On the stability and nonexistence of turing patterns for the generalized Lengyel‐Epstein model
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4457
Abstract: This paper studies the dynamics of the generalized Lengyel-Epstein reaction-diffusion model proposed in a recent study by Abdelmalek and Bendoukha. Two main results are shown in this paper. The first of which is sufficient conditions… read more here.
Keywords: nonexistence turing; model; lengyel epstein; turing patterns ... See more keywords
Linear and Weakly Nonlinear Stability Analyses of Turing Patterns for Diffusive Predator–Prey Systems in Freshwater Marsh Landscapes
Sign Up to like & getrecommendations! Published in 2017 at "Bulletin of Mathematical Biology"
DOI: 10.1007/s11538-017-0245-x
Abstract: We study a diffusive predator–prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a… read more here.
Keywords: diffusive predator; predator prey; weakly nonlinear; marsh landscapes ... See more keywords
Turing Patterns for a Nonlocal Lotka–Volterra Cooperative System
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Nonlinear Mathematical Physics"
DOI: 10.1007/s44198-021-00002-z
Abstract: This paper is devoted to investigating the pattern dynamics of Lotka–Volterra cooperative system with nonlocal effect and finding some new phenomena. Firstly, by discussing the Turing bifurcation, we build the conditions of Turing instability, which… read more here.
Keywords: cooperative system; lotka volterra; system; patterns nonlocal ... See more keywords
Statistical approach for parameter identification by Turing patterns.
Sign Up to like & getrecommendations! Published in 2020 at "Journal of theoretical biology"
DOI: 10.1016/j.jtbi.2020.110319
Abstract: Prevailing theories in biological pattern formation, such as in morphogenesis or multicellular structures development, have been based on purely chemical processes, with the Turing models as the prime example. Recent studies have challenged the approach,… read more here.
Keywords: statistical approach; parameter; model; approach parameter ... See more keywords
Turing Patterns of Non-linear S-I Model on Random and Real-Structure Networks with Diarrhea Data
Sign Up to like & getrecommendations! Published in 2019 at "Scientific Reports"
DOI: 10.1038/s41598-019-45069-3
Abstract: Most developed models for solving problems in epidemiology use deterministic approach. To cover the lack of spatial sense in the method, one uses statistical modeling, reaction-diffusion in continuous medium, or multi-patch model to depict epidemic… read more here.
Keywords: patterns non; non linear; real structure; model ... See more keywords
Turing patterns on polymerized membranes: coarse-grained lattice modelling with an internal degree of freedom for polymer direction.
Sign Up to like & getrecommendations! Published in 2025 at "Soft matter"
DOI: 10.1039/d4sm01309c
Abstract: We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in R3 using a surface model for polymerized membranes. The variables used to describe the membranes correspond to two distinct degrees of… read more here.
Keywords: degree freedom; internal degree; turing patterns; polymer ... See more keywords
Effect of obstructions on growing Turing patterns.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0099753
Abstract: We study how Turing pattern formation on a growing domain is affected by discrete domain discontinuities. We use the Lengyel-Epstein reaction-diffusion model to numerically simulate Turing pattern formation on radially expanding circular domains containing a… read more here.
Keywords: obstructions growing; effect obstructions; growing turing; turing patterns ... See more keywords
From Turing patterns to chimera states in the 2D Brusselator model.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0130539
Abstract: The Brusselator has been used as a prototype model for autocatalytic reactions and, in particular, for the Belousov-Zhabotinsky reaction. When coupled at the diffusive limit, the Brusselator undergoes a Turing bifurcation resulting in the formation… read more here.
Keywords: chimera states; turing patterns; patterns chimera; model ... See more keywords
Robust controlled formation of Turing patterns in three-component systems.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.105.014209
Abstract: Over the past few decades, formation of Turing patterns in reaction-diffusion systems has been shown to be the underlying process in several examples of biological morphogenesis, confirming Alan Turing's hypothesis, put forward in 1952. However,… read more here.
Keywords: controlled formation; robust controlled; turing patterns; three component ... See more keywords
Predictable topological sensitivity of Turing patterns on graphs.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.105.014304
Abstract: Reaction-diffusion systems implemented as dynamical processes on networks have recently renewed the interest in their self-organized collective patterns known as Turing patterns. We investigate the influence of network topology on the emerging patterns and their… read more here.
Keywords: sensitivity turing; topological sensitivity; turing patterns; patterns graphs ... See more keywords
Turing patterns in simplicial complexes.
Sign Up to like & getrecommendations! Published in 2023 at "Physical review. E"
DOI: 10.1103/physreve.107.014216
Abstract: The spontaneous emergence of patterns in nature, such as stripes and spots, can be mathematically explained by reaction-diffusion systems. These patterns are often referred as Turing patterns to honor the seminal work of Alan Turing… read more here.
Keywords: formation; turing patterns; simplicial complexes; patterns simplicial ... See more keywords