A new chaotic model for glucose-insulin regulatory system

Shabestari, Payam Sadeghi; Panahi, Shirin; Hatef, Boshra; Jafari, Sajad; Sprott, Julien Clinton

doi:10.1016/j.chaos.2018.04.029

Cited by 39 publications

(16 citation statements)

References 50 publications

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“…The benefits of fractional-order are mainly to capture the entire time evolution for physical processes, being a kind of memory index, as well as more degrees of freedom for the resulting models. The analysis conducted in this work is inspired by the glucose-insulin regulatory system in [46], as given in Equation (1). This model was derived from the Ackerman, Bajaj, and Rao, and predator-prey Volterra models.…”

Section: Fractional-order Glucose-insulin Regulatory Systemmentioning

confidence: 99%

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The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

2020

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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.

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Section: Fractional-order Glucose-insulin Regulatory Systemmentioning

confidence: 99%

“…Additionally, the increment rate of insulin concentrations released by b-cells is provided by a 7 . Finally, the increasing rate of the β-cells provoked, when the glucose levels also grow, is given by a 15 [46]. From the nature of how this system was conceived, the parameters must be nonnegative [46].…”

Section: Fractional-order Glucose-insulin Regulatory Systemmentioning

confidence: 99%

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

2020

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“…Characterized with ergodicity, nonperiodicity and random, chaos can be able to provide an approach to solve the problem [6][7][8][9][10]. In this paper, chaotic mapping will be introduced into PSO to design the optimization algorithm of BP neural network to achieve URL security detection with better performance.…”

Section: Introductionmentioning

confidence: 99%

URL Security Detection on the Basis of a New Optimization Algorithm

Wang¹,

Zhang²,

Liu³

et al. 2020

ACC

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In this paper, the issue on URL security detection is investigated. Considering the problems about local optimization and speed, chaotic mapping is introduced into PSO to design the optimization algorithm for BP neural network to achieve URL security detection with better performance. Some typical experimental examples are included and corresponding results display the advantage and effectiveness of the optimization algorithm proposed.

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“…In particular, many glucose-insulin interactions have been investigated using first-order differential equation models (see, e.g., [8,11,[29][30][31][32][33][34][35]). However, there were some recent research evidences of the significant usefulness of fractional-order derivatives in constructing glucose-insulin models.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations in a delayed fractional model of glucose–insulin interaction with incommensurate orders

2019

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This paper proposes a delayed fractional-order model of glucose-insulin interaction in the sense of the Caputo fractional derivative with incommensurate orders. This fractional-order model is developed from the first-order model of glucose-insulin interaction. Firstly, we investigate the non-negativity and the boundedness of solutions of the fractional-order model. Secondly, the stability and the bifurcation of the model are studied by separating the associated characteristic equation of the model into its real and imaginary parts and taking a time delay as the bifurcation parameter. The asymptotic stability and the Hopf bifurcation are discussed via the condition of creation of the bifurcation. Furthermore, it is shown that the onset of the bifurcation is related to the fractional orders of the model. Finally, some numerical simulations of the model using the Adam-Bashforth-Moulton predictor corrector scheme are demonstrated to support our obtained theoretical results.

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A new chaotic model for glucose-insulin regulatory system

Cited by 39 publications

References 50 publications

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

URL Security Detection on the Basis of a New Optimization Algorithm

Bifurcations in a delayed fractional model of glucose–insulin interaction with incommensurate orders

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