Results 161 to 170 of about 8,745 (203)

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
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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
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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, Xin Wei
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Turing Instabilities at Hopf Bifurcation

Journal of Nonlinear Science, 2009
A simple procedure for deriving a uniform asymptotic expansion for the limit cycle in the vicinity of the Hopf bifurcation point for a two dimensional reaction system \[ u_{t} =D_{u}\Delta u+f\left( u,v;a\right) , \] \[ v_{t} =D_{v}\Delta v+g\left( u,v;a\right) \tag{b} \] is suggested. First, an algorithm allowing reduction of the system (ref {b}) to a
Ricard, M.R., Mischler, Stéphane
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Turing and Turing–Hopf Bifurcations for a Reaction Diffusion Equation with Nonlocal Advection

Journal of Nonlinear Science, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ducrot, Arnaud, Fu, Xiaoming, Magal, Pierre   +2 more
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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
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Transition from Amplitude to Oscillation Death via Turing Bifurcation

Physical Review Letters, 2013
Coupled oscillators are shown to experience two structurally different oscillation quenching types: amplitude death (AD) and oscillation death (OD). We demonstrate that both AD and OD can occur in one system and find that the transition between them underlies a classical, Turing-type bifurcation, providing a clear classification of these significantly ...
Koseska, A., Volkov, E., Kurths, J.
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Turing Bifurcations and Pattern Selection

1995
Pattern forming instabilities in spatially extended dissipative systems driven away from equilibrium have been the focus of a large activity for many years. The goal of this chapter is to present some theoretical concepts that have been developed to understand and describe these dissipative structures [1] from a macroscopic point of view.
Borckmans, Pierre, Dewel, Guy, De Wit, Anne, Walgraef, Daniel   +3 more
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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.
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Spatiotemporal patterns induced by Turing and Turing-Hopf bifurcations in a predator-prey system

Applied Mathematics and Computation, 2020
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Chen, Mengxin, Wu, Ranchao, Chen, Liping
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