Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells
Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimension...
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| Autor*in: |
Kumari, Preety [verfasserIn] Singh, Swarn [verfasserIn] Singh, Harendra Pal [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© Shiraz University 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Iranian journal of science and technology - Cham, Switzerland : Springer International Pubishing, 2004, 45(2021), 5 vom: 11. Juli, Seite 1743-1756 |
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| Übergeordnetes Werk: |
volume:45 ; year:2021 ; number:5 ; day:11 ; month:07 ; pages:1743-1756 |
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| DOI / URN: |
10.1007/s40995-021-01152-x |
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SPR044957203 |
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| 520 | |a Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. | ||
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10.1007/s40995-021-01152-x doi (DE-627)SPR044957203 (SPR)s40995-021-01152-x-e DE-627 ger DE-627 rakwb eng 500 600 ASE 500 600 ASE Kumari, Preety verfasserin aut Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2021 Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. Glucose (dpeaa)DE-He213 Insulin (dpeaa)DE-He213 -cells (dpeaa)DE-He213 Equilibrium (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Bifurcation (dpeaa)DE-He213 Singh, Swarn verfasserin aut Singh, Harendra Pal verfasserin aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 45(2021), 5 vom: 11. Juli, Seite 1743-1756 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:45 year:2021 number:5 day:11 month:07 pages:1743-1756 https://dx.doi.org/10.1007/s40995-021-01152-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA AR 45 2021 5 11 07 1743-1756 |
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10.1007/s40995-021-01152-x doi (DE-627)SPR044957203 (SPR)s40995-021-01152-x-e DE-627 ger DE-627 rakwb eng 500 600 ASE 500 600 ASE Kumari, Preety verfasserin aut Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2021 Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. Glucose (dpeaa)DE-He213 Insulin (dpeaa)DE-He213 -cells (dpeaa)DE-He213 Equilibrium (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Bifurcation (dpeaa)DE-He213 Singh, Swarn verfasserin aut Singh, Harendra Pal verfasserin aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 45(2021), 5 vom: 11. Juli, Seite 1743-1756 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:45 year:2021 number:5 day:11 month:07 pages:1743-1756 https://dx.doi.org/10.1007/s40995-021-01152-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA AR 45 2021 5 11 07 1743-1756 |
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10.1007/s40995-021-01152-x doi (DE-627)SPR044957203 (SPR)s40995-021-01152-x-e DE-627 ger DE-627 rakwb eng 500 600 ASE 500 600 ASE Kumari, Preety verfasserin aut Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2021 Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. Glucose (dpeaa)DE-He213 Insulin (dpeaa)DE-He213 -cells (dpeaa)DE-He213 Equilibrium (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Bifurcation (dpeaa)DE-He213 Singh, Swarn verfasserin aut Singh, Harendra Pal verfasserin aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 45(2021), 5 vom: 11. Juli, Seite 1743-1756 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:45 year:2021 number:5 day:11 month:07 pages:1743-1756 https://dx.doi.org/10.1007/s40995-021-01152-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA AR 45 2021 5 11 07 1743-1756 |
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10.1007/s40995-021-01152-x doi (DE-627)SPR044957203 (SPR)s40995-021-01152-x-e DE-627 ger DE-627 rakwb eng 500 600 ASE 500 600 ASE Kumari, Preety verfasserin aut Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2021 Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. Glucose (dpeaa)DE-He213 Insulin (dpeaa)DE-He213 -cells (dpeaa)DE-He213 Equilibrium (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Bifurcation (dpeaa)DE-He213 Singh, Swarn verfasserin aut Singh, Harendra Pal verfasserin aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 45(2021), 5 vom: 11. Juli, Seite 1743-1756 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:45 year:2021 number:5 day:11 month:07 pages:1743-1756 https://dx.doi.org/10.1007/s40995-021-01152-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA AR 45 2021 5 11 07 1743-1756 |
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10.1007/s40995-021-01152-x doi (DE-627)SPR044957203 (SPR)s40995-021-01152-x-e DE-627 ger DE-627 rakwb eng 500 600 ASE 500 600 ASE Kumari, Preety verfasserin aut Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Shiraz University 2021 Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. Glucose (dpeaa)DE-He213 Insulin (dpeaa)DE-He213 -cells (dpeaa)DE-He213 Equilibrium (dpeaa)DE-He213 Stability (dpeaa)DE-He213 Bifurcation (dpeaa)DE-He213 Singh, Swarn verfasserin aut Singh, Harendra Pal verfasserin aut Enthalten in Iranian journal of science and technology Cham, Switzerland : Springer International Pubishing, 2004 45(2021), 5 vom: 11. Juli, Seite 1743-1756 (DE-627)SPR038034816 (DE-600)2843077-3 2364-1819 nnns volume:45 year:2021 number:5 day:11 month:07 pages:1743-1756 https://dx.doi.org/10.1007/s40995-021-01152-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA AR 45 2021 5 11 07 1743-1756 |
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Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells |
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Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. © Shiraz University 2021 |
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Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. © Shiraz University 2021 |
| abstract_unstemmed |
Abstract Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and β-cells non-invasively. Therefore, to study the impact of β-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis. © Shiraz University 2021 |
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Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells |
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https://dx.doi.org/10.1007/s40995-021-01152-x |
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Singh, Swarn Singh, Harendra Pal |
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2024-07-04T02:56:44.960Z |
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