Equivariant Hopf Bifurcation in a Class of Partial Functional Differential Equations on a Circular Domain
Dynamical Systems
2023-05-11 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2305.05979,
title = {Equivariant Hopf Bifurcation in a Class of Partial Functional Differential Equations on a Circular Domain},
author = {Yaqi Chen and Xianyi Zeng and Ben Niu},
journal= {arXiv preprint arXiv:2305.05979},
year = {2023}
}