Results 31 to 40 of about 116,098 (200)

Additive Global Noise Delays Turing Bifurcations

Physical Review Letters, 2007
We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order,
Hutt, Axel, Longtin, Andre, Schimansky-Geier, Lutz   +2 more
openaire   +2 more sources

Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity, 2020
In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model.
Feifan Zhang, Wenjiao Zhou, Lei Yao, Xuanwen Wu, Huayong Zhang   +4 more
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

Studies on the Existence of Unstable Oscillatory Patterns Bifurcating from Hopf Bifurcations in a Turing Model [PDF]

Journal of Applied Mathematics, 2014
We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and ...
Yan Zhang, Zhenhua Bao
openaire   +5 more sources

The Turing Way: A Handbook for Reproducible Data Science

, 2019
<p>Reproducible research is necessary to ensure that scientific work can be trusted. Funders and publishers are beginning to require that publications include access to the underlying data and the analysis code.
The Turing Way Community (6945962), Alexander Morley (4487878), Anna Krystalli, Alexander Morley, Sarah Gibson, Louise Bowler, Martin O'Reilly, Patricia Herterich, Anna Krystalli (5268592), Kirstie Whitaker (5481308), Patricia Herterich (8294097), Rosie Higman, The Turing Way Community, Sarah Gibson (5095877), Martin O'Reilly (212859), Becky Arnold (5051687), Kirstie Whitaker, Louise Bowler (7107143), Rosie Higman (7107146), Becky Arnold   +19 more
core   +4 more sources

Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model

Boundary Value Problems, 2019
In this paper, Turing patterns and steady state bifurcation of a diffusive Beddington–DeAngelis-type predator–prey model with density-dependent death rate for the predator are considered.
Hongwu Xu, Shengmao Fu
doaj   +1 more source

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Mathematics, 2020
In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered.
Maria Francesca Carfora, Isabella Torcicollo   +1 more
doaj   +1 more source

Turing–Hopf bifurcation and spatiotemporal patterns in a Gierer–Meinhardt system with gene expression delay

Nonlinear Analysis, 2021
In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by
Shuangrui Zhao, Hongbin Wang, Weihua Jiang   +2 more
doaj   +1 more source

Convective Turing bifurcation

Mathematical Models and Methods in Applied Sciences
Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction–diffusion systems, we justify rigorously by Lyapunov–Schmidt reduction the formal amplitude (complex Ginzburg–Landau) equations describing Turing-type bifurcations of general reaction–diffusion–convection systems, showing that small spatially periodic traveling wave
Aric Wheeler, Kevin Zumbrun
openaire   +2 more sources

Self-Organized Patterns Induced by Neimark-Sacker, Flip and Turing Bifurcations in a Discrete Predator-Prey Model with Lesie-Gower Functional Response

Entropy, 2017
The formation of self-organized patterns in predator-prey models has been a very hot topic recently. The dynamics of these models, bifurcations and pattern formations are so complex that studies are urgently needed.
Feifan Zhang, Huayong Zhang, Shengnan Ma, Tianxiang Meng, Tousheng Huang, Hongju Yang   +5 more
doaj   +1 more source