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Turing‐Turing and Turing‐Hopf bifurcations in a general diffusive Brusselator model
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2023AbstractA general reaction‐diffusion Brusselator model subject to homogeneous Neumann boundary conditions is investigated in this paper. First, the stability of the unique positive equilibrium is studied, and we identify the existence of the Hopf bifurcation.
Chen, Mengxin +3 more
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Turing on Super-Turing and adaptivity
Progress in Biophysics and Molecular Biology, 2013Biological processes are often compared to computation and modeled on the Universal Turing Machine. While many systems or aspects of systems can be well described in this manner, Turing computation can only compute what it has been programmed for. It has no ability to learn or adapt to new situations.
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estetica. studi e ricerche, 2022
Analisi ed applicazione all'arte digitale della nozione di morfogenesi elaborata da Alan Turing.
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Analisi ed applicazione all'arte digitale della nozione di morfogenesi elaborata da Alan Turing.
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Science, 2012
In his Perspective “Beyond Turing's machines” (13 April, p. [163][1]), A. Hodges claims that in 1945 Turing “used his wartime technological knowledge to design a first digital computer.” He also suggests that Turing's work of 1936 laid the foundation for encoding “all known processes,” going “far beyond the vision of others at the time.” These ...
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In his Perspective “Beyond Turing's machines” (13 April, p. [163][1]), A. Hodges claims that in 1945 Turing “used his wartime technological knowledge to design a first digital computer.” He also suggests that Turing's work of 1936 laid the foundation for encoding “all known processes,” going “far beyond the vision of others at the time.” These ...
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The Journal of Chemical Physics, 2014
Formation of Turing patterns of nanoscopic length scale is simulated using molecular dynamics. Based on Fourier spectra of the concentrations of species, we compare stabilities of the structures of different wavelengths and for different intermolecular potentials. Long range attraction is shown to oppose the formation of structures.
Piotr, Dziekan +2 more
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Formation of Turing patterns of nanoscopic length scale is simulated using molecular dynamics. Based on Fourier spectra of the concentrations of species, we compare stabilities of the structures of different wavelengths and for different intermolecular potentials. Long range attraction is shown to oppose the formation of structures.
Piotr, Dziekan +2 more
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Transcending Turing Computability
Minds and Machines, 2003Summary: It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing-machine computation; proofs have been offered on both sides, subject to differing assumptions. In this article I argue that the important comparisons between the two models of computation are not so much mathematical as ...
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Localized Turing and Turing-Hopf Patterns
1995In systems driven away from thermodynamic equilibrium, patchiness often arises through the occurrence of symmetry breaking bifurcations. Diffusive instabilities resulting from differential diffusion processes acting in the presence of some autocatalytic kinetic scheme enter that class of phenomena to produce stationary space periodic (Turing) or ...
Borckmans, Pierre +5 more
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Turing reducibility and Turing degrees
2018A reducibility is a relation of comparative computational complexity (which can be made precise in various non-equivalent ways) between mathematical objects of appropriate sorts. Much of recursion theory concerns such relations, initially between sets of natural numbers (in so-called classical recursion theory), but later between sets of other sorts ...
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