A statistical model of the human core-temperature circadian rhythm

2000 ◽  
Vol 279 (3) ◽  
pp. E669-E683 ◽  
Author(s):  
Emery N. Brown ◽  
Yong Choe ◽  
Harry Luithardt ◽  
Charles A. Czeisler
Keyword(s):  
Circadian Rhythm ◽  
Statistical Model ◽  
Core Temperature ◽  
Biological Clock ◽  
Autoregressive Process ◽  
Van Der Pol Oscillator ◽  
Model Parameters ◽  
Circadian Pacemaker ◽  
Van Der Pol ◽  
New Model

We formulate a statistical model of the human core-temperature circadian rhythm in which the circadian signal is modeled as a van der Pol oscillator, the thermoregulatory response is represented as a first-order autoregressive process, and the evoked effect of activity is modeled with a function specific for each circadian protocol. The new model directly links differential equation-based simulation models and harmonic regression analysis methods and permits statistical analysis of both static and dynamical properties of the circadian pacemaker from experimental data. We estimate the model parameters by using numerically efficient maximum likelihood algorithms and analyze human core-temperature data from forced desynchrony, free-run, and constant-routine protocols. By representing explicitly the dynamical effects of ambient light input to the human circadian pacemaker, the new model can estimate with high precision the correct intrinsic period of this oscillator (∼24 h) from both free-run and forced desynchrony studies. Although the van der Pol model approximates well the dynamical features of the circadian pacemaker, the optimal dynamical model of the human biological clock may have a harmonic structure different from that of the van der Pol oscillator.

scholarly journals MODELING AND CHARACTERIZATION OF OSCILLATOR CIRCUITS BY VAN DER POL MODEL USING PARAMETER ESTIMATION

2012 ◽  
Vol 21 (05) ◽  
pp. 1250043 ◽  
Author(s):  
IULIA DUMITRESCU ◽  
SMAIL BACHIR ◽  
DAVID CORDEAU ◽  
JEAN-MARIE PAILLOT ◽  
MIHAI IORDACHE
Keyword(s):  
Parameter Estimation ◽  
Optimal Parameter ◽  
Estimation Method ◽  
Van Der Pol Oscillator ◽  
Space Representation ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Van Der Pol ◽  
Oscillator Circuit

In this paper, we present a new method for the modeling and characterization of oscillator circuit with a Van Der Pol (VDP) model using parameter identification. We also discussed and investigated the problem of estimation in nonlinear system based on time domain data. The approach is based on an appropriate state space representation of Van der Pol oscillator that allows an optimal parameter estimation. Using sampled output voltage signal, model parameters are obtained by an iterative identification algorithm based on Output Error method. Normalization issues are fixed by an appropriate transformation allowing a quickly global minimum search. Finally, the proposed estimation method is tested and validated using simulation data from a 1 GHz oscillator circuit in GaAs technology.

scholarly journals A New Flexible Statistical Model: Simulating and Modeling the Survival Times of COVID-19 Patients in China

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Xiaofeng Liu ◽  
Zubair Ahmad ◽  
Saima K. Khosa ◽  
M. Yusuf ◽  
Osama Abdulaziz Alamri ◽  
...  
Keyword(s):  
Statistical Model ◽  
Monte Carlo Study ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Survival Times ◽  
New Model ◽  
Proposed Model ◽  
Likelihood Approach ◽  
Extended Weibull Distribution

The spread of the COVID-19 epidemic, since December 2019, has caused much damage around the world, disturbed every aspect of daily life, and has become a serious health threat. The COVID-19 epidemic impacted nearly 150 countries around the globe between December 2019 and March 2020. Since December 2019, researchers have been trying to develop new suitable statistical models to adequately describe the behavior of this deadly pandemic. In this paper, a flexible statistical model has been proposed that can be used to model the lifetime events associated with this deadly pandemic. The new distribution is derived from the combination of an extended Weibull distribution and a trigonometric strategy referred to as the arcsine-X approach. Hence, the new model may be referred to as the arcsine new flexible extended Weibull model. The proposed model is capable of capturing five different behaviors of the hazard rate function. The model parameters are estimated via the maximum likelihood approach. Furthermore, a Monte Carlo study is conducted to assess the behavior of the estimators. Finally, the applicability of the new model is demonstrated using the data of fifty-three patients taken from a hospital in China.

NUMERICAL SOLUTION FOR DUFFING-VAN DER POL OSCILLATOR VIA BLOCK METHOD

2020 ◽  
Vol 10 (1) ◽  
pp. 1857-8365
Author(s):  
A. F. Nurullah ◽  
M. Hassan ◽  
T. J. Wong ◽  
L. F. Koo
Keyword(s):  
Numerical Solution ◽  
Van Der Pol Oscillator ◽  
Block Method ◽  
Van Der Pol

Nonphotic entrainment of the human circadian pacemaker

1998 ◽  
Vol 274 (4) ◽  
pp. R991-R996 ◽  
Author(s):  
Elizabeth B. Klerman ◽  
David W. Rimmer ◽  
Derk-Jan Dijk ◽  
Richard E. Kronauer ◽  
Joseph F. Rizzo ◽  
...  
Keyword(s):  
Circadian Rhythms ◽  
Light Exposure ◽  
Core Body Temperature ◽  
Biological Clock ◽  
Bright Light ◽  
Circadian Pacemaker ◽  
Temperature Rhythms ◽  
Blind Individuals ◽  
Nonphotic Entrainment ◽  
Core Body

In organisms as diverse as single-celled algae and humans, light is the primary stimulus mediating entrainment of the circadian biological clock. Reports that some totally blind individuals appear entrained to the 24-h day have suggested that nonphotic stimuli may also be effective circadian synchronizers in humans, although the nonphotic stimuli are probably comparatively weak synchronizers, because the circadian rhythms of many totally blind individuals “free run” even when they maintain a 24-h activity-rest schedule. To investigate entrainment by nonphotic synchronizers, we studied the endogenous circadian melatonin and core body temperature rhythms of 15 totally blind subjects who lacked conscious light perception and exhibited no suppression of plasma melatonin in response to ocular bright-light exposure. Nine of these fifteen blind individuals were able to maintain synchronization to the 24-h day, albeit often at an atypical phase angle of entrainment. Nonphotic stimuli also synchronized the endogenous circadian rhythms of a totally blind individual to a non-24-h schedule while living in constant near darkness. We conclude that nonphotic stimuli can entrain the human circadian pacemaker in some individuals lacking ocular circadian photoreception.

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

Analysis of fractional order Bonhoeffer–van der Pol oscillator

2008 ◽  
Vol 387 (2-3) ◽  
pp. 418-424 ◽  
Author(s):  
V. Gafiychuk ◽  
B. Datsko ◽  
V. Meleshko
Keyword(s):  
Fractional Order ◽  
Van Der Pol Oscillator ◽  
Van Der Pol

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

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