^{1}

^{2}

^{1}

^{2}

The synchronization phenomenon that occurs in the Langerhans islets among pancreatic

In nature, an interesting example of synchrony occurs in the coupling of pancreatic

One of the principal characteristics among

The above commentary lays out a number of challenges in one specific area where mathematical models can help us address some of our biggest needs: how

However, if the electrical activity is a result of the internal process that occurs in the cell due to the permeation of some agents and it is known that not all cells burst in synchrony among the islet, then the coupling among cells must not only be given through electrical activity, but through the permeation and concentration of certain agents that regulate the insulin secretion in order that every inactive cell in the cluster begin to oscillate when the release of insulin is required, thus they synchronize with its neighbors. This work proposes a mechanism on how to force an inactive

The paper is organized as follows: In Section

It is known that the mathematical models of the

The mathematical model implemented throughout the paper has been taken from Pernarowski [

The functions

Figure

Time series of the system states given by (

It can be seen that when the concentration of calcium

As Pernarowski has shown in [

Others refer to cells that present continuous spiking activity which is commonly attributed to isolated cells (see [

Based on these characteristic behaviors of

The forced coupling is enabled by discrete time via Poincaré plane as described in [

We are going to consider a master system as

Time series of the

The forced system is given by the following equation:

This system is considered to be an inactive

First we adjust the coupling strength

Time series of the system states

The proposed coupling can make an inactive

In order to force an inactive

Time series of the system state

Now that the inactive cell has been coupled and forced to produce in-phase BEA with the master system, it is straightforward to think if this type of coupling works with the other (active or continuous spiking)

So we considered two more systems to apply the coupling:

Time series of the system states

A similar thing results when coupling a continuous spiking

Based on the above results, we conjecture that even if the coupling is applied to an islet with different behaviors in its containing cells, all cells are constrained to produce BEA in phase. As the BEA is related to the insulin secretion we can say that all cells are synchronized in the release of insulin.

The synchronization in the BEA among

Although the coupling signal

Projection of the master

The autonomous system is monitored by a Poincaré plane with values

L. J. Ontañón-García is a Doctoral Fellow of CONACYT at the Graduate Program on Applied Science at IICO-UASLP. E. Campos-Cantón acknowledges CONACYT for the financial support through Project no. 181002.

^{+}ions on electrical bursting activity of pancreatic

^{2+}and voltage-inactivated Ca

^{2+}channels

^{+}can synchronize bursting oscillations in a model islet of Langerhans