Pattern formation of a diffusive predator‐prey model with herd behavior and nonlocal prey competition
Salih Djilali
Abstract
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.
Topics & Concepts
MathematicsHopf bifurcationBifurcationPredationPopulationBifurcation theoryAllee effectTranscritical bifurcationApplied mathematicsSaddle-node bifurcationCompetition (biology)Herd behaviorBogdanov–Takens bifurcationStability (learning theory)Mathematical analysisNonlinear systemEcologyPhysicsBiologyComputer scienceHerdingDemographySociologyGeographyForestryQuantum mechanicsMachine learningMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Dynamics and Pattern FormationMathematical Biology Tumor Growth