Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 26, Issue 2, Pages 545-580Publisher
SPRINGER
DOI: 10.1007/s00332-016-9285-x
Keywords
Reaction-diffusion; Lyapunov-Schmidt reduction; Normal form; Center manifold; Hopf bifurcation; Stability
Categories
Funding
- Natural Science Foundation of China [11271115]
- Ministry of Education of China [20120161110018]
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In this paper, we study the dynamics of a diffusive equation with time delay subject to Dirichlet boundary condition in a bounded domain. The existence of spatially nonhomogeneous steady-state solution is investigated by applying Lyapunov-Schmidt reduction. The existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues. The direction of Hopf bifurcation and stability of the bifurcating periodic solution are also investigated by means of normal form theory and center manifold reduction. Moreover, we illustrate our general results by applications to the Nicholson's blowflies models with one- dimensional spatial domain.
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