Turing Instability and Pattern Formation on Directed Networks
نویسندگان
چکیده
منابع مشابه
Pattern Formation (ii): the Turing Instability
1. Growing modes in a reaction-diffusion system In this section we summarize the classical linear Turing instability criterion for a reaction-diffusion system. Consider a reaction-diffusion system of 2-species as ∂U ∂t = ∇ · (D1 (U,V )∇U) + f (U,V ) , (1.1) ∂V ∂t = ∇ · (D2 (U,V )∇V ) + g (U,V ) , where U (x,t) ,V (x,t) are concentration for species, D1, D2 diffusion coefficients, f, g reaction ...
متن کاملPattern Formation on Networks: from Localised Activity to Turing Patterns
Networks of interactions between competing species are used to model many complex systems, such as in genetics, evolutionary biology or sociology and knowledge of the patterns of activity they can exhibit is important for understanding their behaviour. The emergence of patterns on complex networks with reaction-diffusion dynamics is studied here, where node dynamics interact via diffusion via t...
متن کاملTuring Pattern Formation without Diffusion
The reaction-diffusion mechanism, presented by AM Turing more than 60 years ago, is currently the most popular theoretical model explaining the biological pattern formation including the skin pattern. This theory suggested an unexpected possibility that the skin pattern is a kind of stationary wave (Turing pattern or reaction-diffusion pattern) made by the combination of reaction and diffusion....
متن کاملTuring Instability and Pattern Formation in a Semi-discrete Brusselator Model
In this paper, a semi-discrete Brusselator system is considered. The Turing instability theory analysis will be given for the model, then Turing instability conditions can be deduced combining linearization method and inner product technique. A series of numerical simulations of the system are performed in the Turing instability region, various patterns such as square, labyrinthine, spotlike pa...
متن کاملTuring instability and pattern formation in a two-population neuronal network model
A two-population firing-rate model describing the dynamics of excitatory and inhibitory neural activity in one spatial dimension is investigated with respect to formation of patterns, in particular stationary periodic patterns and spatiotemporal oscillations. Conditions for existence of spatially homogeneous equilibrium states are first determined, and the stability properties of these equilibr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Social Science Research Network
سال: 2022
ISSN: ['1556-5068']
DOI: https://doi.org/10.2139/ssrn.4147447