Results 171 to 180 of about 519,227 (204)

TURING INSTABILITY FOR THE SCHNACKENBERG SYSTEM

Waves and Stability in Continuous Media, 2008
The linear stability-instability of the equilibrium state of the Schnackemberg system is studied. The onset of Turing instability is obtained.
GENTILE, MAURIZIO, TATARANNI, ASSUNTA
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Interspecific Influence on Mobility and Turing Instability

Bulletin of Mathematical Biology, 2003
In this paper we formulate a multi-patch multi-species model in which the per-capita emigration rate of one species depends on the density of some other species. We then focus on Turing instability to examine if and when this cross-emigration response has crucial effects. We find that the type of interaction matters greatly.
Huang, Y., Diekmann, O.
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On the origin of Turing instability

Journal of Mathematical Chemistry, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Szili, L., Tóth, J.
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Turing instability in reaction-subdiffusion systems

Physical Review E, 2008
We determine the conditions for the occurrence of Turing instabilities in activator-inhibitor systems, where one component undergoes subdiffusion and the other normal diffusion. If the subdiffusing species has a nonlinear death rate, then coupling between the nonlinear kinetics and the memory effects of the non-Markovian transport process advances the ...
A, Yadav, Shane M, Milu, Werner, Horsthemke   +2 more
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Turing Instabilities are Not Enough to Ensure Pattern Formation

Bulletin of Mathematical Biology
AbstractSymmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing’s reaction–diffusion theory, which connects cellular signalling and transport with the development of growth and form.
Václav Klika, Andrew L. Krause, Eamonn A. Gaffney   +2 more
exaly   +7 more sources

A new necessary condition for Turing instabilities

Mathematical Biosciences, 2012
Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition.
Elragig, Aiman, Townley, Stuart
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Analysis of Turing Instability for Biological Models

2014
Reaction-diffusion equations are often used to model biological phenomena. This type of system can produce stable spatial patterns from an uniform initial distribution. This phenomenon is known as Turing instability. This paper presents an analysis of the Turing instability for three biological models: a) Schnakenberg model, b) glycolysis model and c ...
Daiana Rodrigues, Luis Paulo da Silva Barra, Marcelo Lobosco, Flávia de Souza Bastos   +3 more
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Turing Instability of Liquid–Solid Metal Systems

Advanced Materials, 2023
AbstractThe classical Turing morphogenesis often occurs in nonmetallic solution systems due to the sole competition of reaction and diffusion processes. Here, this work conceives that gallium (Ga) based liquid metals (LMs) possess the ability to alloy, diffuse, and react with a range of solid metals (SMs) and thus should display Turing instability ...
Zerong Xing, Genpei Zhang, Jianye Gao, Jiao Ye, Zhuquan Zhou, Biying Liu, Xiaotong Yan, Xueqing Chen, Minghui Guo, Kai Yue, Xuanze Li, Qian Wang, Jing Liu   +12 more
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Turing Instability and Hopf Bifurcation in Cellular Neural Networks

International Journal of Bifurcation and Chaos, 2021
In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and
Zunxian Li, Chengyi Xia
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Dynamics of pattern formation in the Turing optical instability

Physical Review A, 1989
The transient dynamical evolution of spatial pattern formation in a nonlinear passive optical system in a Fabry-P\'erot cavity driven by an external coherent field is studied. The associated decay of the unstable homogeneous state of the system is described analytically, with the inclusion of noise effects, in terms of a stochastic amplitude equation ...
, Aguado, , Rodrguez, , San Miguel M
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