We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis andnumerical simulations.Simple Turing patterns and complex superlattice structures are observed.We find that the shapeand type of Turing patterns depend on dynamical parameters and external periodic forcing,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars Speaker: 梅林锋 副教授, 浙江师范大学 Inviter: Title: Hopf bifurcation from spike solutions for some Turing reaction diffusion systems Time & Venue: 2021.11.13 10:00-11:00 腾讯会议:273 279 347 Abstract: Turing systems are ...
#艾伦·图灵(Alan Turing)1952年发表的论文《形态发生的化学基础》(The Chemical Basis of Morphogenesis),这是一篇古老但经典的论文。在这篇论文中,图灵阐述了一个观点,即反应-扩散(react - LOOLO于20240528发布在抖音,已经收获了1.6万个喜欢,来抖音,记录美好生活!
Here we show that this regulation in Arabidopsis thaliana is achieved by an organ-autonomous Turing reaction‐diffusion system centred on mobile small RNAs. The data illustrate how Turing dynamics transiently instructed by prepatterned information is sufficient to self‐sustain properly oriented polarity ...
Moreover, according to our knowledge, this case has not been found in the reaction diffusion system in the literature. The remaining paper is organized as follows. In Section 2, we prove the existence/nonexistence of Turing/Turing–Hopf bifurcation and give the concrete range of parameter c ...
reaction-diffusion systemsself-assembly/ network organized activator-inhibitor systemTuring instabilitynonequilibrium self organizationTuring patternlarge random networklinear instabilityTuring instability in activator鈥搃nhibitor systems provides a paradigm of non-equilibrium self-organization; it has been ...
We introduce a two-species fractional reaction-diffusion system to model activator-inhibitor dynamics with anomalous diffusion such as occurs in spatially inhomogeneous media. Conditions are derived for Turing-instability induced pattern formation in these fractional activator- inhibitor systems whereby the ho...
In this paper, we investigate the effect of any delay on the formation of Turing patterns of reaction-diffusion equations. First, for a delay system in a general form, we propose a technique calculating the critical value of the time delay, above which a Turing instability occurs. Then we ...
50:17 The Phase-Field-Crystal Model at Large and Small Scales 46:13 The Manhattan Curve and Rough Similarity Rigidity 1:12:04 Recent Progress and Open Frontiers in Turing-Type Morphogenesis 50:19 Localized slow patterns in singularly perturbed 2-component reaction-diffusion e 46:51 Localised patt...
A generic Turing type reaction–diffusion system derived from the Taylor expansion near a constant equilibrium is analyzed. The existence of Hopf bifurcations and steady state bifurcations is obtained. The bifurcation direction and the stability of the bifurcating periodic obits are calculated. Numerical...