Results 71 to 80 of about 8,750 (185)

Generic spatiotemporal dynamics near codimension-two Turing-Hopf bifurcations

Physical Review E, 1997
The coupling of spatial and temporal symmetry breaking instabilities is studied in a two-variable reaction-diffusion model describing semiconductor transport. A variety of spatiotemporal patterns corresponding to pure Hopf and Turing modes, localized patterns, and mixed Turing-Hopf modes including subharmonic spatiotemporal spiking are found.
Meixner, Matthias, De Wit, Anne, Bose, S., Schöll, Eckehard   +3 more
openaire   +2 more sources

Dynamic complexity in a modified Leslie-Gower model with taxis mechanism and digestion delay

AIMS Mathematics
In this paper, we investigate the complex spatiotemporal dynamics of a modified Leslie-Gower model with taxis mechanism and digestion delay. First, the boundedness of solutions and the global stability of the positive equilibrium point without digestion ...
Yan Meng, Jiaxin Xiao, Caijuan Jia
doaj   +1 more source

Surviving the winds through pattern formation: Mathematical modelling of heather stripes in Scotland

Journal of Ecology, Volume 113, Issue 12, Page 3510-3521, December 2025.
Heather (Calluna vulgaris) and bare soil sometimes form striking patterns in Scottish windy environments. Our simple mathematical model shows that interactions between vegetation, soil and wind—particularly local erosion reduction by plants and upwind shelter of plants by microtopography—are sufficient to generate these self‐organised patterns and ...
Toyo Vignal, Mara Baudena, Jonathan Sherratt, Angeles G. Mayor   +3 more
wiley   +1 more source

Pattern Formation Mechanisms of Spatiotemporally Discrete Activator–Inhibitor Model with Self- and Cross-Diffusions

Fractal and Fractional
In this paper, we aim to solve the issue of pattern formation mechanisms in a spatiotemporally discrete activator–inhibitor model that incorporates self- and cross-diffusions.
You Li, Ying Sun, Jingyu Luo, Jiayi Pang, Bingjie Liu   +4 more
doaj   +1 more source

Steady-state bifurcation of FHN-type oscillator on a square domain

Nonlinear Analysis, 2023
The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations.
Chunrui Zhang, Xiaoxiao Liu, Baodong Zheng   +2 more
doaj   +1 more source

Aperiodic Clustered and Periodic Hexagonal Vegetation Spot Arrays Explained by Inhomogeneous Environments and Climate Trends in Arid Ecosystems

Geophysical Research Letters, Volume 52, Issue 21, 16 November 2025.
Abstract Due to climate change, overgrazing, and deforestation, arid ecosystems are vulnerable to desertification and land degradation. As aridity increases, vegetation cover loses spatial homogeneity and self‐organizes into heterogeneous vegetation patterns, a step before a catastrophic shift to bare soil.
David Pinto‐Ramos, Marcel Gabriel Clerc, Abdelkader Makhoute, Mustapha Tlidi   +3 more
wiley   +1 more source

The spatial dynamics of a zebrafish model with cross-diffusions

Mathematical Biosciences and Engineering, 2017
This paper investigates the spatial dynamics of a zebrafish model with cross-diffusions. Sufficient conditions for Hopf bifurcation and Turing bifurcation are obtained by analyzing the associated characteristic equation.
Hongyong Zhao, Qianjin Zhang, Linhe Zhu
doaj   +1 more source

Mesa-type patterns in the one-dimensional Brusselator and their stability

, 2005
The Brusselator is a generic reaction-diffusion model for a tri-molecular chemical reaction. We consider the case when the input and output reactions are slow.
Alikakos, Alikakos, Auchmuty, Bard, Berestycki, Chakravarti, Chen, De Wit, De Wit, De Wit, Doelman, Doelman, Erneux, Erneux, Goldstein, Iron, J. Wei, Muratov, Muratov, Muratov, Nicolis, Nishiura, Nishiura, Nishiura, Nishiura, Nishiura, Osipov, Peña, Prigogine, Ren, Reyna, Sun, T. Erneux, T. Kolokolnikov, Turing, Tyson, Ward, Yang, Yu   +38 more
core   +1 more source

Reactor Design for Chemical Reaction‐Diffusion Systems

ChemSystemsChem, Volume 7, Issue 6, November 2025.
This review discusses methods for the design of reactors for studying reaction‐diffusion (RD) phenomena. Abstract The experimental study of reaction–diffusion‐driven chemical and biological systems is a key to understanding pattern formation in nature. Starting from experiments performed in a Petri dish or test tube, various reactors have been designed
Brigitta Dúzs, István Lagzi, István Szalai   +2 more
wiley   +1 more source

Numerical bifurcation analysis of a 3D turing-type reaction–diffusion model [PDF]

Communications in Nonlinear Science and Numerical Simulation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Song, Weiyan, Wubs, Fred W., Thies, Jonas, Baars, Sven   +3 more
openaire   +5 more sources