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 paper we investigate the bifurcation structure of the triangular SKTmodel in the weak competition regime and of the corresponding fast-reactionsystem in 1D and 2D domains via numerical continuation methods. We show thatthe software pde2path can be adapted to treat cross-diffusion systems,reproducing the already computed bifurcation diagrams on 1D domains. We showthe convergence of the bifurcation structure obtained selecting the growth rateas bifurcation parameter. Then, we compute the bifurcation diagram on a 2Drectangular domain providing the shape of the solutions along the branches andlinking the results with the Turing instability analysis. In 1D and 2D, we payparticular attention to the fast-reaction limit by always computing sequencesof bifurcation diagrams as the time-scale separation parameter tends to zero.We show that the bifurcation diagram undergoes major deformations once thefast-reaction systems limits onto the cross-diffusion singular limit.Furthermore, we find evidence for time-periodic solutions by detecting Hopfbifurcations, we characterize several regions of multi-stability, and improveour understanding of the shape of patterns in 2D for the SKT model.

Numerical continuation for a fast-reaction system and its cross-diffusion limit