Properties of Hopf Bifurcation in a Diffusive Population Model with Advection Term and Nonlocal Delay Effect

• Published in: Journal of nonlinear science Vol. 35; no. 1
• Main Authors: Yan, Xiang-Ping, Zhang, Cun-Hua
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2025; Springer Nature B.V
• Subjects: Advection; Analysis; Boundary conditions; Canonical forms; Centre manifold theory; Classical Mechanics; Differential equations; Economic Theory/Quantitative Economics/Mathematical Methods; Hopf bifurcation; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Orbital stability; Steady state models; Theoretical; Nonlocal delay; 37G05; Advection; 34K18; Normal form; 35B32; Reaction–diffusion population model; 92D05; Hopf bifurcation
• ISSN: 0938-8974; 1432-1467
• DOI: 10.1007/s00332-024-10125-4

The present paper is concerned with a generalized logistic reaction–diffusion–advection population model with nonlocal delay effect and subject to homogeneous Dirichlet boundary condition. Normal form of Hopf bifurcation of model at the positive steady-state solution is computed in virtue of the normal form method and the center manifold theorem for partial functional differential equations. Then the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are determined in terms of the obtained normal form. It is shown that Hopf bifurcations of model at the positive steady-state solution are forward and the associated bifurcating periodic solutions are locally orbitally asymptotically stable on the center manifold.