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Pattern formation of a diffusive predator‐prey model with herd behavior and nonlocal prey competition
Author(s) -
Djilali Salih
Publication year - 2020
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.6036
Subject(s) - mathematics , hopf bifurcation , bifurcation , predation , population , bifurcation theory , allee effect , transcritical bifurcation , saddle node bifurcation , competition (biology) , herd behavior , bogdanov–takens bifurcation , stability (learning theory) , mathematical analysis , nonlinear system , ecology , physics , biology , demography , quantum mechanics , sociology , geography , forestry , herding , machine learning , computer science
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.