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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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Turing Instabilities in Homogeneous Systems
2010Alan Turing’s paper entitled “The Chemical Basis of Morphogenesis” [440] ranks without doubt among the most important papers of the last century. In that seminal work Turing laid the foundation for the theory of chemical pattern formation. Turing showed that diffusion can have nontrivial effects in nonequilibrium systems.
Vicenç Méndez +2 more
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Turing instability in pioneer/climax species interactions
Mathematical Biosciences, 2005Systems of pioneer and climax species are used to model interactions of species whose reproductive capacity is sensitive to population density in their shared ecosystem. Intraspecies interaction coefficients can be adjusted so that spatially homogeneous solutions are stable to small perturbations.
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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
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,
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Delay-induced Turing instability in reaction-diffusion equations
Physical Review E, 2014Time delays have been commonly used in modeling biological systems and can significantly change the dynamics of these systems. Quite a few works have been focused on analyzing the effect of small delays on the pattern formation of biological systems. In this paper, we investigate the effect of any delay on the formation of Turing patterns of reaction ...
Zhang, Tonghua, Zang, Hong
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Chemical Turing Patterns and Diffusive Instabilities
2017The Brusselator activator-inhibitor reaction-diffusion model is considered and conditions deduced by a normal-mode linear stability analysis for the development of chemical Turing instabilities over a parameter range for which the dynamical system in the absence of diffusion would exhibit a stable homogeneous distribution.
David J. Wollkind, Bonni J. Dichone
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Turing instabilities with nearly equal diffusion coefficients
The Journal of Chemical Physics, 1989We show that if a Turing instability occurs in a reaction–diffusion system with a nearly scalar diffusion matrix, then the parameters of the corresponding well-mixed system are necessarily such that the well-mixed system has at least two eigenvalues near zero.
John E. Pearson, Werner Horsthemke
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