scholarly journals The Markets of Green Cars of Three Countries: Analysis Using Lotka–Volterra and Bertalanffy–Pütter Models

2020 ◽  
Vol 6 (3) ◽  
pp. 67
Author(s):  
Annika Maria Ziegler ◽  
Norbert Brunner ◽  
Manfred Kühleitner
Keyword(s):  
Growth Curve ◽  
Model Uncertainty ◽  
Open Innovation ◽  
Logistic Growth ◽  
Growth Trajectories ◽  
Predator Prey ◽  
Akaike Weight ◽  
Registration Data ◽  
Market Shares ◽  
Best Fitting

Did the diesel scandal of 2015 affect the market for cars? We consider this question in relation to Germany, Austria, and Switzerland. Starting with historical registration data of cars with different drivetrain technologies, we considered each technology in isolation and fitted a five-parameter Bertalanffy–Pütter (BP) growth model to the stocks of cars. We used this model as it generalizes several well-known three-parameter models, which are distinguished by their exponent pair, e.g., Brody model BP (0, 1), West model BP (0.75, 1), and logistic growth BP (1, 2). We then used these models to derive a Lotka–Volterra (LV) model for the co-evolution of the (annual) market shares of the different drivetrain technologies. We augmented this model by a consideration of model uncertainty and found that initially all technologies were in a state of competition, except for Austria, which changed in 2015 to a predator–prey situation with diesel as the sole prey. This analysis of model uncertainty compared the best-fitting growth curve with the growth trajectories of other likely (Akaike weight 5% or higher) models of BP type. We conclude with remarks about open innovation.

scholarly journals Comparison of growth models to describe growth from birth to 6 years in a Beninese cohort of children with repeated measurements

BMJ Open ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. e035785
Author(s):  
Shukrullah Ahmadi ◽  
Florence Bodeau-Livinec ◽  
Roméo Zoumenou ◽  
André Garcia ◽  
David Courtin ◽  
...  
Keyword(s):  
Growth Model ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Height Growth ◽  
Sub Saharan Africa ◽  
Individual Growth ◽  
Secondary Outcome ◽  
Growth Trajectories ◽  
Best Fitting

ObjectiveTo select a growth model that best describes individual growth trajectories of children and to present some growth characteristics of this population.SettingsParticipants were selected from a prospective cohort conducted in three health centres (Allada, Sekou and Attogon) in a semirural region of Benin, sub-Saharan Africa.ParticipantsChildren aged 0 to 6 years were recruited in a cohort study with at least two valid height and weight measurements included (n=961).Primary and secondary outcome measuresThis study compared the goodness-of-fit of three structural growth models (Jenss-Bayley, Reed and a newly adapted version of the Gompertz growth model) on longitudinal weight and height growth data of boys and girls. The goodness-of-fit of the models was assessed using residual distribution over age and compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The best-fitting model allowed estimating mean weight and height growth trajectories, individual growth and growth velocities. Underweight, stunting and wasting were also estimated at age 6 years.ResultsThe three models were able to fit well both weight and height data. The Jenss-Bayley model presented the best fit for weight and height, both in boys and girls. Mean height growth trajectories were identical in shape and direction for boys and girls while the mean weight growth curve of girls fell slightly below the curve of boys after neonatal life. Finally, 35%, 27.7% and 8% of boys; and 34%, 38.4% and 4% of girls were estimated to be underweight, wasted and stunted at age 6 years, respectively.ConclusionThe growth parameters of the best-fitting Jenss-Bayley model can be used to describe growth trajectories and study their determinants.

scholarly journals Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration

2019 ◽  
Vol 14 (2) ◽  
pp. 588-611
Author(s):  
M.P. Kulakov ◽  
E.V. Kurilova ◽  
E.Ya. Frisman
Keyword(s):  
Phase Synchronization ◽  
Oscillation Period ◽  
Logistic Growth ◽  
Predator Prey ◽  
Different Types ◽  
The Difference ◽  
Minimum Numbers ◽  
Fast Oscillations ◽  
Bursting Activity ◽  
Type Ii Functional Response

The papers is devoted to a model for two non-identical predator-prey communities coupled by migration and characterized by logistic growth of prey and Holling type II functional response. The coupling is a predator migration at constant weak rate. The non-identity is the difference in the prey growth rates or predator mortalities in each patch. We studied the equilibrium states of model and scenarios of loss of their stability and emerge of complex periodic solutions. It was shown that in some domains of the parameter space there is a bursting activity which are that the dynamics of two communities contain segments of slowly resting dynamic (as part of a fast-slow cycle or canard) and regular bursts of spikes. In the resting part, the dynamics of the second community, as a rule, follow the slow changes in the first community, i.e. the dynamics in different patches are synchronous. But in the fast part there is only phase synchronization between the fast-slow cycle in first patch and bursts in second. We classified the scenarios of transition between different types of bursting activity by location spiking manifold and canard. These types differ not so much in size, shape or numbers of spikes as in the order of bursts emerge relative a slow-fast cycle. In a typical case the start of burst (divergent fast oscillations) coincides with the minimum numbers or quasi-extinction of prey in the first patch. After a rapid increase in the prey number in the first patch, diverging fluctuations give way to damped in the second patch. Such dynamics correspond to the rhombus-wave shape of spikes cluster. Another case is interesting, when the burst of spikes is formed after the full recovery of prey and with a certain predator number in the first patch. In this case, the spikes cluster takes the shape of a triangle-wave or a truncated rhombus-wave. It was shown that transitions between these types of bursts are accompanied by a change in the oscillation period and the degree of synchronization. Triangular-wave bursters correspond to complete synchronization of the predator dynamics in the resting part and rhomboid-wave correspond to antiphase synchronization. In the fast part with many spikes, communities are completely asynchronous to each other.

scholarly journals Hopf Bifurcation on a Cancer Therapy Model by Oncolytic Virus Involving the Malignancy Effect and Therapeutic Efficacy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
F. Adi-Kusumo ◽  
L. Aryati ◽  
S. Risdayati ◽  
S. Norhidayah
Keyword(s):  
Hopf Bifurcation ◽  
Oncolytic Virus ◽  
Oncolytic Viruses ◽  
Logistic Growth ◽  
Human Immune System ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Therapy Model ◽  
Human Immune ◽  
Numerical Bifurcation

We introduce a mathematical model that shows the interaction dynamics between the uninfected and the infected cancer cell populations with oncolytic viruses for the benign and the malignant cancer cases. There are two important parameters in our model that represent the malignancy level of the cancer cells and the efficacy of the therapy. The parameters play an important role to determine the possibility to have successful therapy for cancer. Our model is based on the predator-prey model with logistic growth, functional response, and the saturation effect that show the possibility for the virus to be deactivated and blocked by the human immune system after they reach a certain value. In this paper, we consider the appearance of the Hopf bifurcation on the system to characterize the treatment response based on the malignancy effect of the disease. We employ numerical bifurcation analysis when the value of the malignancy parameter is varied to understand the dynamics of the system.

scholarly journals The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Shaoli Wang ◽  
Zhihao Ge
Keyword(s):  
Hopf Bifurcation ◽  
Logistic Growth ◽  
Positive Equilibrium ◽  
Prey Refuge ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Prey System ◽  
Form Theory ◽  
The Stability

The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.

Responses of Subterranean Clover Communities to Temperature. I. Dry Matter Production and Plant Morphogenesis

1976 ◽  
Vol 3 (4) ◽  
pp. 527 ◽  
Author(s):  
S Fukai ◽  
JH Silsbury
Keyword(s):  
Leaf Area ◽  
Growth Curve ◽  
Dry Matter ◽  
Subterranean Clover ◽  
Experimental Period ◽  
Main Stem ◽  
Logistic Growth ◽  
Similar Time ◽  
Plant Parts ◽  
Leaf Appearance

Subterranean clover communities were grown in temperature-controlled naturally lit glasshouses at 15, 20, 25 and 30�C. Dry matter yield, leaf area and the distribution of dry matter between plant parts were determined at about 14-day intervals for up to 130 days from planting. Leaf appearance, leaf death, leaf number and growth of laterals were observed for individual plants in the community over a similar time period. A logistic growth curve was found for each temperature and crop growth rate calculated from the equation fitted for each growth curve. The optimum temperature for growth was relatively high (20-25°C) when plants were young, but decreased during growth so that after 100 days total dry matter was inversely related to temperature over the range 15-30°C. Both the rate of leaf appearance and the rate of leaf death on the main stem were constant at each temperature during the experimental period and were directly related to temperature. The number of leaves per unit ground area was determined mainly by the rates of leaf appearance and leaf death on the main stem, since the contribution of laterals was small. The proportion of stem and petiole to total dry matter increased, and that of green leaf lamina decreased, with increase in total dry matter. Neither was markedly affected by temperature. An inverse relationship between specific leaf area and temperature resulted in a lower ratio of leaf area to total dry matter at 15°C compared with that at 20, 25 or 30°C.

scholarly journals Discrepant Inferences When Modeling Associations Between Time-Varying Exposures and Linear Growth Trajectories in Infancy Using Length-For-Age Z Scores Versus Raw Length

2020 ◽  
Vol 4 (Supplement_2) ◽  
pp. 1059-1059
Author(s):  
Huma Qamar ◽  
Ulaina Tariq ◽  
Diego Bassani ◽  
Akpevwe Onoyovwi ◽  
Abdullah Al Mahmud ◽  
...  
Keyword(s):  
Growth Factor ◽  
Fibroblast Growth Factor ◽  
Linear Growth ◽  
Growth Trajectories ◽  
Time Varying ◽  
Fibroblast Growth ◽  
Z Scores ◽  
Best Fitting ◽  
Random Slopes ◽  
Fitting Model

Abstract Objectives To compare inferences from longitudinal models of the relationships between biomarkers of interest and linear growth outcomes in infancy using length-for-age z-scores (LAZ) based on age- and sex-specific growth standards, or raw length. Methods This was a secondary analysis of data from a study of the association between bone-related biomarkers and infant linear growth trajectories up to 1 year of life in a subset of infants (n = 820) enrolled in the Maternal Vitamin D for Infant Growth trial. The linear growth outcome (LAZ or raw length) was modelled as a function of the interaction between each biomarker and age using linear mixed effect models with restricted cubic splines. Models were specified to obtain the best fit and reconcile discrepancies in results from LAZ and length models. Inferences from marginal effects at birth, 3 months, 6 months, and 12 months were compared, for a total 4 effect estimates from each of 10 pairs of LAZ and length models, resulting in 40 pairs of estimates. The following biomarkers were included: fibroblast growth factor 21 (FGF21), fibroblast growth factor 23 (FGF23), N-terminal propeptide of C-type natriuretic peptide (NT-proCNP), osteocalcin, osteoprotegerin, receptor activator of nuclear activator kappa-b ligand (RANKL), 25-hydroxyvitamin D (25OHD), C-reactive protein (CRP), Interleukin 6 (IL6), and insulin-like growth factor-1 (IGF1). Biomarkers were time-varying, measured in cord blood and at 3 and 6 months of age. Results The best fitting model for LAZ had 3 knots with random slopes, and the best fitting model for raw length had 5 knots, random slopes, and an exponential residual covariance structure. Comparisons of the pairs of marginal estimates from the LAZ vs length models resulted in discrepant inferences for 25% of effect estimates (10/40). Results were consistently concordant only for FGF23, 25OHD, CRP, and IL6. Conclusions Length and LAZ represent the same biological construct but their use in longitudinal modelling may lead to different inferences about associations between time-varying exposures and infant growth, possibly due to residual confounding by age. These findings raise concerns about the reliability of studies of determinants or markers of infant linear growth based on longitudinal modelling of growth trajectories. Funding Sources Bill and Melinda Gates Foundation.

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