Article Dans Une Revue International journal of bifurcation and chaos in applied sciences and engineering Année : 2024

Equivariant Hopf Bifurcation in a Class of Partial Functional Differential Equations on a Circular Domain

Résumé

Circular domains frequently appear in mathematical modeling 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 at 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.
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Dates et versions

hal-04694148 , version 1 (11-09-2024)

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Yaqi Chen, Xianyi Zeng, Ben Niu. Equivariant Hopf Bifurcation in a Class of Partial Functional Differential Equations on a Circular Domain. International journal of bifurcation and chaos in applied sciences and engineering , 2024, Int. J. Bifurcation Chaos, 34, ⟨10.1142/S0218127424500792⟩. ⟨hal-04694148⟩

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