scholarly journals A composite computational model of liver glucose homeostasis. II. Exploring system behaviour

2012 ◽  
Vol 9 (69) ◽  
pp. 701-706 ◽  
Author(s):  
T. Sumner ◽  
J. Hetherington ◽  
R. M. Seymour ◽  
L. Li ◽  
M. Varela Rey ◽  
...  
Keyword(s):  
Insulin Sensitivity ◽  
Computational Model ◽  
Glucose Homeostasis ◽  
Bifurcation Analysis ◽  
Stable Limit Cycle ◽  
Glucose Variability ◽  
Composite Model ◽  
Model Parameters ◽  
Stable Limit ◽  
Oscillatory Behaviour

Using a composite model of the glucose homeostasis system, consisting of seven interconnected submodels, we enumerate the possible behaviours of the model in response to variation of liver insulin sensitivity and dietary glucose variability. The model can reproduce published experimental manipulations of the glucose homeostasis system and clearly illustrates several important properties of glucose homeostasis—boundedness in model parameters of the region of efficient homeostasis, existence of an insulin sensitivity that allows effective homeostatic control and the importance of transient and oscillatory behaviour in characterizing homeostatic failure. Bifurcation analysis shows that the appearance of a stable limit cycle can be identified.

scholarly journals A composite computational model of liver glucose homeostasis. I. Building the composite model

2011 ◽  
Vol 9 (69) ◽  
pp. 689-700 ◽  
Author(s):  
J. Hetherington ◽  
T. Sumner ◽  
R. M. Seymour ◽  
L. Li ◽  
M. Varela Rey ◽  
...  
Keyword(s):  
Computational Model ◽  
Composite Model ◽  
Physiological Data ◽  
Small Scale ◽  
Model Parameters ◽  
High Scale ◽  
Composite Models ◽  
The Individual ◽  
Component Models

A computational model of the glucagon/insulin-driven liver glucohomeostasis function, focusing on the buffering of glucose into glycogen, has been developed. The model exemplifies an ‘engineering’ approach to modelling in systems biology, and was produced by linking together seven component models of separate aspects of the physiology. The component models use a variety of modelling paradigms and degrees of simplification. Model parameters were determined by an iterative hybrid of fitting to high-scale physiological data, and determination from small-scale in vitro experiments or molecular biological techniques. The component models were not originally designed for inclusion within such a composite model, but were integrated, with modification, using our published modelling software and computational frameworks. This approach facilitates the development of large and complex composite models, although, inevitably, some compromises must be made when composing the individual models. Composite models of this form have not previously been demonstrated.

scholarly journals The Effects of Harvesting on the Dynamics of a Leslie–Gower Model

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jingli Xie ◽  
Hanyan Liu ◽  
Danfeng Luo
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Stable Limit Cycle ◽  
Local Bifurcation ◽  
Stable Limit ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Bifurcation Analysis

In this paper, we study a Leslie–Gower predator-prey model with harvesting effects. We carry out local bifurcation analysis and stability analysis. Under certain conditions, the model is shown to undergo a supercritical Hopf bifurcation resulting in a stable limit cycle. Numerical simulations are presented to illustrate our theoretic results.

ANALYSIS OF GLUCOSE REGULATION USING FUZZY CLUSTERING BASED PIECEWISE AFFINE APPROXIMATION APPROACH

2010 ◽  
Vol 18 (02) ◽  
pp. 299-324 ◽  
Author(s):  
S. GHOSH ◽  
S. MAKA
Keyword(s):  
Insulin Secretion ◽  
Insulin Sensitivity ◽  
Nonlinear System ◽  
Fuzzy Clustering ◽  
Stable Limit Cycle ◽  
Glucose Regulation ◽  
Regulation System ◽  
Stable Limit ◽  
Affine Systems ◽  
Piecewise Affine

This paper deals with the analysis of the nonlinear glucose regulation system from its Piecewise Affine (PWA) equivalent Piecewise Affine (PWA) equivalent model. The use of PWA model was motivated by the fact that it has developed as an attractive tool for nonlinear system analysis in recent years, since it allows the use of well developed concepts in the field of linear systems and control theory. The analysis mainly involves the behavioral study of the system at steady state for different types of input and different sets of physiological parameters. The number of affine systems required to represent a nonlinear system is an important consideration in PWA modeling. In this paper, the optimal number of piecewise affine systems is obtained by a technique based on a fuzzy clustering. From the PWA representation, it is possible to determine the equilibrium point (basal condition) of the glucose regulation system quite easily without solving a complex transcendental equation. The presence of a compensating mechanism between insulin sensitivity and insulin secretion is utilized by the PWA model to determine a particular profile (characteristics) for insulin sensitivity for a modified insulin secretion characteristics that would maintain a normal basal glucose level. A condition for the existence of a stable limit cycle of plasma glucose concentration as a function of delay in hepatic glucose production is determined from the model. This allowed determining the point of hopf bifurcation without carrying out extensive simulations, as is done with the existing models. The response obtained from the numerical simulation of the model, is in line with the experimental results.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

Application of a Composite Model in the Analysis of Creep Deformation at Low and Intermediate Temperatures

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Xinjun Yang ◽  
Xiang Ling
Keyword(s):  
Projection Method ◽  
Power Law ◽  
Creep Deformation ◽  
Primary Creep ◽  
Composite Model ◽  
Intermediate Temperature ◽  
Model Parameters ◽  
Creep Life ◽  
Temperature Creep ◽  
Multiaxial Creep

The creep behaviors of TA2 and R60702 at low and intermediate temperature were presented and discussed in this paper. Experimental results indicated that an apparent threshold stress was exhibited in the creep deformation of R60702. Meanwhile, the primary creep phase was found as the main pattern in the room temperature creep behavior of TA2. Compared with the exponential law, the power law has been proved to be a proper constitutive model in the description of primary creep phase. It also showed that θ projection method had its significant advantage in the evaluation of accelerated creep stage. Thus, a composite model which combined power law with θ projection method was applied in the creep curves evaluation at low and intermediate temperature. Based on the multiaxial creep deformation results, the model was modified and discussed. A linear relationship existed between composite model parameters and applied load. Finally, the creep life of TA2 and R60702 could be accurately predicted by the composite model, and it is suitable for the application in low and intermediate temperature creep life analysis.

scholarly journals TRIB3 R84 variant affects glucose homeostasis by altering the interplay between insulin sensitivity and secretion

Diabetologia ◽  
2010 ◽  
Vol 53 (7) ◽  
pp. 1354-1361 ◽  
Author(s):  
S. Prudente ◽  
R. Baratta ◽  
F. Andreozzi ◽  
E. Morini ◽  
M. G. Farina ◽  
...  
Keyword(s):  
Insulin Sensitivity ◽  
Glucose Homeostasis

scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

scholarly journals Méthode d'agrégation des variables appliquée à la dynamique des populations

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Pierre Auger ◽  
Abderrahim El Abdllaoui ◽  
Rachid Mchich
Keyword(s):  
Stable Limit Cycle ◽  
Stable Limit ◽  
Dynamique Des Populations ◽  
Globally Asymptotically Stable ◽  
Density Dependent ◽  
Migration Rates ◽  
First Case ◽  
International Audience ◽  
Predator Model ◽  
Predator System

International audience We present the method of aggregation of variables in the case of ordinary differential equations. We apply the method to a prey - predator model in a multi - patchy environment. In this model, preys can go to a refuge and therefore escape to predation. The predator must return regularly to his terrier to feed his progeny. We study the effect of density-dependent migration on the global stability of the prey-predator system. We consider constant migration rates, but also density-dependent migration rates. We prove that the positif equilibrium is globally asymptotically stable in the first case, and that its stability changes in the second case. The fact that we consider density-dependent migration rates leads to the existence of a stable limit cycle via a Hopf bifurcation. Nous présentons les grandes lignes de laméthode d'agrégation des variables dans les systèmes d'équations différentielles ordinaires. Nous appliquons laméthode à un modèle proie-prédateur spatialisé. Dans ce modèle, les proies peuvent échapper à la prédation en se réfugiant sur un site. Le prédateur doit aussi retourner régulièrement dans son terrier pour nourrir sa progéniture. Nous étudions les effets de migration dépendant de la densité des populations sur la stabilité globale du système proie-prédateur. Nous considérons des taux de migration constants, puis densité-dépendants. Dans le cas de taux constants il existe un équilibre positif toujours stable alors que dans le cas de taux de migration densité-dépendants, il existe un cycle limite stable via une bifurcation de Hopf.

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