Rate-induced tipping in savanna–forest ecosystems: effects of fast-varying fitness parameters in the framework of compactification.
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| Title: | Rate-induced tipping in savanna–forest ecosystems: effects of fast-varying fitness parameters in the framework of compactification. |
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| Authors: | Kumar K, Ravi1 (AUTHOR), Dutta, Partha Sharathi1 (AUTHOR) parthasharathi@iitrpr.ac.in |
| Source: | Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences. 5/20/2026, Vol. 482 Issue 2338, p1-28. 28p. |
| Subjects: | Compactification (Mathematics), Mathematical models, Savanna ecology, Biological fitness, Bifurcation theory, Ecosystem dynamics, Tropical forests |
| Abstract: | Savannas are grass-dominated ecosystems with scattered shrubs and savanna trees, often coexisting with tropical forests. They host a diverse range of plants and animals, act as a major carbon sink, regulate the global climate and support local economies. However, rapid environmental change is degrading these ecosystems, ultimately leading to a decline in biodiversity. Here, we consider a mathematical model of savanna–forest ecosystems to investigate rate-induced tipping (R-tipping) between distinct states under rapid variations in fitness parameters of different functional types (i.e. grass, savanna saplings and adult trees and forest trees) over time. To establish the existence of R-tipping, we determine basin instability (BI) in the corresponding frozen system with fixed-in-time inputs. Since time-dependent parameters make the model non-autonomous, it lacks compact invariant sets, which preclude the use of classical bifurcation theory. To address this, we reformulate the non-autonomous system with bi-asymptotically constant inputs as an autonomous one using compactification with an additional bounded variable. Furthermore, compactification enables us to identify the R-tipping threshold, which is crossed when tipping occurs. Overall, our analysis reveals distinct rate-induced transitions, including shifts to dominant states of grass, adult savanna trees and oscillatory dynamics. [ABSTRACT FROM AUTHOR] |
| Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society 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: 193859766 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Rate-induced tipping in savanna–forest ecosystems: effects of fast-varying fitness parameters in the framework of compactification. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kumar+K%2C+Ravi%22">Kumar K, Ravi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Dutta%2C+Partha+Sharathi%22">Dutta, Partha Sharathi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> parthasharathi@iitrpr.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+Royal+Society+A%3A+Mathematical%2C+Physical+%26+Engineering+Sciences%22">Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences</searchLink>. 5/20/2026, Vol. 482 Issue 2338, p1-28. 28p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Compactification+%28Mathematics%29%22">Compactification (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Savanna+ecology%22">Savanna ecology</searchLink><br /><searchLink fieldCode="DE" term="%22Biological+fitness%22">Biological fitness</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Ecosystem+dynamics%22">Ecosystem dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Tropical+forests%22">Tropical forests</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Savannas are grass-dominated ecosystems with scattered shrubs and savanna trees, often coexisting with tropical forests. They host a diverse range of plants and animals, act as a major carbon sink, regulate the global climate and support local economies. However, rapid environmental change is degrading these ecosystems, ultimately leading to a decline in biodiversity. Here, we consider a mathematical model of savanna–forest ecosystems to investigate rate-induced tipping (R-tipping) between distinct states under rapid variations in fitness parameters of different functional types (i.e. grass, savanna saplings and adult trees and forest trees) over time. To establish the existence of R-tipping, we determine basin instability (BI) in the corresponding frozen system with fixed-in-time inputs. Since time-dependent parameters make the model non-autonomous, it lacks compact invariant sets, which preclude the use of classical bifurcation theory. To address this, we reformulate the non-autonomous system with bi-asymptotically constant inputs as an autonomous one using compactification with an additional bounded variable. Furthermore, compactification enables us to identify the R-tipping threshold, which is crossed when tipping occurs. Overall, our analysis reveals distinct rate-induced transitions, including shifts to dominant states of grass, adult savanna trees and oscillatory dynamics. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society 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: 10.1098/rspa.2025.0803 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 1 Subjects: – SubjectFull: Compactification (Mathematics) Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Savanna ecology Type: general – SubjectFull: Biological fitness Type: general – SubjectFull: Bifurcation theory Type: general – SubjectFull: Ecosystem dynamics Type: general – SubjectFull: Tropical forests Type: general Titles: – TitleFull: Rate-induced tipping in savanna–forest ecosystems: effects of fast-varying fitness parameters in the framework of compactification. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kumar K, Ravi – PersonEntity: Name: NameFull: Dutta, Partha Sharathi IsPartOfRelationships: – BibEntity: Dates: – D: 20 M: 05 Text: 5/20/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13645021 Numbering: – Type: volume Value: 482 – Type: issue Value: 2338 Titles: – TitleFull: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences Type: main |
| ResultId | 1 |
