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Bifurcation and stability of a Mimura–Tsujikawa model with nonlocal delay effect
Authors:Dong Li  Shangjiang Guo
Affiliation:College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, China
Abstract:In this paper, we investigate a Mimura–Tsujikawa model with nonlocal delay effect under the homogeneous Neumann boundary condition. By using Lyapunov–Schmidt reduction, we investigate the existence, multiplicity, stability, and Hopf bifurcation of nontrivial steady‐state solutions bifurcating from the nonzero steady‐state solution. Moreover, we illustrate our general results by applications to models with a one‐dimensional spatial domain. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords:Mimura–  Tsujikawa model  nonlocal delay effect  steady‐state solutions  Hopf bifurcation
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