Abstract
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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This work has been supported by the Natural Science Foundation of China (Grant No. 11271115) and by the Doctoral Fund of Ministry of Education of China (Grant No. 20120161110018).
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Communicated by Sue Ann Campbell.
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Guo, S., Ma, L. Stability and Bifurcation in a Delayed Reaction–Diffusion Equation with Dirichlet Boundary Condition. J Nonlinear Sci 26, 545–580 (2016). https://doi.org/10.1007/s00332-016-9285-x
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DOI: https://doi.org/10.1007/s00332-016-9285-x