Results 11 to 20 of about 2,033 (212)
Turing pattern outside of the Turing domain
Applied Mathematics Letters, 2007 There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter mu gives rise to a 'space-invariant' solution, and mu versus the ratio of the diffusion coefficients gives rise to a 'time-invariant' solution.
E. H. Flach +2 more
openaire +6 more sources
Physical Review Letters, 1993 Turing patterns involve regions of different chemical compositions which lead to density gradients that, in liquids, are potentially unstable hydrodynamically. Nonlinear hydrodynamics coupled with a model of Turing pattern formation show that convection modifies and coexists with some Turing patterns and excludes others, and thereby plays a significant
Vasquez, D. A. +2 more
openaire +5 more sources
Pattern formation (II): The Turing Instability [PDF]
Proceedings of the American Mathematical Society, 2007 We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the finite number of linear growing modes over a time scale of
Guo, Y, Hwang, HJ
openaire +4 more sources
Turing pattern dynamics in a fractional-diffusion oregonator model under PD control
Nonlinear AnalysisIn this paper, fractional-order diffusion and proportional-derivative (PD) control are introduced in oregonator model, and the Turing pattern dynamics is investigated for the first time.
Hongliang Li +4 more
doaj +3 more sources
A non-linear analysis of Turing pattern formation.
PLoS ONE, 2019 Reaction-diffusion schemes are widely used to model and interpret phenomena in various fields. In that context, phenomena driven by Turing instabilities are particularly relevant to describe patterning in a number of biological processes.
Yanyan Chen, Javier Buceta
doaj +2 more sources
Turing and Non-Turing patterns in diffusive plankton model
Computational Ecology and Software, 2015 In this paper, we investigate a Rosenzweig-McAurthur model and its variant for phytoplankton, zooplankton and fish population dynamics with Holling type II and III functional responses. We present the theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with
N. K. Thakur, R. Gupta, R. K. Upadhyay
openaire +2 more sources
The Turing Model for Biological Pattern Formation [PDF]
, 2019 How spatial patterning arises in biological systems is still an unresolved mystery. Here, we consider the first model for spatial pattern formation, proposed by Alan Turing, which showed that structure could emerge from processes that, in themselves, are non-patterning.
Maini, Philip K., Woolley, Thomas
openaire +3 more sources
Bifurcations and Turing patterns in a diffusive Gierer–Meinhardt model
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, the Hopf bifurcations and Turing bifurcations of the Gierer–Meinhardt activator-inhibitor model are studied. The very interesting and complex spatially periodic solutions and patterns induced by bifurcations are analyzed from both ...
Yong Wang, Mengping Guo, Weihua Jiang
doaj +1 more source
Hyperbolic Chaos of Turing Patterns [PDF]
Physical Review Letters, 2012 We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as 1:3 emerge in succession.
Kuptsov, Pavel V. +2 more
openaire +3 more sources
Turing pattern with proportion preservation [PDF]
Journal of Theoretical Biology, 2006 Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the proportionality of the pattern, i.e., the ratio of the wavelength to the size, that is often required in biological ...
Ishihara, Shuji, Kaneko, Kunihiko
openaire +4 more sources