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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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Necessary condition of the Turing instability
Physical Review E, 1993A 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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TURING INSTABILITY FOR THE SCHNACKENBERG SYSTEM
Waves and Stability in Continuous Media, 2008The 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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Turing Instability of Liquid–Solid Metal Systems
Advanced Materials, 2023AbstractThe classical Turing morphogenesis often occurs in nonmetallic solution systems due to the sole competition of reaction and diffusion processes. Here, this work conceives that gallium (Ga) based liquid metals (LMs) possess the ability to alloy, diffuse, and react with a range of solid metals (SMs) and thus should display Turing instability ...
Zerong Xing +12 more
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Turing instability in reaction-subdiffusion systems
Physical Review E, 2008We determine the conditions for the occurrence of Turing instabilities in activator-inhibitor systems, where one component undergoes subdiffusion and the other normal diffusion. If the subdiffusing species has a nonlinear death rate, then coupling between the nonlinear kinetics and the memory effects of the non-Markovian transport process advances the ...
A, Yadav +2 more
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Interspecific Influence on Mobility and Turing Instability
Bulletin of Mathematical Biology, 2003In 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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Turing instability in the reaction-diffusion network
Physical Review E, 2020It 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 controlled by spatiotemporal imposed dynamics
Physical Review E, 2005The study of the spatiotemporal response of pattern forming systems to spatially resonant external forcing has unveiled striking new phenomena which challenge the understanding of self-organization in nonlinear, nonequilibrium systems. Here we show that a simple spatiotemporal two-dimensional forcing of a system supporting an intrinsic wavelength but ...
David G, Míguez +2 more
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A new necessary condition for Turing instabilities
Mathematical Biosciences, 2012Reactivity (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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Turing Instabilities and Rotating Spiral Waves in Glycolytic Processes
Bulletin of Mathematical Biology, 2022We study single-frequency oscillations and pattern formation in the glycolytic process modeled by a reduction in the well-known Sel'kov's equations (Sel'kov in Eur J Biochem 4:79, 1968), which describe, in the whole cell, the phosphofructokinase enzyme reaction. By using averaging theory, we establish the existence conditions for limit cycles and their
Luis A. Cisneros-Ake +2 more
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