Found 54 Documents (Results 1–54)
Existence, stability and slow dynamics of spikes in a 1D minimal Keller-Segel model with logistic growth. (English) Zbl 1542.37074
Large amplitude radially symmetric spots and gaps in a dryland ecosystem model. (English) Zbl 1526.35025
A finite difference scheme for the two-dimensional Gray-Scott equation with fractional Laplacian. (English) Zbl 07751247
MSC:
65Mxx
An effective operator splitting method based on spectral deferred correction for the fractional Gray-Scott model. (English) Zbl 07700220
Oscillatory translational instabilities of spot patterns in the Schnakenberg system on general 2D domains. (English) Zbl 1511.35018
Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system. (English) Zbl 07880323
Stability of spike solutions to the fractional Gierer-Meinhardt system in a one-dimensional domain. (English) Zbl 1524.35692
Dynamics of patchy vegetation patterns in the two-dimensional generalized Klausmeier model. (English) Zbl 1498.35057
Quorum-sensing induced transitions between bistable steady-states for a cell-bulk ODE-PDE model with lux intracellular kinetics. (English) Zbl 1483.35289
Spot patterns in the 2-D Schnakenberg model with localized heterogeneities. (English) Zbl 1467.35045
Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. (English) Zbl 1466.35024
An asymptotic analysis of localized three-dimensional spot patterns for the Gierer-Meinhardt model: existence, linear stability, and slow dynamics. (English) Zbl 1462.35031
Analysis of spot patterns on a coordinate-invariant model for vegetation on a curved terrain. (English) Zbl 1462.35039
Weakly nonlinear analysis of peanut-shaped deformations for localized spots of singularly perturbed reaction-diffusion systems. (English) Zbl 1472.35026
TT-M finite element algorithm for a two-dimensional space fractional Gray-Scott model. (English) Zbl 1451.65150
Stable and unstable periodic spiky solutions for the Gray-Scott system and the Schnakenberg system. (English) Zbl 1437.35054
Spot patterns of the Schnakenberg reaction-diffusion system on a curved torus. (English) Zbl 1430.35133
Reviewer: Dian K. Palagachev (Bari)
The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and space. (English) Zbl 1448.34096
Fractional Gray-Scott model: well-posedness, discretization, and simulations. (English) Zbl 1440.35344
Refined stability thresholds for localized spot patterns for the Brusselator model in \(\mathbb{R}^2\). (English) Zbl 1427.35107
Asymptotic formulas for extreme statistics of escape times in 1, 2 and 3-dimensions. (English) Zbl 1415.60054
J. Nonlinear Sci. 29, No. 2, 461-499 (2019); correction ibid. 30, No. 6, 3443-3444 (2020).
Generative complexity of Gray-Scott model. (English) Zbl 1510.92279
MSC:
92E20
The stability and slow dynamics of spot patterns in the 2D Brusselator model: the effect of open systems and heterogeneities. (English) Zbl 1392.35039
Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems. (English) Zbl 1393.35106
Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions. (English) Zbl 1391.35225
Rigorous computation of non-uniform patterns for the 2-dimensional Gray-Scott reaction-diffusion equation. (English) Zbl 1376.65134
Spatially periodic multipulse patterns in a generalized Klausmeier-Gray-Scott model. (English) Zbl 1369.34067
A hybrid asymptotic-numerical method for calculating drag coefficients in 2-D low Reynolds number flows. (English) Zbl 1365.76273
Existence, stability, and dynamics of ring and near-ring solutions to the saturated Gierer-Meinhardt model in the semistrong regime. (English) Zbl 1434.35017
The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. (English) Zbl 1434.35019
Localized spot patterns on the sphere for reaction-diffusion systems: theory and open problems. (English) Zbl 1357.35189
Bélair, Jacques (ed.) et al., Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7–15, 2015. Cham: Springer (ISBN 978-3-319-30377-2/hbk; 978-3-319-30379-6/ebook). 641-651 (2016).
An asymptotic analysis of a 2-D model of dynamically active compartments coupled by bulk diffusion. (English) Zbl 1439.92024
Explicitly solvable nonlocal eigenvalue problems and the stability of localized stripes in reaction-diffusion systems. (English) Zbl 1338.35246
Reviewer: Denise Huet (Nancy)
On accurately estimating stability thresholds for periodic spot patterns of reaction-diffusion systems in \(\mathbb{R}^2\). (English) Zbl 1382.35134
Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes. (English) Zbl 1374.92167
A numerical framework for singular limits of a class of reaction diffusion problems. (English) Zbl 1349.65325
Logarithmic expansions and the stability of periodic patterns of localized spots for reaction-diffusion systems in \(\mathbb R^2\). (English) Zbl 1334.35347
Reviewer: Catalin Popa (Iaşi)
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. (English) Zbl 1304.35051
The stability of localized spot patterns for the Brusselator on the sphere. (English) Zbl 1302.35033
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