Eur. Phys. J. Special Topics 227, 907–919 (2018)
https://doi.org/10.1140/epjst/e2018-800017-1

Regular Article

Synchronization in a fractional-order model of pancreatic β-cells

¹ Faculty of Electronics Sciences, Autonomous University of Puebla, Av. San Claudio y 18 Sur, Edif. FCE2, 72570 Puebla, Mexico
² Department of Electronic Engineering, City University of Hong Kong, Hong Kong, P.R. China

^a e-mail: erneszambrano@gmail.com

Received: 8 February 2018
Received in final form: 24 March 2018
Published online: 19 October 2018

Abstract

β-cells in the pancreas can be described by a model of coupled biological oscillators with communication links, which can synchronize their electrical activities, giving rise to a square-wave bursting-like insulin release. In fact, β-cells play a vital role in analyzing and characterizing diabetes conditions. This research work studies the synchronization between two fractional-order pancreatic β-cells. Numerically, the fractional-order model of the pancreatic β-cell is analyzed using an algorithm derived from the Grünwald–Letnikov scheme. It is found that, by modifying only the fractional-order while preserving the system parameter values, different types of bursting activities can be observed. Then, synchronization in the coupled fractional-order pancreatic β-cells is studied in detail by considering different patterns of the bursting activities. Simulation results demonstrate that a complete synchronization is effectively attained by choosing a proper value for the control gain.