Results 11 to 20 of about 8,745 (203)

Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay [PDF]

Journal of Dynamics and Differential Equations, 2018
For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf bifurcations are established.
Jiang, Weihua, Wang, Hongbin, Cao, Xun
openaire   +4 more sources

Unravelling the Turing bifurcation using spatially varying diffusion coefficients [PDF]

Journal of Mathematical Biology, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benson, D, Maini, P, Sherratt, J
openaire   +4 more sources

On the Proper Treatment of Dynamics in Cognitive Science

Topics in Cognitive Science, EarlyView., 2023
Abstract This essay examines the relevance of dynamical ideas for cognitive science. On its own, the mere mathematical idea of a dynamical system is too weak to serve as a scientific theory of anything, and dynamical approaches within cognitive science are too rich and varied to be subsumed under a single “dynamical hypothesis.” Instead, after first ...
Randall D. Beer
wiley   +1 more source

Convective Turing Bifurcation

, 2021
Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction diffusion systems [E, M1, M2, S1, S2, SZJV], we systematically derive formally by multiscale expansion and justify rigorously by Lyapunov-Schmidt reduction amplitude equations describing Turing-type bifurcations of general reaction diffusion convection systems ...
Wheeler, Aric, Zumbrun, Kevin
openaire   +2 more sources

Turing mechanism underlying a branching model for lung morphogenesis. [PDF]

PLoS ONE, 2017
The mammalian lung develops through branching morphogenesis. Two primary forms of branching, which occur in order, in the lung have been identified: tip bifurcation and side branching.
Hui Xu, Mingzhu Sun, Xin Zhao
doaj   +1 more source

Spatiotemporal Dynamics in a Predator–Prey Model with Functional Response Increasing in Both Predator and Prey Densities

Mathematics, 2021
In this paper, a diffusive predator–prey system with a functional response that increases in both predator and prey densities is considered. By analyzing the characteristic roots of the partial differential equation system, the Turing instability and ...
Ruizhi Yang, Qiannan Song, Yong An
doaj   +1 more source

Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation

Open Mathematics, 2022
In this article, we study Hopf bifurcation and Turing instability of a diffusive predator-prey model with hunting cooperation. For the local model, we analyze the stability of the equilibrium and derive conditions for determining the direction of Hopf ...
Miao Liangying, He Zhiqian
doaj   +1 more source

Convective Turing bifurcation with conservation laws

, 2023
Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation in the presence of conservation laws. In the nonconvective, reaction-diffusion case, this is seen similarly as in \
Wheeler, Aric, Zumbrun, Kevin
openaire   +2 more sources

Turing–Hopf bifurcation of a ratio-dependent predator-prey model with diffusion

Advances in Difference Equations, 2019
In this paper, the Turing–Hopf bifurcation of a ratio-dependent predator-prey model with diffusion and Neumann boundary condition is considered. Firstly, we present a kind of double parameters selection method, which can be used to analyze the Turing ...
Qiushuang Shi, Ming Liu, Xiaofeng Xu
doaj   +1 more source

Differential susceptibility to noise of mixed Turing and Hopf modes in a photosensitive chemical medium [PDF]

, 2007
We report on experiments with the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) when forced with a random (spatiotemporally) distributed illumination. Acting on a mixed mode consisting of oscillating spots, close enough to the Hopf
Alonso Muñoz, Sergio, Míguez, David G., Sagués Mestres, Francesc   +2 more
core   +1 more source