Hopf bifurcation of a delayed reaction–diffusion model with advection term

• Published in: Nonlinear analysis Vol. 212; p. 112455
• Main Authors: Ma, Li, Wei, Dan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2021
• Subjects: Hopf bifurcation; Lyapunov–Schmidt reduction; Reaction–diffusion–advection equation; Spatial heterogeneity; Time delay; 92B05; Lyapunov–Schmidt reduction; Spatial heterogeneity; Reaction–diffusion–advection equation; 35B40; Time delay; 35K57; Hopf bifurcation
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2021.112455

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 λ1 of the elliptic operator Lλ. 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.