文章基本信息

标题：Bifurcations in a delayed fractional model of glucose–insulin interaction with incommensurate orders
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作者：Natchapon Lekdee ; Sekson Sirisubtawee ; Sanoe Koonprasert 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-22
DOI：10.1186/s13662-019-2262-6
出版社：Hindawi Publishing Corporation
摘要：This paper proposes a delayed fractional-order model of glucose–insulin interaction in the sense of the Caputo fractional derivative with incommensurate orders. This fractional-order model is developed from the first-order model of glucose–insulin interaction. Firstly, we investigate the non-negativity and the boundedness of solutions of the fractional-order model. Secondly, the stability and the bifurcation of the model are studied by separating the associated characteristic equation of the model into its real and imaginary parts and taking a time delay as the bifurcation parameter. The asymptotic stability and the Hopf bifurcation are discussed via the condition of creation of the bifurcation. Furthermore, it is shown that the onset of the bifurcation is related to the fractional orders of the model. Finally, some numerical simulations of the model using the Adam–Bashforth–Moulton predictor corrector scheme are demonstrated to support our obtained theoretical results.
关键词：Hopf bifurcation;Glucose-Insulin;Fractional model;Time delay;Stability analysis