6533b823fe1ef96bd127e2aa
RESEARCH PRODUCT
Pattern formation driven by cross–diffusion in a 2D domain
Maria Carmela LombardoMarco SammartinoGaetana Gambinosubject
Pattern formationFOS: Physical sciencesSaddle-node bifurcationPattern Formation and Solitons (nlin.PS)Dynamical Systems (math.DS)Bifurcation diagramDomain (mathematical analysis)Reaction–diffusion systemFOS: MathematicsMathematics - Dynamical SystemsBifurcationMathematical PhysicsMathematicsApplied MathematicsNonlinear diffusionTuring instabilityDegenerate energy levelsMathematical analysisGeneral EngineeringGeneral MedicineMathematical Physics (math-ph)Nonlinear Sciences - Pattern Formation and SolitonsBiological applications of bifurcation theoryComputational MathematicsAmplitude equationGeneral Economics Econometrics and FinanceSubcritical bifurcationAnalysisdescription
Abstract In this work we investigate the process of pattern formation in a two dimensional domain for a reaction–diffusion system with nonlinear diffusion terms and the competitive Lotka–Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, and hexagonal patterns.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-11-19 |