Open AccessBifurcation structure of nonconstant positive steady states for a diffusive predator-prey model
Author(s) -
Dong Fu Tong,
Yong Li Cai,
Bing Xian Wang,
Wei Ming Wang
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019197
Subject(s) - bifurcation , mathematics , neumann boundary condition , steady state (chemistry) , mathematical analysis , eigenvalues and eigenvectors , constant (computer programming) , implicit function theorem , saddle node bifurcation , transcritical bifurcation , instability , biological applications of bifurcation theory , bifurcation theory , bifurcation diagram , boundary value problem , nonlinear system , physics , mechanics , computer science , chemistry , programming language , quantum mechanics
In this paper, we make a detailed descriptions for the local and global bifurcation structure of nonconstant positive steady states of a modified Holling-Tanner predator-prey system under homogeneous Neumann boundary condition. We first give the stability of constant steady state solution to the model, and show that the system exhibits Turing instability. Second, we establish the local structure of the steady states bifurcating from double eigenvalues by the techniques of space decomposition and implicit function theorem. It is shown that under certain conditions, the local bifurcation can be extended to the global bifurcation.