Stability and bifurcation in a two-species reaction-diffusion-advection competition model with time delay

In this paper, we are concerned with the dynamics of a class of two-species reaction-diffusion-advection competition models with time delay subject to the homogeneous Dirichlet boundary condition or no-flux boundary condition in a bounded domain. The existence of steady state solution is investigated by means of the Lyapunov-Schmidt reduction method. The stability and Hopf bifurcation at the spatially nonhomogeneous steady-state are obtained by analyzing the distribution of the associated eigenvalues. Finally, the effect of advection on Hopf bifurcation is explored, which shows that with the increase of convection rate, the Hopf bifurcation phenomenon is more likely to emerge. (C) 2021 Elsevier Ltd. All rights reserved.

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This paper investigates the dynamics of a class of two-species reaction-diffusion-advection competition models with time delay in a bounded domain, subject to homogeneous Dirichlet or no-flux boundary conditions. The study explores the existence of steady state solutions using the Lyapunov-Schmidt reduction method, and analyzes the stability and Hopf bifurcation at spatially nonhomogeneous steady states. Furthermore, the effect of advection on Hopf bifurcation is examined, revealing that an increase in convection rate makes the Hopf bifurcation phenomenon more likely to occur.