Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 30, Issue 9, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127420501308
Keywords
Lyapunov-Schmidt reduction; equivariant Hopf bifurcation; reaction-diffusion model; Lie group
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In this paper, we extend the equivariant Hopf bifurcation theory for semilinear functional differential equations in general Banach spaces and then apply it to reaction-diffusion models with delay effect and homogeneous Dirichlet boundary condition on a general open domain with a smooth boundary. In the process we derive the criteria for the existence and directions of branches of bifurcating periodic solutions, avoiding the process of center manifold reduction.
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