Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 43, Issue 5, Pages 2233-2250Publisher
WILEY
DOI: 10.1002/mma.6036
Keywords
general biology and biomathematics; herd behavior; nonlocal competition; pattern formation; predator-prey model; Turing-Hopf bifurcation
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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 undergoesHopf 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.
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