We use equivariant bifurcation theory to investigate pattern selection at the onset of a Turing instability in a general two-component reaction–diffusion system. The analysis is restricted to patterns that periodically tile the plane in either a square or hexagonal fashion. Both simple periodic ...
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 ...
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 ...
Reaction-Diffusion SystemBoundary ConditionsSystem Parametershalf a century ago a reaction-diffusion system of two chemicals was introduced by alan turing to account for morphogenesis, i.e., the development of patterns, shapes and structures found in nature. here we will discuss the formation of ...
Mathematically this is equivalent to Turing’s reaction-diffusion system that was first proposed for chemical patterns. Stripe patterns. Credit: Hermes Gadêlha In the case of sperm swimming, chemical reactions of molecular motors power the flagellum, and bending movement diffuses along t...
Mathematical analysis of the equations provides explanation for the phenomenon postulated by Turing, for details see [33,39]. The mechanism is related to a local behavior of solutions of a reaction-diffusion system in the neighborhood of a constant stationary solution that is destabilized through di...
the effect of external influence on Turing pattern formation in coupled systems, we employ two-layer-coupled reaction-diffusion system whose kinetic terms are determined by the modified Lengyel–Epstein model [16], [17] for the photosensitive chlorine dioxide-iodine-malonic acid (CDIMA) reaction. ...
be seen as a single-domain model with a step function heterogeneity, which has been studied extensively as an example of spatially heterogeneous reaction–diffusion systems (Benson et al.1998; Page et al.2003; Kozák et al.2019). Nonetheless, pattern formation in the system above, as well as...
Reaction-diffusion systemPattern formationElectric fieldDifferential mobilityWe report a general formula for the critical electric field required to trigger a pattern formation in a Turing system in the presence of an electric field (drift term). Our result encompasses all situations from pure diffusion...
In particular, it is shown that Turing instability of the reaction–diffusion system can disappear due to the presence of the cross-diffusion, which implies that the cross-diffusion induced stability can be regarded as the cross-stability of the corresponding reaction–diffusion system. Furthermore,...