Results 31 to 40 of about 8,750 (185)
A graph-theoretic method for detecting potential Turing bifurcations [PDF]
The Journal of Chemical Physics, 2006 The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical ...
Mincheva, Maya, Roussel, Marc R.
openaire +2 more sources
Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems [PDF]
Bulletin of Mathematical Biology, 2022 AbstractTuring’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux ...
openaire +3 more sources
Two-dimensional localized structures in harmonically forced oscillatory systems [PDF]
, 2016 Two-dimensional spatially localized structures in the complex Ginzburg–Landau equation with 1:1 resonance are studied near the simultaneous presence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcation on ...
Knobloch, Edgar, Ma, Yi-Ping
core +1 more source
Spatio-temporal secondary instabilities near the Turing-Hopf bifurcation [PDF]
Scientific Reports, 2019 AbstractIn this work, we provide a framework to understand and quantify the spatiotemporal structures near the codimension-two Turing-Hopf point, resulting from secondary instabilities of Mixed Mode solutions of the Turing-Hopf amplitude equations.
Aldo Ledesma–Durán, J. L. Aragón
openaire +2 more sources
Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model
Discrete Dynamics in Nature and Society, 2019 In this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis.
Lili Meng +3 more
doaj +1 more source
Entropy, 2017 Wind-induced vegetation patterns were proposed a long time ago but only recently a dynamic vegetation-sand relationship has been established. In this research, we transformed the continuous vegetation-sand model into a discrete model.
Feifan Zhang +4 more
doaj +1 more source
Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
Scientific Reports, 2021 The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation.
Shan Guo, Ming-zhu Sun, Xin Zhao
doaj +1 more source
Turing instabilities and patterns near a Hopf bifurcation [PDF]
Applied Mathematics and Computation, 2005 27 pages, 5 ...
openaire +3 more sources
Turing pattern formation in the Brusselator system with nonlinear diffusion [PDF]
, 2013 In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries.
Gambino, G. +3 more
core +1 more source
Subcritical Turing bifurcation and the morphogenesis of localized patterns
Physical Review E, 2014 6 pages, 4 ...
Breña-Medina, Víctor, Champneys, Alan
openaire +3 more sources