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Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domains.

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Title: Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domains.
Authors: Duan, Daifeng1 (AUTHOR), Liu, Biao1,2 (AUTHOR) liubiao0807@126.com, Wei, Junjie3 (AUTHOR)
Source: Mathematics & Computers in Simulation. Jul2026, Vol. 245, p366-383. 18p.
Subjects: Pattern formation (Physical sciences), Kernel functions, Boundary value problems, Square, Spatiotemporal processes, Mathematical models, Hopf bifurcations, Bifurcation theory
Abstract: We investigate the effects of periodic boundary conditions on a nonlocal Holling–Tanner model defined on a square domain. A top-hat kernel function with finite support is employed to characterize nonlocal interactions, which we further adapt to accommodate periodic boundary conditions. Subsequently, we derive the Turing and spatiotemporal Hopf bifurcation curves and conduct numerical simulations across the parameter ranges delineated by these curves. Our findings demonstrate substantial differences in spatiotemporal patterns between the square domain and the one-dimensional case, including squares, stripes, mixed states, irregular spot-like hexagonal patterns, and coexistence states of three-stripes and spots. These observed patterns exhibit remarkable consistency with both chemical experimental results and the skin pigmentation patterns of fish, thereby offering valuable theoretical insights and predictive frameworks for understanding spatiotemporal patterns in chemical and biological systems. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 192483781
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  Data: Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domains.
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  Data: <searchLink fieldCode="AR" term="%22Duan%2C+Daifeng%22">Duan, Daifeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Biao%22">Liu, Biao</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> liubiao0807@126.com</i><br /><searchLink fieldCode="AR" term="%22Wei%2C+Junjie%22">Wei, Junjie</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Jul2026, Vol. 245, p366-383. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Pattern+formation+%28Physical+sciences%29%22">Pattern formation (Physical sciences)</searchLink><br /><searchLink fieldCode="DE" term="%22Kernel+functions%22">Kernel functions</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Square%22">Square</searchLink><br /><searchLink fieldCode="DE" term="%22Spatiotemporal+processes%22">Spatiotemporal processes</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Hopf+bifurcations%22">Hopf bifurcations</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We investigate the effects of periodic boundary conditions on a nonlocal Holling–Tanner model defined on a square domain. A top-hat kernel function with finite support is employed to characterize nonlocal interactions, which we further adapt to accommodate periodic boundary conditions. Subsequently, we derive the Turing and spatiotemporal Hopf bifurcation curves and conduct numerical simulations across the parameter ranges delineated by these curves. Our findings demonstrate substantial differences in spatiotemporal patterns between the square domain and the one-dimensional case, including squares, stripes, mixed states, irregular spot-like hexagonal patterns, and coexistence states of three-stripes and spots. These observed patterns exhibit remarkable consistency with both chemical experimental results and the skin pigmentation patterns of fish, thereby offering valuable theoretical insights and predictive frameworks for understanding spatiotemporal patterns in chemical and biological systems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.matcom.2026.01.025
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 366
    Subjects:
      – SubjectFull: Pattern formation (Physical sciences)
        Type: general
      – SubjectFull: Kernel functions
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Square
        Type: general
      – SubjectFull: Spatiotemporal processes
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Hopf bifurcations
        Type: general
      – SubjectFull: Bifurcation theory
        Type: general
    Titles:
      – TitleFull: Pattern formation of the Holling–Tanner model with top-hat kernel functions on square domains.
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            NameFull: Duan, Daifeng
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            NameFull: Liu, Biao
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          Name:
            NameFull: Wei, Junjie
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          Dates:
            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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              Value: 245
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            – TitleFull: Mathematics & Computers in Simulation
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