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

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 lambda of the model (9) closes to the principle eigenvalue lambda(1) of the elliptic operator epsilon(lambda). 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. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

The article focuses on the Hopf bifurcation of a delayed reaction-diffusion equation with advection term, showing the existence of spatially non-homogeneous steady-state solutions and elucidating the effect of advection on Hopf bifurcation values.