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Demonstratio Mathematica

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Volume 49, Issue 3


Persistence and Global Attractivity for a Discretized Version of a General Model of Glucose-Insulin Interaction

Dinh Cong Huong
Published Online: 2016-08-20 | DOI: https://doi.org/10.1515/dema-2016-0026


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.

Keywords: delay difference equations; !-limit set of a persistent solution; full time solution; non-standard difference; numerical discretized model


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About the article

Received: 2014-09-08

Published Online: 2016-08-20

Published in Print: 2016-09-01

Citation Information: Demonstratio Mathematica, Volume 49, Issue 3, Pages 302–318, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.1515/dema-2016-0026.

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© by Dinh Cong Huong. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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