KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction
The behavior of the simplest realistic Oregonator model of the BZ-reaction from the perspective of KCC theory has been investigated. In order to reduce the complexity of the model, we initially transformed the first-order differential equation of the Oregonator model into a system of second-order di...
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MDPI AG
2023-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/12/1133 |
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| author | M. K. Gupta Abha Sahu C. K. Yadav Anjali Goswami Chetan Swarup |
| author_facet | M. K. Gupta Abha Sahu C. K. Yadav Anjali Goswami Chetan Swarup |
| author_sort | M. K. Gupta |
| collection | DOAJ |
| description | The behavior of the simplest realistic Oregonator model of the BZ-reaction from the perspective of KCC theory has been investigated. In order to reduce the complexity of the model, we initially transformed the first-order differential equation of the Oregonator model into a system of second-order differential equations. In this approach, we describe the evolution of the Oregonator model in geometric terms, by considering it as a geodesic in a Finsler space. We have found five KCC invariants using the general expression of the nonlinear and Berwald connections. To understand the chaotic behavior of the Oregonator model, the deviation vector and its curvature around equilibrium points are studied. We have obtained the necessary and sufficient conditions for the parameters of the system in order to have the Jacobi stability near the equilibrium points. Further, a comprehensive examination was conducted to compare the linear stability and Jacobi stability of the Oregonator model at its equilibrium points, and We highlight these instances with a few illustrative examples. |
| first_indexed | 2024-03-08T20:59:47Z |
| format | Article |
| id | doaj.art-79d393e0422048b49e8beeb10a041b3e |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T20:59:47Z |
| publishDate | 2023-12-01 |
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| series | Axioms |
| spelling | doaj.art-79d393e0422048b49e8beeb10a041b3e2023-12-22T13:53:20ZengMDPI AGAxioms2075-16802023-12-011212113310.3390/axioms12121133KCC Theory of the Oregonator Model for Belousov-Zhabotinsky ReactionM. K. Gupta0Abha Sahu1C. K. Yadav2Anjali Goswami3Chetan Swarup4Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, IndiaDepartment of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, IndiaDepartment of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, IndiaDepartment of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaDepartment of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaThe behavior of the simplest realistic Oregonator model of the BZ-reaction from the perspective of KCC theory has been investigated. In order to reduce the complexity of the model, we initially transformed the first-order differential equation of the Oregonator model into a system of second-order differential equations. In this approach, we describe the evolution of the Oregonator model in geometric terms, by considering it as a geodesic in a Finsler space. We have found five KCC invariants using the general expression of the nonlinear and Berwald connections. To understand the chaotic behavior of the Oregonator model, the deviation vector and its curvature around equilibrium points are studied. We have obtained the necessary and sufficient conditions for the parameters of the system in order to have the Jacobi stability near the equilibrium points. Further, a comprehensive examination was conducted to compare the linear stability and Jacobi stability of the Oregonator model at its equilibrium points, and We highlight these instances with a few illustrative examples.https://www.mdpi.com/2075-1680/12/12/1133Oregonator modelKCC theoryBerwald connectionJacobi stability |
| spellingShingle | M. K. Gupta Abha Sahu C. K. Yadav Anjali Goswami Chetan Swarup KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction Axioms Oregonator model KCC theory Berwald connection Jacobi stability |
| title | KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction |
| title_full | KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction |
| title_fullStr | KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction |
| title_full_unstemmed | KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction |
| title_short | KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction |
| title_sort | kcc theory of the oregonator model for belousov zhabotinsky reaction |
| topic | Oregonator model KCC theory Berwald connection Jacobi stability |
| url | https://www.mdpi.com/2075-1680/12/12/1133 |
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