Abstract
For studying biological conditions with higher precision, the memory characteristics defined by the fractional-order versions of living dynamical systems have been pointed out as a meaningful approach. Therefore, we analyze the dynamics of a glucose-insulin regulatory system by applying a non-local fractional operator in order to represent the memory of the underlying system, and whose state-variables define the population densities of insulin, glucose, and β-cells, respectively. We focus mainly on four parameters that are associated with different disorders (type 1 and type 2 diabetes mellitus, hypoglycemia, and hyperinsulinemia) to determine their observation ranges as a relation to the fractional-order. Like many preceding works in biosystems, the resulting analysis showed chaotic behaviors related to the fractional-order and system parameters. Subsequently, we propose an active control scheme for forcing the chaotic regime (an illness) to follow a periodic oscillatory state, i.e., a disorder-free equilibrium. Finally, we also present the electronic realization of the fractional glucose-insulin regulatory model to prove the conceptual findings.
Highlights
Homeostasis is the tendency of organisms to auto-regular and maintain their internal environment in a stable state [1], For instance, an excellent model to describe the homeostatic process in the organism is the glucose-insulin system [1,2]
We observed that the fractional-order q produces a shift concerning the bifurcation diagram showed in Ref. [46]. This consideration exemplifies the importance of considering a fractional-order derivative in the dynamical system, i.e., when values lesser than a1 = 2.3 are set in the integer-order system [46], chaotic behavior was observed; this limit is different for the fractional-order model (a1 ≤ 1.45)
The unbounded behavior is represented by the green regions; chaotic behavior is denoted by red regions and the healthy behavior is given by the blue regions
Summary
Homeostasis is the tendency of organisms to auto-regular and maintain their internal environment in a stable state [1], For instance, an excellent model to describe the homeostatic process in the organism is the glucose-insulin system [1,2]. In [18], the transmission issues of a susceptible-infected-recovered model were analyzed They found a proper yield of memory of the fractional-order systems to forecast the pandemic spread. The study of fractional-order biological models continues been critical for an accurate analysis of several health conditions, as well as being essential to understanding this significant open-topic. The experimental verification of fractional-order models is a topic that has been attracting the attention of researchers [35,36,37,38,39] In this scenario, ARM-based embedded systems have become in a central block integrated with non-embedded technologies, such as FPGAs, DSPs, and microcontrollers.
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