A study for analysing predator–prey ecological system using Legendre polynomial.
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| Title: | A study for analysing predator–prey ecological system using Legendre polynomial. |
|---|---|
| Authors: | Agrawal, Khushbu1 (AUTHOR), Kumar, Sunil1 (AUTHOR) skiitbhu28@gmail.com, Alkahtani, Badr S. T.2 (AUTHOR), Alzaid, Sara S.2 (AUTHOR) |
| Source: | Applied Mathematics in Science & Engineering. Dec2024, Vol. 32 Issue 1, p1-41. 41p. |
| Subjects: | Nonlinear equations, Nonlinear functional analysis, Matrices (Mathematics), Lyapunov exponents, Nonlinear systems |
| Abstract: | This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on Caputo operators, we present a newly developed system of differential equations for the predator–prey system using wavelet method. It is well known that a system of nonlinear singular models cannot operate smoothly since they are singular and nonlinear. Therefore, with the help of this numerical approach, we have converted the system into a nonlinear system of algebraic equations by extending it through operational matrix of Legendre wavelets. Using the wavelet collocation scheme, we have calculated these unknown coefficients. It has been demonstrated in tables and graphs that the developed approach is consistent and proficient. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyse its behaviour. In addition, a nonlinear functional analysis have used to establish uniformly boundedness for the proposed model. Also we have discussed residual error analysis and Lyapunov exponent. The applicability and efficacy of this methodology have been demonstrated through this nonlinear system. Additionally, a comparison with existing results highlights the advantages of our numerical approach. All calculations have been done using MATLAB. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd 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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| Header | DbId: egs DbLabel: Engineering Source An: 181525363 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A study for analysing predator–prey ecological system using Legendre polynomial. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Agrawal%2C+Khushbu%22">Agrawal, Khushbu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kumar%2C+Sunil%22">Kumar, Sunil</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> skiitbhu28@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Alkahtani%2C+Badr+S%2E+T%2E%22">Alkahtani, Badr S. T.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Alzaid%2C+Sara+S%2E%22">Alzaid, Sara S.</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+in+Science+%26+Engineering%22">Applied Mathematics in Science & Engineering</searchLink>. Dec2024, Vol. 32 Issue 1, p1-41. 41p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+functional+analysis%22">Nonlinear functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+exponents%22">Lyapunov exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on Caputo operators, we present a newly developed system of differential equations for the predator–prey system using wavelet method. It is well known that a system of nonlinear singular models cannot operate smoothly since they are singular and nonlinear. Therefore, with the help of this numerical approach, we have converted the system into a nonlinear system of algebraic equations by extending it through operational matrix of Legendre wavelets. Using the wavelet collocation scheme, we have calculated these unknown coefficients. It has been demonstrated in tables and graphs that the developed approach is consistent and proficient. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyse its behaviour. In addition, a nonlinear functional analysis have used to establish uniformly boundedness for the proposed model. Also we have discussed residual error analysis and Lyapunov exponent. The applicability and efficacy of this methodology have been demonstrated through this nonlinear system. Additionally, a comparison with existing results highlights the advantages of our numerical approach. All calculations have been done using MATLAB. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics in Science & Engineering is the property of Taylor & Francis Ltd 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: 10.1080/27690911.2024.2424912 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 41 StartPage: 1 Subjects: – SubjectFull: Nonlinear equations Type: general – SubjectFull: Nonlinear functional analysis Type: general – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Lyapunov exponents Type: general – SubjectFull: Nonlinear systems Type: general Titles: – TitleFull: A study for analysing predator–prey ecological system using Legendre polynomial. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Agrawal, Khushbu – PersonEntity: Name: NameFull: Kumar, Sunil – PersonEntity: Name: NameFull: Alkahtani, Badr S. T. – PersonEntity: Name: NameFull: Alzaid, Sara S. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 27690911 Numbering: – Type: volume Value: 32 – Type: issue Value: 1 Titles: – TitleFull: Applied Mathematics in Science & Engineering Type: main |
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