Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical

DOI10.1088/1361-6544/abcb09zbMath1456.35013OpenAlexW3122531860MaRDI QIDQ5147942

Michael J. Ward, Frédéric Paquin-Lefebvre, Theodore Kolokolnikov

Publication date: 29 January 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/abcb09

zbMATH Keywords

amplitude equationweakly nonlinear theoryinteracting localized spikessubcritcal instabilitysymmetric two-boundary spike equilibria

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Developmental biology, pattern formation (92C15) Bifurcations in context of PDEs (35B32) Pattern formations in context of PDEs (35B36)

Related Items (4)

Continuation and bifurcation in nonlinear PDEs - algorithms, applications, and experiments ⋮ Oscillatory translational instabilities of spot patterns in the Schnakenberg system on general 2D domains ⋮ Steady state solutions for the Gierer-Meinhardt system in the whole space ⋮ A ring of spikes in a Schnakenberg model

Uses Software

• COCO

Cites Work

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