Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense
Maria Francesca Carfora, Isabella Torcicollo
Abstract
In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.
Topics & Concepts
InstabilityDiffusionPredatorPopulationStability (learning theory)BifurcationTuringPredationAmplitudeMathematicsStatistical physicsControl theory (sociology)Applied mathematicsMathematical analysisPhysicsMechanicsComputer scienceBiologyNonlinear systemEcologyArtificial intelligenceDemographyThermodynamicsControl (management)Programming languageQuantum mechanicsSociologyMachine learningMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Dynamics and Pattern FormationEvolution and Genetic Dynamics