6533b823fe1ef96bd127e0bc
RESEARCH PRODUCT
Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion
Maria Carmela LombardoMarco SammartinoEleonora Tulumellosubject
WavefrontWork (thermodynamics)Partial differential equationGinzburg-Landau equationApplied MathematicsNonlinear diffusionTuring instabilityMathematical analysisFOS: Physical sciencesPattern formationPattern Formation and Solitons (nlin.PS)MechanicsNonlinear Sciences - Pattern Formation and SolitonsInstabilityNonlinear systemAmplitudeQuintic Stuart-Landau equationQuantitative Biology::Populations and EvolutionAmplitude equationSettore MAT/07 - Fisica MatematicaMarginal stabilityMathematicsdescription
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a travelling wavefront, we derive the Ginzburg-Landau amplitude equation which is able to describe the shape and the speed of the wave.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-11-07 |