Delay‐included Turing‐Hopf bifurcation in the diffusive mussel‐algae model

In this paper, the main content is the consideration of the dynamics of a diffusive mussel‐algae model with delay subject to Neumann boundary condition. We will analyze the corresponding characteristic equation and study the existence of delay‐induced Hopf bifurcation and steady state bifurcation. W...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 44; no. 11; pp. 8638 - 8647
Main Author Jiang, Heping
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 30.07.2021
Subjects
Algae
Bifurcation theory
Boundary conditions
Canonical forms
Delay
Eigenvalues
Eigenvectors
Hopf bifurcation
Mathematical models
mussel‐algae model
Turing‐Hopf bifurcation
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Summary:In this paper, the main content is the consideration of the dynamics of a diffusive mussel‐algae model with delay subject to Neumann boundary condition. We will analyze the corresponding characteristic equation and study the existence of delay‐induced Hopf bifurcation and steady state bifurcation. What's more, according to the results of Song et al. we calculated the normal form on the center mainfold and obtained the formulae of the delay‐induced Turing‐Hopf bifurcation, and we also investigate the dynamical behaviors near the Turing‐Hopf bifurcation point. Finally, in order to illustrate and extend our theoretical results, some exact numerical simulations are given out as the authentication.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7290