分数阶血糖-胰岛素调节系统的混沌动力学

Karthikeyan RAJAGOPAL; Atiyeh BAYANI; Sajad JAFARI; Anitha KARTHIKEYAN; Iqtadar HUSSAIN

doi:10.1631/FITEE.1900104

Your Location：

Home >

Browse articles >

分数阶血糖-胰岛素调节系统的混沌动力学

常规文章 | Updated：2022-05-19

- 分数阶血糖-胰岛素调节系统的混沌动力学
- Chaotic dynamics of a fractional order glucose-insulin regulatory system
- 信息与电子工程前沿（英文） 2020年21卷第7期页码：1108-1118
- Affiliations：
  
  Center for Nonlinear Dynamics, Defence University, Bishoftu 1041, Ethiopia
  Institute of Energy, Mekelle University, Mekelle 231, Ethiopia
  Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 159163-4311, Iran
  Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700010, Vietnam
  Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
- Author bio：
  
  Karthikeyan RAJAGOPAL, E-mail: rkarthiekeyan@gmail.com
  [ "Atiyeh BAYANI, E-mail: atiyeh.bayani@yahoo.com" ]
  [ "Sajad JAFARI, E-mail:sajad.jafari@tdtu.edu.vn" ]
  [ "Anitha KARTHIKEYAN, E-mail: mrs.anithakarthikeyan@gmail.com" ]
  [ "Iqtadar HUSSAIN, E-mail: iqtadarqau@gmail.com" ]
- Funds：
  
  Project supported by the Institute of Research and Development, Defence University, Ethiopia (No. DU/IRD/002)
- DOI：10.1631/FITEE.1900104
  中图分类号： O415.5
- 收稿：2019-02-24，
  
  修回：2019-10-18，
  
  网络出版：2019-12-21，
  
  纸质出版：2020-07
- Accepted：
Scan QR Code
Karthikeyan RAJAGOPAL, Atiyeh BAYANI, Sajad JAFARI, 等. 分数阶血糖-胰岛素调节系统的混沌动力学[J]. 信息与电子工程前沿（英文）, 2020,21(7):1108-1118.

Karthikeyan RAJAGOPAL, Atiyeh BAYANI, Sajad JAFARI, et al. Chaotic dynamics of a fractional order glucose-insulin regulatory system[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(7): 1108-1118.
Karthikeyan RAJAGOPAL, Atiyeh BAYANI, Sajad JAFARI, 等. 分数阶血糖-胰岛素调节系统的混沌动力学[J]. 信息与电子工程前沿（英文）, 2020,21(7):1108-1118. DOI： 10.1631/FITEE.1900104.

Karthikeyan RAJAGOPAL, Atiyeh BAYANI, Sajad JAFARI, et al. Chaotic dynamics of a fractional order glucose-insulin regulatory system[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(7): 1108-1118. DOI： 10.1631/FITEE.1900104.

摘要

本文推导血糖-胰岛素调节系统的分数阶模型。现有文献已证明复杂系统的分数阶分析能够揭示系统有趣且未知的特征。本文揭示血糖-胰岛素系统在其分数阶形式下表现出多稳定性与反单调性。为体现分数阶分析的有效性，进行了所有数值模拟，包括平衡点稳定性、李雅普诺夫指数、分叉图等。详细研究由未经调节的血糖-胰岛素系统引起的各种生物紊乱，这将有助于更好地理解调节系统。

Abstract

The fractional order model of a glucose-insulin regulatory system is derived and presented. It has been extensively proved in the literature that fractional order analysis of complex systems can reveal interesting and unexplored features of the system. In our investigations we have revealed that the glucose-insulin regulatory system shows multistability and antimonotonicity in its fractional order form. To show the effectiveness of fractional order analysis

all numerical investigations like stability of the equilibrium points

Lyapunov exponents

and bifurcation plots are derived. Various biological disorders caused by an unregulated glucose-insulin system are studied in detail. This may help better understand the regulatory system.

关键词

Keywords

references

E Ackerman , , , JW Rosevear , , , WF McGuckin . . A mathematical model of the glucose-tolerance test . . Phys Med Biol , , 1964 . . 9 ( ( 2 ): ): 203 - - 213 . . DOI: 10.1088/0031-9155/9/2/307 http://doi.org/10.1088/0031-9155/9/2/307 . .

G Adomian . . A review of the decomposition method and some recent results for nonlinear equations . . Math Comput Model , , 1990 . . 13 ( ( 7 ): ): 17 - - 43 . . DOI: 10.1016/0895-7177(90)90125-7 http://doi.org/10.1016/0895-7177(90)90125-7 . .

Z Aram , , , S Jafari , , , J Ma , , , 等 . . Using chaotic artificial neural networks to model memory in the brain . . Commun Nonl Sci Numer Simul , , 2017 . . 44 449 - - 459 . . DOI: 10.1016/j.cnsns.2016.08.025 http://doi.org/10.1016/j.cnsns.2016.08.025 . .

G Baghdadi , , , S Jafari , , , JS Sprott , , , 等 . . A chaotic model of sustaining attention problem in attention deficit disorder . . Commun Nonl Sci Numer Simul , , 2015 . . 20 ( ( 1 ): ): 174 - - 185 . . DOI: 10.1016/j.cnsns.2014.05.015 http://doi.org/10.1016/j.cnsns.2014.05.015 . .

JS Bajaj , , , GS Rao , , , JS Rao , , , 等 . . A mathematical model for insulin kinetics and its application to protein-deficient (malnutrition-related) diabetes mellitus (PDDM) . . J Theor Biol , , 1987 . . 126 ( ( 4 ): ): 491 - - 503 . . DOI: 10.1016/S0022-5193(87)80154-6 http://doi.org/10.1016/S0022-5193(87)80154-6 . .

BC Bao , , , PY Wu , , , H Bao , , , 等 . . Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in third-order autonomous memristive oscillator . . Chaos Sol Fract , , 2018 . . 106 161 - - 170 . . DOI: 10.1016/j.chaos.2017.11.025 http://doi.org/10.1016/j.chaos.2017.11.025 . .

H Bao , , , N Wang , , , BC Bao , , , 等 . . Initial condition- dependent dynamics and transient period in memristor- based hypogenetic jerk system with four line equilibria . . Commun Nonl Sci Numer Simul , , 2018 . . 57 264 - - 275 . . DOI: 10.1016/j.cnsns.2017.10.001 http://doi.org/10.1016/j.cnsns.2017.10.001 . .

A Buscarino , , , L Fortuna , , , M Frasca , , , 等 . . Synchronization of chaotic systems with activity-driven time-varying interactions . . J Compl Netw , , 2018 . . 6 ( ( 2 ): ): 173 - - 186 . . DOI: 10.1093/comnet/cnx027 http://doi.org/10.1093/comnet/cnx027 . .

R Caponetto , , , G Dongola , , , L Fortuna , , , 等 . . New results on the synthesis of FO-PID controllers . . Commun Nonl Sci Numer Simul , , 2010 . . 15 ( ( 4 ): ): 997 - - 1007 . . DOI: 10.1016/j.cnsns.2009.05.040 http://doi.org/10.1016/j.cnsns.2009.05.040 . .

A Charef , , , HH Sun , , , YY Tsao , , , 等 . . Fractal system as represented by singularity function . . IEEE Trans Autom Contr , , 1992 . . 37 ( ( 9 ): ): 1465 - - 1470 . . DOI: 10.1109/9.159595 http://doi.org/10.1109/9.159595 . .

DY Chen , , , YX Liu , , , XY Ma , , , 等 . . Control of a class of fractional-order chaotic systems via sliding mode . . Nonl Dynam , , 2012 . . 67 ( ( 1 ): ): 893 - - 901 . . DOI: 10.1007/s11071-011-0002-x http://doi.org/10.1007/s11071-011-0002-x . .

M Chuedoung , , , W Sarika , , , Y Lenbury . . Dynamical analysis of a nonlinear model for glucose-insulin system incorporating delays and β -cells compartment . . Nonl Anal Theory Methods Appl , , 2009 . . 71 ( ( 12 ): ): e1048 - - e1058 . . DOI: 10.1016/j.na.2009.01.129 http://doi.org/10.1016/j.na.2009.01.129 . .

MF Danca . . Lyapunov exponents of a class of piecewise continuous systems of fractional order . . Nonl Dynam , , 2015 . . 81 ( ( 1-2 ): ): 227 - - 237 . . DOI: 10.1007/s11071-015-1984-6 http://doi.org/10.1007/s11071-015-1984-6 . .

K Diethelm . . An algorithm for the numerical solution of differential equations of fractional order . . Electron Trans Numer Anal , , 1997 . . 5 1 - - 6 . . . .

K Diethelm . . The Analysis of Fractional Differential Equations: an Application-Oriented Exposition Using Differential Operators of Caputo Type , , : : Berlin, Germany Springer , , 2010 . . DOI: 10.1007/978-3-642-14574-2 http://doi.org/10.1007/978-3-642-14574-2 . .

K Diethelm , , , NJ Ford . . Analysis of fractional differential equations . . J Math Anal Appl , , 2002 . . 265 ( ( 2 ): ): 229 - - 248 . . DOI: 10.1006/jmaa.2000.7194 http://doi.org/10.1006/jmaa.2000.7194 . .

K Diethelm , , , AD Freed . . The FracPECE subroutine for the numerical solution of differential equations of fractional order . . Proc Forschung und Wissenschaftliches Rechnen , , 1999 . . p.57 - - 71 . . . .

K Diethelm , , , NJ Ford , , , AD Freed . . Detailed error analysis for a fractional Adams method . . Numer Algor , , 2004 . . 36 ( ( 1 ): ): 31 - - 52 . . DOI: 10.1023/B:NUMA.0000027736.85078.be http://doi.org/10.1023/B:NUMA.0000027736.85078.be . .

D Dudkowski , , , S Jafari , , , T Kapitaniak , , , 等 . . Hidden attractors in dynamical systems . . Phys Rep , , 2016 . . 637 1 - - 50 . . DOI: 10.1016/j.physrep.2016.05.002 http://doi.org/10.1016/j.physrep.2016.05.002 . .

AEA Elsadany , , , HA El-Metwally , , , EM Elabbasy , , , 等 . . Chaos and bifurcation of a nonlinear discrete prey- predator system . . Comput Ecol Softw , , 2012 . . 2 ( ( 3 ): ): 169 - - 180 . . . .

R Garrappa . . Predictor-corrector PECE Method for Fractional Differential Equations . . MATLAB Central , , 2011 . . .

JM Ginoux , , , H Ruskeep , , , M Perc , , , 等 . . Is type 1 diabetes a chaotic phenomenon . . Chaos Sol Fract , , 2018 . . 111 198 - - 205 . . DOI: 10.1016/j.chaos.2018.03.033 http://doi.org/10.1016/j.chaos.2018.03.033 . .

JM Ginoux , , , R Naeck , , , YB Ruhomally , , , 等 . . Chaos in a predator-prey-based mathematical model for illicit drug consumption . . Appl Math Comput , , 2019 . . 347 502 - - 513 . . DOI: 10.1016/j.amc.2018.10.089 http://doi.org/10.1016/j.amc.2018.10.089 . .

F Hadaeghi , , , MRH Golpayegani , , , S Jafari , , , 等 . . Toward a complex system understanding of bipolar disorder: a chaotic model of abnormal circadian activity rhythms in euthymic bipolar disorder . . Aust New Zealand J Psych , , 2016 . . 50 ( ( 8 ): ): 783 - - 792 . . DOI: 10.1177/0004867416642022 http://doi.org/10.1177/0004867416642022 . .

K Hansen . . Oscillations in the blood sugar in fasting normal persons . . J Int Med , , 1923 . . 57 ( ( S4 ): ): 27 - - 32 . . DOI: 10.1111/j.0954-6820.1923.tb16365.x http://doi.org/10.1111/j.0954-6820.1923.tb16365.x . .

RC Hilborn . . Chaos and Nonlinear Dynamics: an Introduction for Scientists and Engineers (2 nd Ed.) , , : : Oxford, USA Oxford University Press , , 2000 . . .

TA Holt . . Nonlinear dynamics and diabetes control . . Endocrinologist , , 2003 . . 13 ( ( 6 ): ): 452 - - 456 . . DOI: 10.1097/01.ten.0000089917.44590.5d http://doi.org/10.1097/01.ten.0000089917.44590.5d . .

H Korn , , , P Faure . . Is there chaos in the brain. Ⅱ. Experimental evidence and related models . . Comptes Rendus Biol , , 2003 . . 326 ( ( 9 ): ): 787 - - 840 . . DOI: 10.1016/j.crvi.2003.09.011 http://doi.org/10.1016/j.crvi.2003.09.011 . .

MH Kroll . . Biological variation of glucose and insulin includes a deterministic chaotic component . . Biosystems , , 1999 . . 50 ( ( 3 ): ): 189 - - 201 . . DOI: 10.1016/S0303-2647(99)00007-6 http://doi.org/10.1016/S0303-2647(99)00007-6 . .

PRAV Kumar , , , V Sreedevi . . A review on influence of antidiabetic medications on quality of life . . Eur J Pharm Med Res , , 2017 . . 4 ( ( 5 ): ): 276 - - 288 . . . .

V Lakshmikantham , , , AS Vatsala . . Basic theory of fractional differential equations . . Nonl Anal Theory Methods Appl , , 2008 . . 69 ( ( 8 ): ): 2677 - - 2682 . . DOI: 10.1016/j.na.2007.08.042 http://doi.org/10.1016/j.na.2007.08.042 . .

DA Lang , , , DR Matthews , , , J Peto , , , 等 . . Cyclic oscillations of basal plasma glucose and insulin concentrations in human beings . . N Engl J Med , , 1979 . . 301 ( ( 19 ): ): 1023 - - 1027 . . DOI: 10.1056/NEJM197911083011903 http://doi.org/10.1056/NEJM197911083011903 . .

GA Leonov , , , NV Kuznetsov , , , VI Vagaitsev . . Localization of hidden Chua's attractors . . Phys Lett A , , 2011 . . 375 ( ( 23 ): ): 2230 - - 2233 . . DOI: 10.1016/j.physleta.2011.04.037 http://doi.org/10.1016/j.physleta.2011.04.037 . .

GA Leonov , , , NV Kuznetsov , , , VI Vagaitsev . . Hidden attractor in smooth Chua systems . . Phys D , , 2012 . . 241 ( ( 18 ): ): 1482 - - 1486 . . DOI: 10.1016/j.physd.2012.05.016 http://doi.org/10.1016/j.physd.2012.05.016 . .

GA Leonov , , , NV Kuznetsov , , , TN Mokaev . . Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity . . Commun Nonl Sci Numer Simul , , 2015a . . 28 ( ( 1-3 ): ): 166 - - 174 . . DOI: 10.1016/j.cnsns.2015.04.007 http://doi.org/10.1016/j.cnsns.2015.04.007 . .

GA Leonov , , , NV Kuznetsov , , , TN Mokaev . . Homoclinic orbits, and self-excited and hidden attractors in a Lorenz- like system describing convective fluid motion . . Eur Phys J Spec Top , , 2015b . . 224 ( ( 8 ): ): 1421 - - 1458 . . DOI: 10.1140/epjst/e2015-02470-3 http://doi.org/10.1140/epjst/e2015-02470-3 . .

JJ Liszka-Hackzell . . Prediction of blood glucose levels in diabetic patients using a hybrid AI technique . . Comput Biomed Res , , 1999 . . 32 ( ( 2 ): ): 132 - - 144 . . DOI: 10.1006/cbmr.1998.1506 http://doi.org/10.1006/cbmr.1998.1506 . .

GD Molnar , , , WF Taylor , , , AL Langworthy . . Plasma immunoreactive insulin patterns in insulin-treated diabetics. Studies during continuous blood glucose monitoring . . Mayo Clin Proc , , 1972 . . 47 ( ( 10 ): ): 709 - - 719 . . . .

I Petr . . Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , , : : Berlin, Germany Springer , , 2011 . . DOI: 10.1007/978-3-642-18101-6 http://doi.org/10.1007/978-3-642-18101-6 . .

EF Pfeiffer , , , C Meyerhoff , , , F Bischof , , , 等 . . On line continuous monitoring of subcutaneous tissue glucose is feasible by combining portable glucosensor with microdialysis . . Horm Metab Res , , 1993 . . 25 ( ( 2 ): ): 121 - - 124 . . DOI: 10.1055/s-2007-1002057 http://doi.org/10.1055/s-2007-1002057 . .

VT Pham , , , M Frasca , , , R Caponetto , , , 等 . . Control and synchronization of fractional-order differential equations of phase-locked loop . . Chaot Model Simul , , 2012 . . 4 623 - - 631 . . . .

H Preissl , , , W Lutzenberger , , , F Pulvermller . . Is there chaos in the brain . . Behav Brain Sci , , 1996 . . 19 ( ( 2 ): ): 307 - - 308 . . DOI: 10.1017/S0140525X00042825 http://doi.org/10.1017/S0140525X00042825 . .

K Rajagopal , , , A Akgul , , , S Jafari , , , 等 . . Chaotic chameleon: dynamic analyses, circuit implementation, FPGA design and fractional-order form with basic analyses . . Chaos Sol Fract , , 2017a . . 103 476 - - 487 . . DOI: 10.1016/j.chaos.2017.07.007 http://doi.org/10.1016/j.chaos.2017.07.007 . .

K Rajagopal , , , A Karthikeyan , , , AK Srinivasan . . FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization . . Nonl Dynam , , 2017b . . 87 ( ( 4 ): ): 2281 - - 2304 . . DOI: 10.1007/s11071-016-3189-z http://doi.org/10.1007/s11071-016-3189-z . .

K Rajagopal , , , A Karthikeyan , , , P Duraisamy , , , 等 . . Bifurcation, chaos and its control in a fractional order power system model with uncertainties . . Asian J Contr , , 2019 . . 21 ( ( 1 ): ): 184 - - 193 . . DOI: 10.1002/asjc.1826 http://doi.org/10.1002/asjc.1826 . .

FA Rihan , , , A Hashish , , , F Al-Maskari , , , 等 . . Dynamics of tumor-immune system with fractional-order . . J Tumor Res , , 2016 . . 2 ( ( 1 ): ): 1000109J . .

A Rocco , , , BJ West . . Fractional calculus and the evolution of fractal phenomena . . Phys A , , 1999 . . 265 ( ( 3-4 ): ): 535 - - 546 . . DOI: 10.1016/S0378-4371(98)00550-0 http://doi.org/10.1016/S0378-4371(98)00550-0 . .

SJ Schiff , , , K Jerger , , , DH Duong , , , 等 . . Controlling chaos in the brain . . Nature , , 1994 . . 370 ( ( 6491 ): ): 615 - - 620 . . DOI: 10.1038/370615a0 http://doi.org/10.1038/370615a0 . .

PS Shabestari , , , S Panahi , , , B Hatef , , , 等 . . A new chaotic model for glucose-insulin regulatory system . . Chaos Sol Fract , , 2018 . . 112 44 - - 51 . . DOI: 10.1016/j.chaos.2018.04.029 http://doi.org/10.1016/j.chaos.2018.04.029 . .

PR Sharma , , , MD Shrimali , , , A Prasad , , , 等 . . Control of multistability in hidden attractors . . Eur Phys J Spec Top , , 2015a . . 224 ( ( 8 ): ): 1485 - - 1491 . . DOI: 10.1140/epjst/e2015-02474-y http://doi.org/10.1140/epjst/e2015-02474-y . .

PR Sharma , , , MD Shrimali , , , A Prasad , , , 等 . . Controlling dynamics of hidden attractors . . Int J Bifurc Chaos , , 2015b . . 25 ( ( 4 ): ): 1550061 DOI: 10.1142/S0218127415500613 http://doi.org/10.1142/S0218127415500613 . .

MS Tavazoei , , , M Haeri . . Unreliability of frequency- domain approximation in recognising chaos in fractional- order systems . . IET Signal Process , , 2007 . . 1 ( ( 4 ): ): 171 - - 181 . . DOI: 10.1049/iet-spr:20070053 http://doi.org/10.1049/iet-spr:20070053 . .

MF Tolba , , , AM AbdelAty , , , NS Soliman , , , 等 . . FPGA implementation of two fractional order chaotic systems . . AEU-Int J Electron Commun , , 2017 . . 78 162 - - 172 . . DOI: 10.1016/j.aeue.2017.04.028 http://doi.org/10.1016/j.aeue.2017.04.028 . .

G Tsirimokou , , , C Psychalinos , , , AS Elwakil , , , 等 . . Electronically tunable fully integrated fractional-order resonator . . IEEE Trans Circ Syst Ⅱ , , 2018 . . 65 ( ( 2 ): ): 166 - - 170 . . DOI: 10.1109/TCSII.2017.2684710 http://doi.org/10.1109/TCSII.2017.2684710 . .

A Wolf , , , JB Swift , , , HL Swinney , , , 等 . . Determining Lyapunov exponents from a time series . . Phys D , , 1985 . . 16 ( ( 3 ): ): 285 - - 317 . . DOI: 10.1016/0167-2789(85)90011-9 http://doi.org/10.1016/0167-2789(85)90011-9 . .

C Yin , , , SM Zhong , , , WF Chen . . Design of sliding mode controller for a class of fractional-order chaotic systems . . Commun Nonl Sci Numer Simul , , 2012 . . 17 ( ( 1 ): ): 356 - - 366 . . DOI: 10.1016/j.cnsns.2011.04.024 http://doi.org/10.1016/j.cnsns.2011.04.024 . .

CN Zhao , , , DY Xue , , , YQ Chen . . A fractional order PID tuning algorithm for a class of fractional order plants . . Proc IEEE Int Conf on Mechatronics and Automation , , 2005 . . p.216 - - 221 . . DOI: 10.1109/ICMA.2005.1626550 http://doi.org/10.1109/ICMA.2005.1626550 . .

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

A geographic information encryption system based on Chaos-LSTM and chaos sequence proliferation

Motor speed estimation and failure detection of a small UAV using density of maxima

Dynamics of a neuron exposed to integer-and fractional-order discontinuous external magnetic flux