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On the origin of Turing instability
Journal of Mathematical Chemistry, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Szili, L., Tóth, J.
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Linear Instability, Turing Instability and Pattern Formation
Lecture Notes on Mathematical Modelling in the Life Sciences, 2015This 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
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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 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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Analysis of Turing Instability for Biological Models
2014Reaction-diffusion equations are often used to model biological phenomena. This type of system can produce stable spatial patterns from an uniform initial distribution. This phenomenon is known as Turing instability. This paper presents an analysis of the Turing instability for three biological models: a) Schnakenberg model, b) glycolysis model and c ...
Daiana Rodrigues +3 more
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Turing Instability and Hopf Bifurcation in Cellular Neural Networks
International Journal of Bifurcation and Chaos, 2021In 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 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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On Turing Instability in Nonhomogeneous Reaction-Diffusion CNN’s
IEEE Transactions on Circuits and Systems I: Regular Papers, 2017Several results on instability in nonhomogeneous architectures able to generate Turing patterns are presented. The approach makes use of the continuity theorem regarding the dependence of polynomial roots on coefficients and of the root-locus techniques for small, and large parameter deviations from their homogeneous values, respectively.
Liviu Goras +2 more
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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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Dynamics of pattern formation in the Turing optical instability
Physical Review A, 1989The transient dynamical evolution of spatial pattern formation in a nonlinear passive optical system in a Fabry-P\'erot cavity driven by an external coherent field is studied. The associated decay of the unstable homogeneous state of the system is described analytically, with the inclusion of noise effects, in terms of a stochastic amplitude equation ...
, Aguado, , Rodrguez, , San Miguel M
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