Results 181 to 189 of about 32,448 (189)

Turing instability in a general system

Nonlinear Analysis: Theory, Methods & Applications, 2013
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Hoang, T, Hwang, HJ
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Turing Instabilities in Homogeneous Systems

2010
Alan 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, Sergei Fedotov, Werner Horsthemke   +2 more
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Turing instability in pioneer/climax species interactions

Mathematical Biosciences, 2005
Systems 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, 1997
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Szili, L., Tóth, J.
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Linear Instability, Turing Instability and Pattern Formation

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,
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Delay-induced Turing instability in reaction-diffusion equations

Physical Review E, 2014
Time 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

2017
The 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, 1989
We 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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An instability framework of Hopf–Turing–Turing singularity in 2-component reaction–diffusion systems

Japan Journal of Industrial and Applied Mathematics
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Hirofumi Izuhara, Shunusuke Kobayashi
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