Existence, Stability, and Dynamics of Ring and Near-Ring Solutions to the Saturated Gierer--Meinhardt Model in the Semistrong Regime
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Publication:2967816
DOI10.1137/16M1060327zbMath1434.35017MaRDI QIDQ2967816
Michael J. Ward, Iain R. Moyles
Publication date: 2 March 2017
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Computational methods for bifurcation problems in dynamical systems (37M20) Second-order parabolic systems (35K40) Pattern formations in context of PDEs (35B36)
Related Items (8)
Dynamics of a depletion-type Gierer-Meinhardt model with Langmuir-Hinshelwood reaction scheme ⋮ The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation ⋮ Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems ⋮ Turing–Hopf Bifurcation in Diffusive Gierer–Meinhardt Model ⋮ A time-delay in the activator kinetics enhances the stability of a spike solution to the Gierer-Meinhardt model ⋮ Dihedral rings of patterns emerging from a Turing bifurcation ⋮ The explicit solution to the initial-boundary value problem of Gierer-Meinhardt model ⋮ Pattern Dynamics in a Diffusive Gierer–Meinhardt Model
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