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Analysis of Turing Instability for Biological Models
2014Reaction-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 +3 more
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Turing instability in reaction-subdiffusion systems
Physical Review E, 2008We 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 +2 more
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Turing Instability of Liquid–Solid Metal Systems
Advanced Materials, 2023AbstractThe 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 +12 more
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Turing Instability and Hopf Bifurcation in Cellular Neural Networks
International Journal of Bifurcation and Chaos, 2021In 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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On Turing Instability in Nonhomogeneous Reaction-Diffusion CNN’s
IEEE Transactions on Circuits and Systems I: Regular Papers, 2017Several results on instability in nonhomogeneous architectures able to generate Turing patterns are presented. The approach makes use of the continuity theorem regarding the dependence of polynomial roots on coefficients and of the root-locus techniques for small, and large parameter deviations from their homogeneous values, respectively.
Liviu Goras +2 more
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Turing instability controlled by spatiotemporal imposed dynamics
Physical Review E, 2005The study of the spatiotemporal response of pattern forming systems to spatially resonant external forcing has unveiled striking new phenomena which challenge the understanding of self-organization in nonlinear, nonequilibrium systems. Here we show that a simple spatiotemporal two-dimensional forcing of a system supporting an intrinsic wavelength but ...
David G, Míguez +2 more
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Dynamics of pattern formation in the Turing optical instability
Physical Review A, 1989The 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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Turing Instabilities in Homogeneous Systems
2010Alan Turing’s paper entitled “The Chemical Basis of Morphogenesis” [440] ranks without doubt among the most important papers of the last century. In that seminal work Turing laid the foundation for the theory of chemical pattern formation. Turing showed that diffusion can have nontrivial effects in nonequilibrium systems.
Vicenç Méndez +2 more
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Numerical Experiments on the Turing Instability in the Oregonator Model
Journal of the Physical Society of Japan, 1997Summary: Numerical experiments on the Oregonator model of the Belousov-Zhabotinsky reaction with 2 variables (activator and inhibitor) are carried out. Influences of an inhibitory diffusion coefficient and inhibitory initial condition (concentration) on its pattern dynamics are studied for several values of a stoichiometric factor of the model.
Nomura, Atsushi +3 more
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INSTABILITIES OF WAVE TRAINS AND TURING PATTERNS IN LARGE DOMAINS
International Journal of Bifurcation and Chaos, 2007We classify generic instabilities of wave trains in reaction–diffusion systems on the real line as the wavenumber and system parameters are varied. We find three types of robust instabilities: Hopf with nonzero modulational wavenumber, sideband and spatio-temporal period-doubling.
Jens D. M. Rademacher, Arnd Scheel
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