Persistence and global attractivity for a discretized version of a general model of glucose-insulin interaction

• Autorzy: Huong D. C.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we construct a non-standard finite difference scheme for a general model of glucose-insulin interaction. We establish some new sufficient conditions to ensure that the discretized model preserves the persistence and global attractivity of the continuous model. One of the main findings in this paper is that we derive two important propositions (Proposition 3.1 and Proposition 3.2) which are used to prove the global attractivity of the discretized model. Furthermore, when investigating the persistence and, in some cases, the global attractivity of the discretized model, the nonlinear functions f and h are not required to be differentiable. Hence, our results are more realistic because the statistical data of glucose and insulin are collected and reported in discrete time. We also present some numerical examples and their simulations to illustrate our results.

Słowa kluczowe

EN

delay difference equation; ω-limit set of a persistent solution; full time solution; non-standard difference; numerical discretized model

PL

równania różnicowe; różnica nietypowa; numeryczny model zdyskretyzowany

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 3
• Strony: 302--318
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Huong D. C.

• Department of Mathematics, Quynhon University 170 An Duong Vuong Quy Nhon, Binh Dinh, Viet Nam

Bibliografia

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• [3] P. Palumbo, S. Panunzi, A. De Gaetano, Qualitative behavior of a family of delay-differential models of the glucose-insulin system, Discrete Contin. Dyn. Syst. Ser. B 7 (2007), 399–424.
• [4] L. Li, W. Zheng, Global stability of a delay model of glucose-insulin interaction, Math. Comput. Modelling 52 (2010), 472–480.
• [5] J. D. Lambert, Numerical Methods for Ordinary Differential Systems: the Initial Value Problem , Wiley, Chichester, 1994.
• [6] R. E. Mickens, Nonstandard Finite Difference Model of Differential Equations, World Scientific, Singapore, 1994.
• [7] R. E. Mickens, Application of Nonstandard Finite Difference Schemes, World Scientific, Singapore, 2000.
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• [12] M. Chen, D. P. Clemence, Stability properties of a nonstandard finite difference scheme for a hantavirus epidemic model, J. Difference Equ. Appl. 12 (2006), 1243–1256.
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• [14] D. C. Huong, N. V. Mau, On a nonlinear difference equation with variable delay, Demonstratio Math. 46 (2013), 123–135.
• [15] D. V. Giang, Y. Lenbury, A. De Gaetano, P. Palumbo, Delay models of glucose-insulin systems: Global stability and oscillated solutions conditional on delays, J. Math. Anal. Appl. 343 (2008), 996–1006.
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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.