Bifurcation analysis of the Topp model

In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

Periodicity and Chaos Amidst Twisting and Folding in Two-Dimensional Maps

We study the dynamics of three planar, noninvertible maps which rotate and fold the plane. Two maps are inspired by real-world applications whereas the third map is constructed to serve as a toy model for the other two maps. The dynamics of the three maps are remarkably similar. A stable fixed point bifurcates through a Hopf-Neimark-Sacker which leads to a countably infinite set of resonance tongues in the parameter plane of the map. Within a resonance tongue a periodic point can bifurcate through a period-doubling cascade. At the end of the cascade we detect Henon-like attractors which are conjectured to be the closure of the unstable manifold of a saddle periodic point. These attractors have a folded structure which can be explained by means of the concept of critical lines. We also detect snap-back repellers which can either coexist with Henon-like attractors or which can be formed when the saddle-point of a Henon-like attractor becomes a source

On the predictability of extremes: Does the butterfly effect ever decrease?

This is the peer reviewed version of the following article: Sterk, A. E., Stephenson, D. B., Holland, M. P. and Mylne, K. R. (2015), On the predictability of extremes: Does the butterfly effect ever decrease?. Quarterly Journal of the Royal Meteorological Society, which has been published in final form at http://dx.doi.org/10.1002/qj.2627. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving: http://olabout.wiley.com/WileyCDA/Section/id-820227.html#termsThis study investigates whether or not predictability always decreases for more extreme events. Predictability is measured by the Mean Squared Error (MSE), estimated here from the difference of pairs of ensemble forecasts, conditioned on one of the forecast variables (the 'pseudo-observation') exceeding a threshold. Using an exchangeable linear regression model for pairs of forecast variables, we show that the MSE can be decomposed into the sum of three terms: a threshold-independent constant, a mean term that always increases with threshold, and a variance term that can either increase, decrease, or stay constant with threshold. Using the generalised Pareto distribution to model wind speed excesses over a threshold, we show that MSE always increases with threshold at sufficiently high threshold. However, MSE can be a decreasing function of threshold at lower thresholds but only if the forecasts have finite upper bounds. The methods are illustrated by application to daily wind speed forecasts for London made using the 24 member Met Office Global and Regional Ensemble Prediction System from 1 January 2009 to 31 May 2011. For this example, the mean term increases faster than the variance term decreases with increasing threshold, and so predictability decreases for more extreme events.Engineering and Physical Sciences Research Council (EPSRC)Netherlands Organisation for Scientific Research (NWO

Susceptibility to chronic mucus hypersecretion, a genome wide association study

Background: Chronic mucus hypersecretion (CMH) is associated with an increased frequency of respiratory infections, excess lung function decline, and increased hospitalisation and mortality rates in the general population. It is associated with smoking, but it is unknown why only a minority of smokers develops CMH. A plausible explanation for this phenomenon is a predisposing genetic constitution. Therefore, we performed a genome wide association (GWA) study of CMH in Caucasian populations. Methods: GWA analysis was performed in the NELSON-study using the Illumina 610 array, followed by replication and meta-analysis in 11 additional cohorts. In total 2,704 subjects with, and 7,624 subjects without CMH were included, all current or former heavy smokers (≥20 pack-years). Additional studies were performed to test the functional relevance of the most significant single nucleotide polymorphism (SNP). Results: A strong association with CMH, consistent across all cohorts, was observed with rs6577641 (p = 4.25x10-6, OR = 1.17), located in intron 9 of the special AT-rich sequence-binding protein 1 locus (SATB1) on chromosome 3. The risk allele (G) was associated with higher mRNA expression of SATB1 (4.3x10 -9) in lung tissue. Presence of CMH was associated with increased SATB1 mRNA expression in bronchial biopsies from COPD patients. SATB1 expression was induced during differentiation of primary human bronchial epithelial cells in culture. Conclusions: Our findings, that SNP rs6577641 is associated with CMH in multiple cohorts and is a cis-eQTL for SATB1, together with our additional observation that SATB1 expression increases during epithelial differentiation provide suggestive evidence that SATB1 is a gene that affects CMH