Open AccessHopf bifurcation in a reaction-diffusive-advection two-species competition model with one delay
Author(s) -
Qiong Meng,
Guirong Liu,
Zhen Jin
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.72
Subject(s) - mathematics , hopf bifurcation , center manifold , mathematical analysis , eigenvalues and eigenvectors , advection , dirichlet boundary condition , multiplicity (mathematics) , pitchfork bifurcation , saddle node bifurcation , stability (learning theory) , bifurcation , boundary value problem , physics , nonlinear system , quantum mechanics , machine learning , computer science , thermodynamics
In this paper, we investigate a reaction-diffusive-advection two-species competition model with one delay and Dirichlet boundary conditions. The existence and multiplicity of spatially non-homogeneous steady-state solutions are obtained. The stability of spatially nonhomogeneous steady-state solutions and the existence of Hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic orbits are derived. Finally, numerical simulations are given to illustrate the theoretical results.