Instability and Sustained Oscillations in Neo-Classical Growth Models with Unemployment

Author(s):  
Luciano Fanti ◽  
Piero Manfredi
Author(s):  
Kevin S. McCann

This chapter examines the dynamics of basic population models, with a particular focus on the general biological conditions under which population dynamics are stabilized, or destabilized, by increased population growth rates. Three classes of population models are discussed in relation to excitable and nonexcitable interactions: continuous logistic growth models, discrete equations, and continuous models with stage-structured lags. The chapter shows how increasing per capita growth rates tend to stabilize population models as a result of excitable interactions; that is, when dynamic trajectories monotonically approach an equilibrium after a localized perturbation. However, lags in population models tend to give rise to dynamics with oscillatory decays to equilibrium or sustained oscillations around the carrying capacity. Such oscillatory decays or sustained oscillations are only further destabilized by increased growth or production rates. The chapter concludes with a review of empirical evidence for excitable dynamics.


2000 ◽  
Vol 39 (02) ◽  
pp. 118-121 ◽  
Author(s):  
S. Akselrod ◽  
S. Eyal

Abstract:A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.


Author(s):  
Mario Lesina ◽  
Lovorka Gotal Dmitrovic

The paper shows the relation among the number of small, medium and large companies in the leather and footwear industry in Croatia, as well as the relation among the number of their employees by means of the Spearman and Pearson correlation coefficient. The data were collected during 21 years. The warning zone and the risk zone were determined by means of the Statistical Process Control (SPC) for a certain number of small, medium and large companies in the leather and footwear industry in Croatia. Growth models, based on externalities, models based on research and development and the AK models were applied for the analysis of the obtained research results. The paper shows using the correlation coefficients that The relation between the number of large companies and their number of employees is the strongest, i.e. large companies have the best structured work places. The relation between the number of medium companies and the number of their employees is a bit weaker, while there is no relation in small companies. This is best described by growth models based on externalities, in which growth generates the increase in human capital, i.e. the growth of the level of knowledge and skills in the entire economy, but also deductively in companies on microeconomic level. These models also recognize the limit of accumulated knowledge after which growth may be expected. The absence of growth in small companies results from an insufficient level of human capital and failure to reach its limit level which could generate growth. According to Statistical Process Control (SPC), control charts, as well as regression models, it is clear that the most cost-effective investment is the investment into medium companies. The paper demonstrates the disadvantages in small, medium and large companies in the leather and footwear industry in Croatia. Small companies often emerge too quickly and disappear too easily owing to the employment of administrative staff instead of professional production staff. As the models emphasize, companies need to invest into their employees and employ good production staff. Investment and support to the medium companies not only strengthens the companies which have a well-arranged technological process and a good systematization of work places, but this also helps large companies, as there is a strong correlation between the number of medium and large companies.


2019 ◽  
Vol 16 (4) ◽  
pp. 302-315 ◽  
Author(s):  
G. Peggy McFall ◽  
Lars Bäckman ◽  
Roger A. Dixon

Background: Apolipoprotein E (APOE) is a prominent genetic risk factor for Alzheimer’s disease (AD) and a frequent target for associations with non-demented and cognitively impaired aging. APOE offers a unique opportunity to evaluate two dichotomous comparisons and selected gradations of APOE risk. Some evidence suggests that APOE effects may differ by sex and emerge especially in interaction with other AD-related biomarkers (e.g., vascular health). Methods: Longitudinal trajectories of non-demented adults (n = 632, 67% female, Mage = 68.9) populated a 40-year band of aging. Focusing on memory performance and individualized memory trajectories, a sequence of latent growth models was tested for predictions of (moderation between) APOE and pulse pressure (PP) as stratified by sex. The analyses (1) established robust benchmark PP effects on memory trajectories, (2) compared predictions of alternative dichotomous groupings (ε4- vs ε4+, ε2- vs ε2+), and (3) examined precision-based predictions by disaggregated APOE genotypes. Results: Healthier (lower) PP was associated with better memory performance and less decline. Therefore, all subsequent analyses were conducted in the interactive context of PP effects and sex stratification. The ε4-based dichotomization produced no differential genetic predictions. The ε2-based analyses showed sex differences, including selective protection for ε2-positive females. Exploratory follow-up disaggregated APOE genotype analyses suggested selective ε2 protection effects for both homozygotic and heterozygotic females. Conclusion: Precision analyses of AD genetic risk will advance the understanding of underlying mechanisms and improve personalized implementation of interventions.


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