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Turing instabilities in prey–predator systems with dormancy of predators
Journal of Mathematical Biology, 2014In this paper, we study the stationary and oscillatory Turing instabilities of a homogeneous equilibrium in prey-predator reaction-diffusion systems with dormant phase of predators. We propose a simple criterion which is useful in classifying these Turing instabilities.
Masataka Kuwamura
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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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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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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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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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Linear Instability, Turing Instability and Pattern Formation
2015This chapter treats of one of the most fundamental observation for biological systems: the Turing instability mechanism. In his seminal paper, A. Turing suggests that a system of chemical substances reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis, that is boundary formation. Surprisingly,
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Turing instability in pioneer/climax species interactions
Mathematical Biosciences, 2005Systems of pioneer and climax species are used to model interactions of species whose reproductive capacity is sensitive to population density in their shared ecosystem. Intraspecies interaction coefficients can be adjusted so that spatially homogeneous solutions are stable to small perturbations.
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Impact of non-diffusive interactions on Turing instability
Communications in Nonlinear Science and Numerical SimulationzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nannan Zhao, Haohao Xie, Xuexue Zhang
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Turing instability of periodic solutions for the Gierer–Meinhardt model with cross-diffusion
Chaos, Solitons and Fractals, 2022Bin Ge
exaly