Results 161 to 170 of about 116,098 (200)

Turing bifurcation in a diffusive predator–prey model with schooling behavior

Applied Mathematics Letters, 2019
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Heping Jiang
exaly   +4 more sources

Turing-Turing bifurcation and multi-stable patterns in a Gierer-Meinhardt system

Applied Mathematical Modelling, 2022
Hongbin Wang
exaly   +2 more sources

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
exaly   +2 more sources

Unravelling the Turing bifurcation using spatially varying diffusion coefficients [PDF]

Journal of Mathematical Biology, 1998
The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry.
Philip Maini, Jonathan A Sherratt
exaly   +2 more sources

Turing‐Turing and Turing‐Hopf bifurcations in a general diffusive Brusselator model

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2023
AbstractA general reaction‐diffusion Brusselator model subject to homogeneous Neumann boundary conditions is investigated in this paper. First, the stability of the unique positive equilibrium is studied, and we identify the existence of the Hopf bifurcation.
Chen, Mengxin, Wu, Ranchao, Liu, Biao, Chen, Liping   +3 more
openaire   +2 more sources

Turing–Hopf Bifurcation in Diffusive Gierer–Meinhardt Model

International Journal of Bifurcation and Chaos, 2022
Gierer–Meinhardt system is a molecularly plausible model to describe pattern formation. When gene expression time delay is added, the behavior of the Gierer–Meinhardt model profoundly changes. In this paper, we study the delayed reaction–diffusion Gierer–Meinhardt system with Neumann boundary condition.
Rui Yang, Xiao-Qing Yu
openaire   +3 more sources

Turing Instability and Hopf Bifurcation in Cellular Neural Networks

International Journal of Bifurcation and Chaos, 2021
In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and
Zunxian Li, Chengyi Xia
openaire   +1 more source

Turing–Hopf Bifurcation Analysis of the Sel’kov–Schnakenberg System

International Journal of Bifurcation and Chaos, 2023
In this paper, we investigate the spatiotemporal dynamics of the Sel’kov–Schnakenberg system. The stability of the positive constant steady state is studied by the linear stability theory. Hopf bifurcation and Turing–Hopf bifurcation are generated by varying two parameters in the model. The normal form near the Turing–Hopf singularity is calculated to
Yuying Liu 0003, Xin Wei
openaire   +2 more sources

Interaction of Turing and Hopf bifurcations in chemical systems

Physical Review A, 1992
When a Turing bifurcation occurs close to a Hopf bifurcation in the parameter space of a reaction-diffusion system, the Turing and Hopf modes may interact nonlinearly to form, a priori, a variety of complex spatiotemporal patterns. We have studied this type of interaction for three models of chemically active media: the Lengyel-Epstein model of the ...
, Rovinsky, , Menzinger
openaire   +2 more sources

Bifurcations in a predator-prey model with memory and diffusion II: Turing bifurcation

Acta Mathematica Hungarica, 1994
[For part I see the preceding review, Zbl 0809.92017).] The stability of a positive equilibrium \(U\) \((U = (Q_ 0, P_ 0)\), \(Q_ 0 > 0\), \(P_ 0 > 0)\) of a one-dimensional reaction-diffusion system with zero-flux boundary conditions is studied under natural constraints.
Cavani, M., Farkas, M.
openaire   +2 more sources