A New Model For Endocrine Glucose-Insulin Regulatory System

To gain insight into complex biological endocrine glucose-insulin regulatory system where the interactions of components of the metabolic system and time-delay inherent in the biological system give rise to complex dynamics. The modeling has increased interest and importance in physiological research and enhanced the medical treatment protocols. This brief contains a new model using time delay differential equations, which give an accurate result by utilizing two explicit time delays. The bifurcation analysis has been conducted to find the main system parameters bifurcation values and corresponding system behaviors. The results found consistent with the biological experiments results.

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A GAME THEORETICAL MODEL OF INTERNATIONAL FISHING WITH TIME DELAY

International Game Theory Review ◽

10.1142/s0219198904000277 ◽

2004 ◽

Vol 06 (03) ◽

pp. 391-415

Author(s):

FERENC SZIDAROVSZKY ◽

ANDREW ENGEL ◽

CARL CHIARELLA

Keyword(s):

Asymptotic Behavior ◽

Time Delay ◽

Time Delays ◽

Economic Structure ◽

Fish Stock ◽

Time Lags ◽

First Case ◽

Special Cases ◽

Cyclical Behavior ◽

Insight Into

This paper studies the evolution of a fish stock that is exploited by an n-country oligopoly. A feature of the economic structure is that the countries exploiting the fish stock experience time lags in obtaining and implementing information on the fish stock. The local asymptotic behavior of the equilibrium is analyzed, including asymptotic stability, instability, and cyclical behavior. Under the assumption of symmetric countries, two special cases are examined in detail. In the first case identical time delays are assumed, and in the second case it is assumed that one country has a different time delay from the others. This semi-symmetric case gives some insight into the consequence of asymmetry of the countries on the asymptotic behavior of the fish stock.

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A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus

Complexity ◽

10.1155/2018/6815190 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 6

Author(s):

Payam Sadeghi Shabestari ◽

Karthikeyan Rajagopal ◽

Bahareh Safarbali ◽

Sajad Jafari ◽

Prakash Duraisamy

Keyword(s):

Diabetes Mellitus ◽

Numerical Modeling ◽

Time Delay ◽

Mathematical Models ◽

Chaotic Behavior ◽

Dynamical Behavior ◽

Regulatory System ◽

Metabolic System ◽

Novel Approach

Although many mathematical models have been presented for glucose and insulin interaction, none of these models can describe diabetes disease completely. In this work, the dynamical behavior of a regulatory system of glucose-insulin incorporating time delay is studied and a new property of the presented model is revealed. This property can describe the diabetes disease better and therefore may help us in deeper understanding of diabetes, interactions between glucose and insulin, and possible cures for this widespread disease.

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Tumour Oscillation Analysis in Angiogenesis Models

Environment Technology Resources Proceedings of the International Scientific and Practical Conference ◽

10.17770/etr2003vol1.1980 ◽

2006 ◽

Vol 1 ◽

pp. 330

Author(s):

P. Daugulis

Keyword(s):

Time Delay ◽

Differential Equations ◽

Delay Differential Equations ◽

Time Delays ◽

Oscillation Analysis ◽

Point Analysis ◽

Delay Differential

In this paper we describe Hopf point analysis for several systems of ordinary and time delay differential equations which encode the most important assumptions concerning anguigenesis processes induced by tumours It is shown that in most cases Hopf points exist only if time delays are nonzero and for most nonzero time delays there are Hopf points in these families of models.

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A New Time-Delay Model for Chaotic Glucose-Insulin Regulatory System

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420501783 ◽

2020 ◽

Vol 30 (12) ◽

pp. 2050178

Author(s):

Abdul-Basset A. AL-Hussein ◽

Fadhil Rahma ◽

Luigi Fortuna ◽

Maide Bucolo ◽

Mattia Frasca ◽

...

Keyword(s):

Time Delay ◽

Complex Dynamics ◽

Dynamical Behavior ◽

Period Doubling ◽

Regulatory System ◽

Periodic Oscillation ◽

Insulin Level ◽

Insulin Degradation ◽

Delay Model ◽

New Time

Mathematical modeling is very helpful for noninvasive investigation of glucose-insulin interaction. In this paper, a new time-delay mathematical model is proposed for glucose-insulin endocrine metabolic regulatory feedback system incorporating the [Formula: see text]-cell dynamic and function for regulating and maintaining bloodstream insulin level. The model includes the insulin degradation due to glucose interaction. The dynamical behavior of the model is analyzed and two-dimensional bifurcation diagrams with respect to two essential parameters of the model are obtained. The results show that the time-delay in insulin secretion in response to blood glucose level, and the delay in glucose drop due to increased insulin concentration, can give rise to complex dynamics, such as periodic oscillation. These dynamics are consistent with the biological findings and period doubling cascade and chaotic state which represent metabolic disorder that may lead to diabetes mellitus.

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New Model Improves Predictions of Shallow Landslides

Eos ◽

10.1029/2016eo044835 ◽

2016 ◽

Vol 97 ◽

Author(s):

Terri Cook

Keyword(s):

Complex Dynamics ◽

Shallow Landslide ◽

Shallow Landslides ◽

New Model ◽

Insight Into

An advanced, process-based model that incorporates typically neglected processes provides new insight into the complex dynamics controlling shallow landslide formation.

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Decentralized time-delay controller design for systems described by delay differential-algebraic equations

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211015961 ◽

2021 ◽

pp. 014233122110159

Author(s):

H. Ersin Erol ◽

Altuğ İftar

Keyword(s):

Time Delay ◽

Time Delays ◽

Controller Design ◽

Linear Time ◽

Differential Algebraic Equations ◽

Algebraic Equations ◽

Design Algorithm ◽

Linear Time Invariant ◽

Delay Differential ◽

Time Invariant

This paper presents a complete approach for designing stabilizing linear time-invariant decentralized finite-dimensional or retarded time-delay output feedback controllers for linear time-invariant systems of delay differential-algebraic equations. The proposed approach is based on the sequential design of the local controllers by using a centralized controller design algorithm. In this sequential design approach, the local controller to be designed at each step is determined depending on the mobility of the rightmost modes with respect to the controllers that have not yet been designed and closed with the system. Since no predefined sequence is followed, a sequence that can target the least effort and dimension for each agent can be aimed. Also, in the proposed approach, a base controller effort can be targeted for each control agent, so that the effort required to stabilize the system can be distributed among the local controllers. In the centralized controller design algorithm used for the design of each local controller, the parameters of the controllers are changed stepwise in a quasi-continuous way to shift the targeted rightmost modes towards the stable area. For a time-delay controller, the desired mode placement can be achieved by applying small changes stepwise to the elements of the matrices and the time-delays of the controller while time-delays remain always non-negative. The effect of small perturbations on the time-delays in the open-loop system or to be added by the controller to be designed is taken into account to ensure some degree of robustness against all possible perturbations on the delays. The effectiveness of the proposed design approach is demonstrated by a numerical example.

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Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

Mathematical Problems in Engineering ◽

10.1155/2011/605794 ◽

2011 ◽

Vol 2011 ◽

pp. 1-20 ◽

Cited By ~ 2

Author(s):

Chun-xia Dou ◽

Zhi-sheng Duan ◽

Xing-bei Jia ◽

Xiao-gang Li ◽

Jin-zhao Yang ◽

...

Keyword(s):

Time Delay ◽

Fuzzy Control ◽

Upper Bound ◽

Time Delays ◽

Sufficient Conditions ◽

Large System ◽

Disturbance Attenuation ◽

Robust Controller ◽

Large Systems ◽

Delay Dependent

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

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