Explicitly solvable eigenvalue problem and bifurcation delay in sub-diffusive Gierer–Meinhardt model

DOI10.1017/S0956792516000012zbMath1387.35332OpenAlexW2519758744MaRDI QIDQ4594608

Yana Nec

Publication date: 24 November 2017

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0956792516000012

zbMATH Keywords

reaction-diffusionbifurcation delayspike solutionsub-diffusionnon-local eigenvalue problem

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Initial value problems for second-order parabolic systems (35K45) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (5)

Dynamics of pulse solutions in Gierer-Meinhardt model with time dependent diffusivity ⋮ Hopf Bifurcation Analysis in a Gierer–Meinhardt Activator–Inhibitor Model ⋮ Turing Patterns in the Lengyel–Epstein System with Superdiffusion ⋮ Analysis of the Hopf bifurcation in a diffusive Gierer-Meinhardt model ⋮ Pattern Dynamics in a Diffusive Gierer–Meinhardt Model

Cites Work

• Unnamed Item
• Unnamed Item
• Mathematical aspects of pattern formation in biological systems
• Dynamics and stability of spike-type solutions to a one dimensional Gierer-Meinhardt model with sub-diffusion
• Anomalous is ubiquitous
• Anomalous diffusion modeling by fractal and fractional derivatives
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model
• Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems
• Large stable pulse solutions in reaction-diffusion equations
• Random Walks on Lattices. II
• On single interior spike solutions of the Gierer–Meinhardt system: uniqueness and spectrum estimates
• An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals
• An Explicitly Solvable Nonlocal Eigenvalue Problem and the Stability of a Spike for a Sub-Diffusive Reaction-Diffusion System
• DISTRIBUTED ORDER FRACTIONAL SUB-DIFFUSION
• The stability of spike solutions to the one-dimensional Gierer-Meinhardt model

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