2023/05/10 by Yaqi Chen, Chen, Yaqi, Xianyi Zeng +3
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2305.05979
openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a two-dimensional disk. The properties of these bifurcations around equilibriums are analyzed rigorously by studying the equivariant normal forms. Two reaction-diffusion systems with discrete time delays are selected as numerical examples to verify the theoretical results, in which spatially inhomogeneous periodic solutions including standing waves and rotating waves, and spatially homogeneous periodic solutions are found near the bifurcation points.