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Bifurcation and stability of a Mimura–Tsujikawa model with nonlocal delay effect
Author(s) -
Li Dong,
Guo Shangjiang
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4135
Subject(s) - mathematics , multiplicity (mathematics) , hopf bifurcation , bifurcation , neumann boundary condition , stability (learning theory) , mathematical analysis , homogeneous , domain (mathematical analysis) , boundary value problem , nonlinear system , combinatorics , physics , quantum mechanics , machine learning , computer science
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.