Hopf bifurcation in a reaction-diffusion-advection model with nonlocal delay effect and Dirichlet boundary condition
In this paper, the authors follows the approach by \textit{S. Guo} [J. Differ. Equations 259, No. 4, 1409--1448 (2015; Zbl 1323.35082)] and obtain the existence of the spatially nonhomogeneous steady-state solutions of a delayed reaction-diffusion-advection model by using the Lyapunov-Schmidt reduction. The associated eigenvalue problem is investigated and the existence of the Hopf bifurcation near the spatially nonhomogeneous steady states is obtained as well. In particular, the direction of the Hopf bifurcation and the stability of bifurcating periodic orbits are obtained. Finally, some applications and simulations are given to verify the theoretical results.
scientific article; zbMATH DE number 7624116
scientific article