Pattern formation of a diffusive predator‐prey model with herd behavior and nonlocal prey competition

In this paper, we study the influence of the nonlocal interspecific competition of the prey population on the dynamics of the diffusive predator‐prey model with prey social behavior. Using the linear stability analysis, the conditions for the positive constant steady state at which undergoes Hopf bi...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 43; no. 5; pp. 2233 - 2250
Main Author Djilali, Salih
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 30.03.2020
Subjects
Canonical forms
Competition
general biology and biomathematics
Graphical representations
herd behavior
Hopf bifurcation
nonlocal competition
pattern formation
Predator-prey simulation
predator‐prey model
Stability analysis
Turing‐Hopf bifurcation
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Summary:In this paper, we study the influence of the nonlocal interspecific competition of the prey population on the dynamics of the diffusive predator‐prey model with prey social behavior. Using the linear stability analysis, the conditions for the positive constant steady state at which undergoes Hopf bifurcation, T‐H bifurcation (Turing‐Hopf bifurcation) are investigated. The Turing patterns occur in the presence of the nonlocal competition and cannot be found in the original system. For determining the dynamical behavior near T‐H bifurcation point, the normal form of the T‐H bifurcation has been used. Some graphical representations are provided to illustrate the theoretical results.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6036