English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this work we investigate the process of pattern formation induced bynonlinear diffusion in a reaction-diffusion system with Lotka-Volterrapredator-prey kinetics. We show that the cross-diffusion term is responsible ofthe destabilizing mechanism that leads to the emergence of spatial patterns.Near marginal stability we perform a weakly nonlinear analysis to predict theamplitude and the form of the pattern, deriving the Stuart-Landau amplitudeequations. Moreover, in a large portion of the subcritical zone, numericalsimulations show the emergence of oscillating patterns, which cannot bepredicted by the weakly nonlinear analysis. Finally when the pattern invadesthe domain as a travelling wavefront, we derive the Ginzburg-Landau amplitudeequation which is able to describe the shape and the speed of the wave.

Cross-diffusion driven instability in a predator-prey system with cross-diffusion