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| Stability Analysis of a Three-Dimensional Discrete Topp Model |
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| KeyWord:Fixed point, periodic point, local stability, global behavior, regular operator |
| Author Name | Affiliation | | Zafar Boxonov | V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, Universitet str., 100174, Tashkent, Uzbekistan
University of Exact and Social Sciences, Almazor district, Karasaroy street, 341, Tashkent, Uzbekistan | | Utkir Rozikov | V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, Universitet str., 100174, Tashkent, Uzbekistan
National University of Uzbekistan, 4, Universitet str., 100174, Tashkent, Uzbekistan
Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China |
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| Abstract: |
| Mathematical models of glucose, insulin, and pancreatic beta cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the discrete-time dynamics of the Topp model to represent these interactions. We perform a comprehensive analysis of the system's trajectory, examining both local and global behavior. First, we establish the invariance of the positive trajectory and analyze the existence of fixed points. Then, we conduct a complete stability analysis, determining the local and global asymptotic stability of these fixed points. Finally, numerical examples validate the effectiveness and applicability of our theoretical findings. Additionally, we provide biological interpretations of our results. |
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