Delay-induced instability in a reaction-diffusion model with a general advection term

Abstract

In this paper, we consider a delayed reaction-diffusion model with a general advection term. The stability/instability of the positive steady state and delay-induced Hopf bifurcation are investigated when the given parameter is near the principal eigenvalue of a non-self-adjoint elliptic operator. Moreover, some previous methods are improved to derive a priori estimates for the eigenvalue problem, which is crucial to show the existence of a Hopf bifurcation.