Capturing Nonlocal Effects in Fractional Dynamics: Riesz Derivatives as a New Frontier in Modeling Complex Diffusion and Pattern Formation
Sign Up to like & getrecommendations! Published in 2025 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.70120
Abstract: This work addresses the numerical solution of fractional time‐dependent partial differential equations (FTPDEs) that involve the Riesz fractional derivative in space. Motivated by the effectiveness of space‐fractional operators in modeling anomalous diffusion and dispersion phenomena… read more here.
Keywords: fractional dynamics; diffusion; pattern formation; diffusion pattern ... See more keywords
Spatial pattern formation in reaction–diffusion models: a computational approach
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Biology"
DOI: 10.1007/s00285-019-01462-0
Abstract: Reaction–diffusion equations have been widely used to describe biological pattern formation. Nonuniform steady states of reaction–diffusion models correspond to stationary spatial patterns supported by these models. Frequently these steady states are not unique and correspond… read more here.
Keywords: pattern formation; diffusion; steady states; diffusion models ... See more keywords
Structural causes of pattern formation and loss through model-independent bifurcation analysis
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DOI: 10.1007/s00285-025-02296-9
Abstract: During development, precise cellular patterning is essential for the formation of functional tissues and organs. These patterns arise from conserved signaling networks that regulate communication both within and between cells. Here, we develop and present… read more here.
Keywords: causes pattern; model independent; pattern formation; structural causes ... See more keywords
Pattern formation by advection-diffusion in new economic geography
Sign Up to like & getrecommendations! Published in 2024 at "Decisions in Economics and Finance"
DOI: 10.1007/s10203-025-00533-w
Abstract: This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility function and an… read more here.
Keywords: geography; transport costs; advection diffusion; pattern formation ... See more keywords
Some Remarks on Pattern Formation in Vertebrate Embryology
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DOI: 10.1007/s10955-019-02301-8
Abstract: A model of somite formation in vertebrates is presented in which a biochemical wave selects alternating regions of vertebra and somite production. It does so by imposing expression of a relevant gene in the underlying… read more here.
Keywords: vertebrate embryology; remarks pattern; formation; pattern formation ... See more keywords
Emergent impacts of quadratic mortality on pattern formation in a predator–prey system
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DOI: 10.1007/s11071-016-3222-2
Abstract: In this paper, we have investigated the effects of spatial diffusion in the pattern formation of a predator–prey system with quadratic mortality rate of the predator in the presence of habitat complexity. Using linear stability… read more here.
Keywords: predator prey; pattern formation; formation predator; prey system ... See more keywords
Effects of Hydraulic Soil Properties on Vegetation Pattern Formation in Sloping Landscapes
Sign Up to like & getrecommendations! Published in 2017 at "Bulletin of Mathematical Biology"
DOI: 10.1007/s11538-017-0348-4
Abstract: Current models of vegetation pattern formation rely on a system of weakly nonlinear reaction–diffusion equations that are coupled by their source terms. While these equations, which are used to describe a spatiotemporal planar evolution of… read more here.
Keywords: pattern formation; vegetation pattern; sloping landscapes; soil properties ... See more keywords
Phase Transitions in a Logistic Metapopulation Model with Nonlocal Interactions
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of Mathematical Biology"
DOI: 10.1007/s11538-017-0373-3
Abstract: The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one… read more here.
Keywords: metapopulation model; pattern formation; nonlocal interactions; model ... See more keywords
Advances and challenges in programming pattern formation using living cells.
Sign Up to like & getrecommendations! Published in 2022 at "Current opinion in chemical biology"
DOI: 10.1016/j.cbpa.2022.102147
Abstract: Spatial patterning of cell populations is a ubiquitous phenomenon in nature. Patterns occur at various length and time scales and exhibit immense diversity. In addition to offering a deeper understanding of the emergence of patterns… read more here.
Keywords: formation; pattern formation; living cells; programming pattern ... See more keywords
A Design Principle for an Autonomous Post-translational Pattern Formation.
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DOI: 10.1016/j.celrep.2017.03.081
Abstract: Previous autonomous pattern-formation models often assumed complex molecular and cellular networks. This theoretical study, however, shows that a system composed of one substrate with multisite phosphorylation and a pair of kinase and phosphatase can generate… read more here.
Keywords: pattern formation; post translational; design;
Galanin Signaling in the Brain Regulates Color Pattern Formation in Zebrafish
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DOI: 10.1016/j.cub.2019.11.033
Abstract: Summary Color patterns are prominent features of many animals and are of high evolutionary relevance. In basal vertebrates, color patterns are composed of specialized pigment cells that arrange in multilayered mosaics in the skin. Zebrafish… read more here.
Keywords: galanin signaling; color pattern; pattern formation; pigment cells ... See more keywords