Results 141 to 150 of about 2,019 (179)

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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Necessary condition of the Turing instability

Physical Review E, 1993
A reaction-diffusion system in any number of spatial variables consisting of an arbitrary number of chemical species cannot exhibit Turing instability if none of the reaction steps expresses cross inhibition. A corollary of this result underlines the importance of nonlinearity in the formation of stationary spatial structures, a kind of self ...
, Szili, , Tóth
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Switching-induced Turing instability

Physical Review E, 2002
We propose a mechanism for inducing a Turing instability in systems whose only stable state is pattern-free and homogeneous. Global alternation between two dynamics, each of which has the same homogeneous stable state, may induce a Turing instability that leads to pattern formation. We determine what kind of alternation can drive the system to a Turing
J, Buceta, Katja, Lindenberg
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Turing instability in the reaction-diffusion network

Physical Review E, 2020
It is an established fact that a positive wave number plays an essential role in Turing instability. However, the impact of a negative wave number on Turing instability remains unclear. Here, we investigate the effect of the weights and nodes on Turing instability in the FitzHugh-Nagumo model, and theoretical results reveal genesis of Turing ...
Qianqian Zheng, Jianwei Shen, Yong Xu
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TURING INSTABILITY FOR THE SCHNACKENBERG SYSTEM

Waves and Stability in Continuous Media, 2008
The linear stability-instability of the equilibrium state of the Schnackemberg system is studied. The onset of Turing instability is obtained.
GENTILE, MAURIZIO, TATARANNI, ASSUNTA
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Interspecific Influence on Mobility and Turing Instability

Bulletin of Mathematical Biology, 2003
In this paper we formulate a multi-patch multi-species model in which the per-capita emigration rate of one species depends on the density of some other species. We then focus on Turing instability to examine if and when this cross-emigration response has crucial effects. We find that the type of interaction matters greatly.
Huang, Y., Diekmann, O.
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On the origin of Turing instability

Journal of Mathematical Chemistry, 1997
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Szili, L., Tóth, J.
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Potential Turing instability and application to plant–insect models

Mathematical and Computer Modelling, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fabio Della Rossa, Sérgio Rinaldi
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Linear Instability, Turing Instability and Pattern Formation

Lecture Notes on Mathematical Modelling in the Life Sciences, 2015
This chapter treats of one of the most fundamental observation for biological systems: the Turing instability mechanism. In his seminal paper, A. Turing suggests that a system of chemical substances reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis, that is boundary formation. Surprisingly,
Benoit Perthame, Perthame Benoit
exaly   +2 more sources

A new necessary condition for Turing instabilities

Mathematical Biosciences, 2012
Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition.
Elragig, Aiman, Townley, Stuart
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