2013/11/07 by Eleonora Tulumello, Tulumello, Eleonora, Lombardo, Maria Carmela +3 · 1 citation
Computer Science · Mathematics · Medicine · #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1311.1748
openalex publication_date 2013/11/07 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this work we investigate the process of pattern formation induced by\nnonlinear diffusion in a reaction-diffusion system with Lotka-Volterra\npredator-prey kinetics. We show that the cross-diffusion term is responsible of\nthe destabilizing mechanism that leads to the emergence of spatial patterns.\nNear marginal stability we perform a weakly nonlinear analysis to predict the\namplitude and the form of the pattern, deriving the Stuart-Landau amplitude\nequations. Moreover, in a large portion of the subcritical zone, numerical\nsimulations show the emergence of oscillating patterns, which cannot be\npredicted by the weakly nonlinear analysis. Finally when the pattern invades\nthe domain as a travelling wavefront, we derive the Ginzburg-Landau amplitude\nequation which is able to describe the shape and the speed of the wave.\n