Results 161 to 170 of about 519,227 (204)

Emergent stable tissue shapes from the regulatory feedback between morphogens and cell growth. [PDF]

J Theor Biol
Kaity B, Lobo D.
europepmc   +1 more source

Mechanisms causing the transition between spatial pattern long transients. [PDF]

R Soc Open Sci
Xu L, DeAngelis DL.
europepmc   +1 more source

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Turing Instabilities at Hopf Bifurcation

Journal of Nonlinear Science, 2009
A simple procedure for deriving a uniform asymptotic expansion for the limit cycle in the vicinity of the Hopf bifurcation point for a two dimensional reaction system \[ u_{t} =D_{u}\Delta u+f\left( u,v;a\right) , \] \[ v_{t} =D_{v}\Delta v+g\left( u,v;a\right) \tag{b} \] is suggested. First, an algorithm allowing reduction of the system (ref {b}) to a
S Mischler
exaly   +5 more sources

Turing instabilities and patterns near a Hopf bifurcation [PDF]

Applied Mathematics and Computation, 2005
27 pages, 5 ...
Rui Dilão
exaly   +4 more sources

Turing instabilities for three interacting species

Applied Mathematics Letters
In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction system (ordinary differential equation) becomes an unstable homogeneous steady state of the corresponding reaction ...
Vit Pískovský
exaly   +3 more sources

Turing instability in the reaction-diffusion network

Physical Review E, 2020
It is an established fact that a positive wave number plays an essential role in Turing instability. However, the impact of a negative wave number on Turing instability remains unclear. Here, we investigate the effect of the weights and nodes on Turing instability in the FitzHugh-Nagumo model, and theoretical results reveal genesis of Turing ...
Qianqian Zheng, Jianwei Shen, Yong Xu
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Necessary condition of the Turing instability

Physical Review E, 1993
A reaction-diffusion system in any number of spatial variables consisting of an arbitrary number of chemical species cannot exhibit Turing instability if none of the reaction steps expresses cross inhibition. A corollary of this result underlines the importance of nonlinearity in the formation of stationary spatial structures, a kind of self ...
, Szili, , Tóth
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Switching-induced Turing instability

Physical Review E, 2002
We propose a mechanism for inducing a Turing instability in systems whose only stable state is pattern-free and homogeneous. Global alternation between two dynamics, each of which has the same homogeneous stable state, may induce a Turing instability that leads to pattern formation. We determine what kind of alternation can drive the system to a Turing
J, Buceta, Katja, Lindenberg
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