Abstract
Recent studies revealed that chaotic behavior exists in some nonlinear model of diabetes mellitus due to the interaction of externally injected insulin and blood glucose. This work deals with the design of a sliding mode synchronization control technique for a nonlinear model based glucose-insulin regulatory system that takes into account the β-cell kinetics in the model. A sliding mode control technique is used for synchronization between master and slave system where the master system is the healthy diabetes mellitus system and the slave system is the diseased diabetes mellitus system. The simulation results of synchronization are presented to demonstrate the effectiveness of the derived results for curing diseases related to the diabetes mellitus.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Canadian Diabetes Association: Types of diabetes 2017, January 2017. http://www.diabetes.ca/about-diabetes/types-of-diabetes
Ackerman, E., Rosevear, J.W., McGuckin, W.F.: A mathematical model of the glucose-tolerance test. Phys. Med. Biol. 9(2), 203 (1964)
Bajaj, J.S., Rao, G.S., Rao, J.S., Khardori, R.: A mathematical model for insulin kinetics and its application to protein-deficient (malnutrition-related) diabetes mellitus (PDDM). J. Theor. Biol. 126(4), 491–503 (1987)
Sarikaa, W., Lenburya, Y., Kumnungkitb, K., Kunphasuruangc, W.: Modelling glucose-insulin feedback signal interchanges involving β-cells with delays. Differ. Equ. 1(2), 1 (2008)
Chuedoung, M., Sarika, W., Lenbury, Y.: Dynamical analysis of a nonlinear model for glucose–insulin system incorporating delays and β-cells compartment. Nonlinear Anal.: Theory Methods Appl. 71(12), e1048–e1058 (2009)
Li-xiang, L., Hai-peng, P., Bao-zhu, G., Jin-ming, X.: A new sliding mode control for a class of uncertain time-delay chaotic systems. Chin. Phys. 10(8), 708 (2001)
Vasegh, N., Khellat, F.: Projective synchronization of chaotic time-delayed systems via sliding mode controller. Chaos Solitons Fractals 42(2), 1054–1061 (2009)
Palumbo, P., Panunzi, S., De Gaetano, A.: Qualitative behavior of a family of delay-differential models of the glucose-insulin system. Discret. Continuous Dyn. Syst. Ser. B 7(2), 399 (2007)
Prager, R., Wallace, P., Olefsky, J.M.: In vivo kinetics of insulin action on peripheral glucose disposal and hepatic glucose output in normal and obese subjects. J. Clin. Investig. 78(2), 472–481 (1986)
Forrest, E., Robinson, P., Hazel, M.: Insulin, Growth Hormone and Carbohydrate Tolerance in Jamaican Children Rehabilitated from Severe Malnutrition, MedCarib (1925)
Acknowledgments
Authors wish to thank Electrical Engineering Department, NIT Silchar and TEQIP-III for necessary support/funding for presenting this work.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Mohanty, N.P., Dey, R., Roy, B.K. (2020). Synchronization for Nonlinear Time-Delay Chaotic Diabetes Mellitus System via Sliding Mode Control. In: Dawn, S., Balas, V., Esposito, A., Gope, S. (eds) Intelligent Techniques and Applications in Science and Technology. ICIMSAT 2019. Learning and Analytics in Intelligent Systems, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-42363-6_103
Download citation
DOI: https://doi.org/10.1007/978-3-030-42363-6_103
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-42362-9
Online ISBN: 978-3-030-42363-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)