Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain
From MaRDI portal
Publication:5885657
DOI10.4208/nmtma.OA-2022-0003sMaRDI QIDQ5885657
Wei, Juncheng, Daniel Gómez, Wen Yang
Publication date: 4 April 2023
Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.00569
Singular perturbations in context of PDEs (35B25) Bifurcations in context of PDEs (35B32) Fractional partial differential equations (35R11) Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) (60K50)
Related Items (3)
Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system ⋮ Spike solutions to the supercritical fractional Gierer-Meinhardt system ⋮ Unnamed Item
Cites Work
- Unnamed Item
- Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
- 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
- On the Gierer-Meinhardt system with precursors
- Existence, classification and stability analysis of multiple-peaked solutions for the Gierer-Meinhardt system in \(\mathbb R^1\)
- On the interior spike layer solutions to a singularly perturbed Neumann problem
- Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model
- Spikes for the two-dimensional Gierer-Meinhardt system: the weak coupling case
- Mathematical biology. Vol. 2: Spatial models and biomedical applications.
- Spikes for the Gierer-Meinhardt system in two dimensions: the strong coupling case
- Multi-bump ground states of the fractional Gierer-Meinhardt system on the real line
- Multiple interior peak solutions for some singularly perturbed Neumann problems.
- On stability and Hopf bifurcations for chemotaxis systems
- Implicit-explicit methods for reaction-diffusion problems in pattern formation
- Multiple boundary peak solutions for some singularly perturbed Neumann problems
- What is the fractional Laplacian? A comparative review with new results
- Stochastic processes in cell biology
- Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain
- The Stability and Dynamics of Localized Spot Patterns in the Two-Dimensional Gray–Scott Model
- Turing Pattern Formation in the Brusselator Model with Superdiffusion
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- Asymmetric spike patterns for the one-dimensional Gierer–Meinhardt model: equilibria and stability
- Spike‐Type Solutions to One Dimensional Gierer–Meinhardt Model with Lévy Flights
- An Asymptotic Analysis of Localized Three-Dimensional Spot Patterns for the Gierer--Meinhardt Model: Existence, Linear Stability, and Slow Dynamics
- The Linear Stability of Symmetric Spike Patterns for a Bulk-Membrane Coupled Gierer--Meinhardt Model
- Stable asymmetric spike equilibria for the Gierer–Meinhardt model with a precursor field
- The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
This page was built for publication: Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain