Results 141 to 150 of about 970 (177)
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Turing–Hopf Bifurcation in Diffusive Gierer–Meinhardt Model
International Journal of Bifurcation and Chaos, 2022Gierer–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–Hopf Bifurcation Analysis of the Sel’kov–Schnakenberg System
International Journal of Bifurcation and Chaos, 2023In 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
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Turing Instabilities at Hopf Bifurcation
Journal of Nonlinear Science, 2009A 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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Spatiotemporal patterns induced by Turing and Turing-Hopf bifurcations in a predator-prey system
Applied Mathematics and Computation, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mengxin Chen, Ranchao Wu, Liping Chen
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Turing and Turing–Hopf Bifurcations for a Reaction Diffusion Equation with Nonlocal Advection
Journal of Nonlinear Science, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arnaud Ducrot +2 more
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Interaction of Turing and Hopf bifurcations in chemical systems
Physical Review A, 1992When 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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Turing Bifurcations and Pattern Selection
1995Pattern 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 +3 more
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A Turing–Hopf Bifurcation Scenario for Pattern Formation on Growing Domains
Bulletin of Mathematical Biology, 2016In this paper, we study the emergence of different patterns that are formed on both static and growing domains and their bifurcation structure. One of these is the so-called Turing-Hopf morphogenetic mechanism. The reactive part we consider is of FitzHugh-Nagumo type.
Castillo, Jorge A. +2 more
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BIFURCATIONS IN A HUMAN MIGRATION MODEL OF SCHEURLE–SEYDEL TYPE-I: TURING BIFURCATION
International Journal of Bifurcation and Chaos, 2003In this paper we consider a model for the behavior of students in graduate programs at neighboring universities which is a modified form of the model proposed by [Scheurle & Seydel, 2000], and observe that the stationary solution of this two-component system becomes unstable in the presence of diffusion.
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Turing bifurcation in a system with cross diffusion
Nonlinear Analysis, 2004The Turing bifurcation is studied in the following reaction-diffusion systems \(\partial_t S=D\Delta S+f(S)\) of two components \(S=(S_1,S_2),\) with a non-diagonal diffusion matrix \(D\) and the Neumann boundary condition, and with a nonlinearity \(f\) which ensures that the corresponding kinetic system has linearly stable solutions.
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