Results 81 to 90 of about 8,745 (203)

Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type

Discrete Dynamics in Nature and Society, 2020
The reaction diffusion system is one of the important models to describe the objective world. It is of great guiding importance for people to understand the real world by studying the Turing patterns of the reaction diffusion system changing with the ...
Lianchao Gu, Peiliang Gong, Hongqing Wang   +2 more
doaj   +1 more source

Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions

, 2017
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays.
Abbott, Amari, Amit, Aradi, Bosking, Bressloff, Bressloff, Brunel, Buice, Buzsaki, Coombes, Coombes, Coombes, Corless, Destexhe, Diba, Ecker, El Boustani, Engelborghs, Ermentrout, Ermentrout, Ermentrout, Ermentrout, Fregnac, Hale, Hubel, Hutt, Izhikevich, Jonathan Touboul, Kandel, Laing, Lindner, Meinhardt, Nesse, Pham, Renart, Rolls, Roxin, Roxin, Series, Shayer, Spreng, Tabareau, Talay, Thorpe, Touboul, Venkov, Wilson, Wilson, Woosley   +49 more
core   +1 more source

A Thermodynamic Framework for Turing‐Type Instabilities in Porous Media: Part II Applications

Geochemistry, Geophysics, Geosystems, Volume 27, Issue 3, March 2026.
Abstract Compaction bands, desiccation cracks, and melt segregation structures are geological patterns relying on the same fundamental manifestations of a universal Turing‐type instability mechanism, as predicted by the thermodynamically consistent reaction–cross‐diffusion framework developed in Part I (Regenauer‐Lieb et al., 2025, https://doi.org/10 ...
Klaus Regenauer‐Lieb, Manman Hu, Qingpei Sun, Chong Liu, Zhennan Zhu, Victor Calo   +5 more
wiley   +1 more source

On Turing-Turing bifurcation of partial functional differential equations and its induced superposition patterns

, 2022
When two Turing modes interact, i.e., Turing-Turing bifurcation occurs, superposition patterns revealing complex dynamical phenomena appear. In this paper, superposition patterns resulting from Turing-Turing bifurcation are investigated in theory. Firstly, the third-order normal form locally topologically equivalent to original partial functional ...
Cao, Xun, Jiang, Weihua
openaire   +2 more sources

Well‐Posedness and Pattern Formation in a Two‐Species Reaction–Diffusion System with Nonlocal Perception

Studies in Applied Mathematics, Volume 156, Issue 2, February 2026.
ABSTRACT Nonlocal perceptual cues, such as visual, auditory, and olfactory signals, profoundly influence animal movement and the emergence of ecological patterns. To capture these effects, we introduce a two‐species reaction–diffusion system with mutual nonlocal perception on a two‐dimensional periodic domain.
Yaqi Chen, Ben Niu, Hao Wang
wiley   +1 more source

Spatiotemporal Tipping Induced by Turing Instability and Hopf Bifurcation in a Population Ecosystem Model with the Fear Factor

Complexity, 2023
Population ecosystems can display the tipping points at which extinctions of species happens. To predict the appearance of tipping points and to understand their evolution mechanism are of uttermost importance for ecological balance.
Min Xiao, Gong Chen, Feilong Wang, Zunshui Cheng, Yi Yao   +4 more
doaj   +1 more source

Vegetation patterns pinpoint the least resilient dryland sites

Methods in Ecology and Evolution, Volume 17, Issue 1, Page 172-187, January 2026.
Abstract Resource‐limited ecosystems, such as drylands, can exhibit self‐organized spatial patterns. Theory suggests that changes in these patterns can inform about the ecosystem degradation level. While the current theory is expected to work well when following a given site in time, we still lack ways of comparing different field sites using static ...
Benoît Pichon, Sophie Donnet, Isabelle Gounand, Sonia Kéfi   +3 more
wiley   +1 more source

Neimark-Sacker-Turing Instability and Pattern Formation in a Spatiotemporal Discrete Predator-Prey System with Allee Effect

Discrete Dynamics in Nature and Society, 2018
A spatiotemporal discrete predator-prey system with Allee effect is investigated to learn its Neimark-Sacker-Turing instability and pattern formation.
Huayong Zhang, Xuebing Cong, Tousheng Huang, Shengnan Ma, Ge Pan   +4 more
doaj   +1 more source

An economic cross-diffusion mutualistic model for cities emergence

, 2019
We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to profits maximization.
de-Córdoba, Gonzalo F., Galiano, Gonzalo   +1 more
core   +1 more source

Cognitive Familiarity‐Driven Rumor Diffusion: A Dynamic Compartmental Model With Stratified Susceptibility

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
Rumor propagation significantly impacts both individual well‐being and societal stability, with various factors influencing its spread. While existing research has primarily focused on the role of interpersonal familiarity in rumor diffusion, this study introduces a different perspective: an individual’s familiarity with the subject matter itself plays
Weijun Yan, Yuhan Hu, Mengxin Chen
wiley   +1 more source