Results 81 to 90 of about 213 (131)

Turing Bifurcation in the Swift–Hohenberg Equation on Deterministic and Random Graphs

Journal of Nonlinear Science
AbstractThe Swift–Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger and Holzer (SIAM J Math Anal 55(3):2150–2185, 2023), we consider discrete SHE on deterministic and random ...
Georgi S. Medvedev, Dmitry E. Pelinovsky
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Spatiotemporal pattern formation in a three-variable CO oxidation reaction model

Condensed Matter Physics, 2018
The spatiotemporal pattern formation is studied in the catalytic carbon monoxide oxidation reaction that takes into account the diffusion processes over the Pt(110) surface, which may contain structurally different areas. These areas are formed during CO-
I.S. Bzovska, I.M. Mryglod
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Turing conditions for a two-component isotropic growing system from a potential function

Results in Applied Mathematics
We analyze pattern formation in a two-component system within an isotropically growing or shrinking domain. By studying the evolution of a Lyapunov-like function, we derive time-dependent Turing bifurcation conditions through a stability analysis of ...
Aldo Ledesma-Durán, Consuelo García-Alcántara, Iván Santamaría-Holek   +2 more
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Turing–Turing Bifurcation and Normal Form in a Predator–Prey Model with Predator-Taxis and Prey Refuge

International Journal of Bifurcation and Chaos
This paper investigates a predator–prey reaction–diffusion model incorporating predator-taxis and a prey refuge mechanism, subject to homogeneous Neumann boundary conditions. Our primary focus is the analysis of codimension-2 Turing–Turing bifurcation and the calculation of its associated normal form for this model.
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Turing and Hopf bifurcation of Gierer-Meinhardt activator-substrate model

Electronic Journal of Differential Equations, 2017
Gierer-Meinhardt model acts as one of prototypical reaction diffusion systems describing pattern formation phenomena in natural events. Bifurcation analysis, including theoretical and numerical analysis, is carried out on the Gierer-Meinhardt ...
Ranchao Wu, Yan Shao, Yue Zhou, Liping Chen   +3 more
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Stability of Turing bifurcation in a weighted networked reaction–diffusion system

Applied Mathematics Letters, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jia Liu, Jing Chen, Canrong Tian
exaly   +4 more sources

Turing–Hopf bifurcation in the reaction–diffusion equations and its applications

Communications in Nonlinear Science and Numerical Simulation, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yongli Song, Tonghua Zhang, Yahong Peng   +2 more
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Turing bifurcation in a diffusive predator–prey model with schooling behavior

Applied Mathematics Letters, 2019
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Heping Jiang
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Turing-Turing bifurcation and multi-stable patterns in a Gierer-Meinhardt system

Applied Mathematical Modelling, 2022
Hongbin Wang
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Normal Form Formulae of Turing–Turing Bifurcation for Partial Functional Differential Equations With Nonlinear Diffusion

Mathematical Methods in the Applied Sciences
ABSTRACTFor most systems, the appearance of Turing bifurcation means that it is possible to excite Turing–Turing bifurcation, thus inducing superimposed spatial patterns, multistable spatial patterns co‐existing, and others.It is undoubtedly of interest to qualitatively analyze the structures and stability of these spatially heterogeneous solutions ...
Weihua Jiang
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