Hopf bifurcation of a delayed reaction–diffusion model with advection term. (November 2021)

• Record Type: Journal Article
• Authors: Ma, Li; Wei, Dan
• Is Part Of: Nonlinear analysis. Volume 212(2021)
• Publication Date: 2021-11
• Subjects: 92B05 -- 35B40 -- 35K57; Reaction–diffusion–advection equation -- Spatial heterogeneity -- Lyapunov–Schmidt reduction -- Hopf bifurcation -- Time delay; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112455
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This article focus on the Hopf bifurcation of a delayed reaction–diffusion equation with advection term subject to Dirichlet boundary and no-flux boundary conditions in a bounded domain, respectively. It is shown that the existence of spatially non-homogeneous steady-state solutions will be obtained when the parameter λ of the model (9) closes to the principle eigenvalue λ 1 of the elliptic operator L λ . Moreover, a supercritical Hopf bifurcation occurs near the non-homogeneous positive steady-state at a series critical time delay values. Finally, we elucidate the effect of advection on Hopf bifurcation values. It is worth noting that the advective effect has accelerated the generation of Hopf bifurcation to a certain extent.