Saddle-node bifurcation

Physics

Mathematical analysis

Physical chemistry

Pitchfork bifurcation

Nonlinear system

Eigenvalues and eigenvectors

Hopf bifurcation

Chemistry

Instability

Bogdanov–Takens bifurcation

Bifurcation

Mathematics

Advection

Transcritical bifurcation

Mechanics

Quantum mechanics

Steady state (chemistry)

Thermodynamics

Journal of Differential Equations

In this paper, we investigate a reaction–diffusion–advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction–diffusion–advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.

Hopf bifurcation in a delayed reaction–diffusion–advection population model