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

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.

Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes1

1998 ◽  
Vol 122 (1) ◽  
pp. 240-245 ◽  
Author(s):  
M. Basso ◽  
L. Giarre´ ◽  
M. Dahleh ◽  
I. Mezic´
Keyword(s):  
Parameter Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Operating Conditions ◽  
Invariant Sets ◽  
Jones Potential ◽  
Lennard Jones ◽  
Atomic Force

In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynamical behavior of a harmonically forced system. Using nonlinear analysis techniques on attracting limit sets, we numerically verify the presence of chaotic invariant sets. The chaotic behavior appears to be generated via a cascade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained for values of parameters predicted by Melnikov theory. Moreover, the numerical analysis can be fruitfully employed to analyze the region of the parameter space where no theoretical information on the presence of a chaotic invariant set is available. In addition to explaining the experimentally observed chaotic behavior, this analysis can be useful in finding a controller that stabilizes the system on a nonchaotic trajectory. The analysis can also be used to change the AFM operating conditions to a region of the parameter space where regular motion is ensured. [S0022-0434(00)01401-5]

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

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
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.

Hopf bifurcation and chaos in time-delay model of glucose-insulin regulatory system

2020 ◽  
Vol 137 ◽  
pp. 109845 ◽  
Author(s):  
Abdul-Basset A. Al-Hussein ◽  
Fadihl Rahma ◽  
Sajad Jafari
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Regulatory System ◽  
Delay Model ◽  
Bifurcation And Chaos

CHAOTIC BEHAVIOR OF A PERIODICALLY FORCED PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS FUNCTIONAL RESPONSE AND IMPULSIVE PERTURBATIONS

2006 ◽  
Vol 09 (03) ◽  
pp. 209-222 ◽  
Author(s):  
SHUWEN ZHANG ◽  
DEJUN TAN ◽  
LANSUN CHEN
Keyword(s):  
Functional Response ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Periodic Variation ◽  
Periodic Forcing ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Impulsive Perturbations

The effects of periodic forcing and impulsive perturbations on the predator–prey model with Beddington–DeAngelis functional response are investigated. We assume periodic variation in the intrinsic growth rate of the prey as well as periodic constant impulsive immigration of the predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can very easily give rise to complex dynamics, including quasi-periodic oscillating, a period-doubling cascade, chaos, a period-halving cascade, non-unique dynamics, and period windows.

scholarly journals A New Model For Endocrine Glucose-Insulin Regulatory System

2020 ◽  
Vol 16 (1) ◽  
pp. 1-8
Author(s):  
Abdul-Basset Al-Hussein ◽  
Fadhil Tahir
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Complex Dynamics ◽  
Regulatory System ◽  
Metabolic System ◽  
Treatment Protocols ◽  
New Model ◽  
Delay Differential ◽  
Physiological Research ◽  
Insight Into

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.

Bifurcation and Chaos in a Discrete Fractional Order Prey-Predator System Involving Infection in Prey

2020 ◽  
pp. 95-119
Author(s):  
A. George Maria Selvam ◽  
R. Dhineshbabu
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Order System ◽  
Qualitative Behavior ◽  
Uniqueness Of Solutions ◽  
Predator System

This chapter considers the dynamical behavior of a new form of fractional order three-dimensional continuous time prey-predator system and its discretized counterpart. Existence and uniqueness of solutions is obtained. The dynamic nature of the model is discussed through local stability analysis of the steady states. Qualitative behavior of the model reveals rich and complex dynamics as exhibited by the discrete-time fractional order model. Moreover, the bifurcation theory is applied to investigate the presence of Neimark-Sacker and period-doubling bifurcations at the coexistence steady state taking h as a bifurcation parameter for the discrete fractional order system. Also, the trajectories, phase diagrams, limit cycles, bifurcation diagrams, and chaotic attractors are obtained for biologically meaningful sets of parameter values for the discretized system. Finally, the analytical results are strengthened with appropriate numerical examples and they demonstrate the chaotic behavior over a range of parameters. Chaos control is achieved by the hybrid control method.

scholarly journals Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

2009 ◽  
Vol 2009 ◽  
pp. 1-26 ◽  
Author(s):  
Denis de Carvalho Braga ◽  
Luis Fernando Mello ◽  
Marcelo Messias
Keyword(s):  
Analytical Study ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Van Der Pol ◽  
Codimension One ◽  
Local Bifurcations ◽  
Parameter Values ◽  
Small Periodic

We study the local codimension one, two, and three bifurcations which occur in a recently proposed Van der Pol-Duffing circuit (ADVP) with parallel resistor, which is an extension of the classical Chua's circuit with cubic nonlinearity. The ADVP system presents a very rich dynamical behavior, ranging from stable equilibrium points to periodic and even chaotic oscillations. Aiming to contribute to the understand of the complex dynamics of this new system we present an analytical study of its local bifurcations and give the corresponding bifurcation diagrams. A complete description of the regions in the parameter space for which multiple small periodic solutions arise through the Hopf bifurcations at the equilibria is given. Then, by studying the continuation of such periodic orbits, we numerically find a sequence of period doubling and symmetric homoclinic bifurcations which leads to the creation of strange attractors, for a given set of the parameter values.

scholarly journals Complex Dynamical Behavior of a Two-Stage Colpitts Oscillator with Magnetically Coupled Inductors

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
V. Kamdoum Tamba ◽  
H. B. Fotsin ◽  
J. Kengne ◽  
F. Kapche Tagne ◽  
P. K. Talla
Keyword(s):  
Complex Dynamics ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Colpitts Oscillator ◽  
Two Stage ◽  
Frequency Spectra ◽  
Variable Resistor ◽  
Exponential Nonlinearity ◽  
Coupled Inductors

A five-dimensional (5D) controlled two-stage Colpitts oscillator is introduced and analyzed. This new electronic oscillator is constructed by considering the well-known two-stage Colpitts oscillator with two further elements (coupled inductors and variable resistor). In contrast to current approaches based on piecewise linear (PWL) model, we propose a smooth mathematical model (with exponential nonlinearity) to investigate the dynamics of the oscillator. Several issues, such as the basic dynamical behaviour, bifurcation diagrams, Lyapunov exponents, and frequency spectra of the oscillator, are investigated theoretically and numerically by varying a single control resistor. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling and interior crisis routes as the single control resistor is monitored. Furthermore, an experimental study of controlled Colpitts oscillator is carried out. An appropriate electronic circuit is proposed for the investigations of the complex dynamics behaviour of the system. A very good qualitative agreement is obtained between the theoretical/numerical and experimental results.

scholarly journals Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liang’an Huo ◽  
Xiaomin Chen
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Functional Response ◽  
Response Function ◽  
Rapid Development ◽  
Dynamical Behavior ◽  
Deterministic System ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Holling Ii Functional Response

AbstractWith the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

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