Amplitude Equation Analysis and Pattern Transitions in a Superdiffusive Predator–Prey Model with Allee Effect.
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| Title: | Amplitude Equation Analysis and Pattern Transitions in a Superdiffusive Predator–Prey Model with Allee Effect. |
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| Authors: | Liao, Fenglian1 (AUTHOR) 23S058021@stu.hit.edu.cn, Ye, Yong1 (AUTHOR) yong_ye1994@163.com, Zhao, Yi1 (AUTHOR) zhao.yi@hit.edu.cn |
| Source: | International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Jun2026, Vol. 36 Issue 8, p1-25. 25p. |
| Subjects: | Allee effect, Pattern formation (Physical sciences), Ecological models, Predation, Spatial ecology, Mathematical models, Hopf bifurcations |
| Abstract: | This paper proposes and analyzes a superdiffusive predator–prey model incorporating Allee effect to explore parameter-driven spatial pattern formation. Combining linear stability analysis, multiscale technique, and center manifold theory, we systematically derive and analyze the stability of amplitude equations in both two- and three-dimensional spaces. Numerical simulations demonstrate that variations in three core parameters — reproductive advantage, superdiffusion exponent, and Allee coefficient — generate distinct spatial morphologies within the Turing region. A critical dimensional divergence is observed: while 2D systems follow the classical spot-stripe transition, 3D systems exhibit stable planar lamellar structures rather than spots, with BCC configurations remaining unstable. In the Turing–Hopf region, the interplay of diffusion-driven instability and temporal oscillations produces spatially organized periodic dynamics. Pure Hopf bifurcations induce complex spatiotemporal fluctuations. These results establish an integrated analytical framework linking reproductive dynamics, dispersal characteristics, and density-dependent regulation, advancing the theory of ecological pattern formation under superdiffusion constraints with implications for conservation planning and multispecies modeling. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company 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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193401832 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Amplitude Equation Analysis and Pattern Transitions in a Superdiffusive Predator–Prey Model with Allee Effect. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Liao%2C+Fenglian%22">Liao, Fenglian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> 23S058021@stu.hit.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Ye%2C+Yong%22">Ye, Yong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yong_ye1994@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Yi%22">Zhao, Yi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhao.yi@hit.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Jun2026, Vol. 36 Issue 8, p1-25. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Allee+effect%22">Allee effect</searchLink><br /><searchLink fieldCode="DE" term="%22Pattern+formation+%28Physical+sciences%29%22">Pattern formation (Physical sciences)</searchLink><br /><searchLink fieldCode="DE" term="%22Ecological+models%22">Ecological models</searchLink><br /><searchLink fieldCode="DE" term="%22Predation%22">Predation</searchLink><br /><searchLink fieldCode="DE" term="%22Spatial+ecology%22">Spatial ecology</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Hopf+bifurcations%22">Hopf bifurcations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper proposes and analyzes a superdiffusive predator–prey model incorporating Allee effect to explore parameter-driven spatial pattern formation. Combining linear stability analysis, multiscale technique, and center manifold theory, we systematically derive and analyze the stability of amplitude equations in both two- and three-dimensional spaces. Numerical simulations demonstrate that variations in three core parameters — reproductive advantage, superdiffusion exponent, and Allee coefficient — generate distinct spatial morphologies within the Turing region. A critical dimensional divergence is observed: while 2D systems follow the classical spot-stripe transition, 3D systems exhibit stable planar lamellar structures rather than spots, with BCC configurations remaining unstable. In the Turing–Hopf region, the interplay of diffusion-driven instability and temporal oscillations produces spatially organized periodic dynamics. Pure Hopf bifurcations induce complex spatiotemporal fluctuations. These results establish an integrated analytical framework linking reproductive dynamics, dispersal characteristics, and density-dependent regulation, advancing the theory of ecological pattern formation under superdiffusion constraints with implications for conservation planning and multispecies modeling. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company 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: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0218127426501002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 1 Subjects: – SubjectFull: Allee effect Type: general – SubjectFull: Pattern formation (Physical sciences) Type: general – SubjectFull: Ecological models Type: general – SubjectFull: Predation Type: general – SubjectFull: Spatial ecology Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Hopf bifurcations Type: general Titles: – TitleFull: Amplitude Equation Analysis and Pattern Transitions in a Superdiffusive Predator–Prey Model with Allee Effect. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Liao, Fenglian – PersonEntity: Name: NameFull: Ye, Yong – PersonEntity: Name: NameFull: Zhao, Yi IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02181274 Numbering: – Type: volume Value: 36 – Type: issue Value: 8 Titles: – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering Type: main |
| ResultId | 1 |
