michaelis–menten kinetics , diffusion , predator , boundary value problem , mathematical analysis , ecology , thermodynamics , biology , physics , computer science , biochemistry , machine learning , enzyme assay , enzyme
In this paper, we consider a parabolic predator-prey model of Michaelis-Menten and Tanner functional response with random diffusion: ut = d1?u + au-bu2- ?uv/?u + v', vt = d2?v + rv- ?v2/u with d1,d2,a,b,r,?,?,? > 0 under the no-flux boundary condition in a smooth bounded domain ? ? Rn (n = 1,2,3). By applying a new method, we establish much improved global asymptotic stability of the unique positive equilibrium solution than works in literature. We also show the result can be extended to more general type of systems with heterogeneous environment.