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- W4300495478 abstract "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." @default.
- W4300495478 created "2022-10-03" @default.
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- W4300495478 date "2013-11-07" @default.
- W4300495478 modified "2023-09-30" @default.
- W4300495478 title "Cross-diffusion driven instability in a predator-prey system with cross-diffusion" @default.
- W4300495478 doi "https://doi.org/10.48550/arxiv.1311.1748" @default.
- W4300495478 hasPublicationYear "2013" @default.
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