The synchronization of two pendulum clocks hanging from a wall was first observed by Huygens during the XVII century. This type of synchronization is observed in other areas and is fundamentally different from the problem of two clocks hanging from a moveable base. We present a model explaining the phase opposition synchronization of two pendulum clocks in those conditions. The predicted behaviour is observed experimentally, validating the model.

Our main objective is to study a Ricker-type competition model of two species. We give a complete analysis of stability and bifurcation and determine the centre manifolds, as well as stable and unstable manifolds. It is shown that the autonomous Ricker competition model exhibits subcritical bifurcation, bubbles, period-doubling bifurcation, but no Neimark–Sacker bifurcations. We exhibit the region in the parameter space where the competition exclusion principle applies.

A new class of maps called unimodal Allee maps are introduced. Such maps arise in the study of population dynamics in which the population goes extinct if its size falls below a threshold value. A unimodal Allee map is thus a unimodal map with three fixed points, a zero fixed point, a small positive fixed point, called threshold point, and a bigger positive fixed point, called the carrying capacity. In this paper, the properties and stability of the three fixed points are studied in the setting of non-autonomous periodic dynamical systems or difference equations. Finally, we investigate the bifurcation of periodic systems/difference equations when the system consists of two unimodal Allee maps.

Background: Community-acquired pneumonia (CAP) is one of the leading causes of morbidity and mortality worldwide. It remains unknown whether recently introduced prevention strategies, such as vaccination, may have impacted its mortality. Moreover, it is important to understand whether these trends are similar for all patients or if some groups may have different outcomes. Methods: We evaluated the CAP hospitalization data for adult patients, from the Portuguese mainland Hospital diagnosis database. We included all patients discharged with CAP between 2010 and 2019. We assessed Hospital mortality for the whole population and according to age and gender. We also examined the monthly number of admissions and mortality. Results: We identified 462,910 CAP admissions, of which 54% were male (mean age 76.8 ± 14.5years). We divided our population into 4 age groups: 18-40years (3.2% of episodes); 41-65years (14.9%); 66-80years (31.6%); >80 years (50.2%). Mortality increased sharply with age, to more than 40% in older patients, highlighting the disproportionate burden of respiratory diseases in this age group. Although CAP mortality remained stable until 2016 (roughly 23%), a slight decreasing trend was noted afterwards (from 23.1 to 21.8%). In hospitalized patients, the relative risk of dying with CAP, consistently decreased during this period, from odds ratio 5.5, 95% CI 5.4–5.7 to odds ratio 4.3, 95% CI 4.2–4.4. As much as 25% of deaths related to CAP occurred during the first 48 h after hospital admission. While CAP admissions peaked in January, mortality was higher during the summertime. Conclusions: Community-acquired pneumonia remains associated with a high risk of death. Mortality increased with age from 40 years onwards. However, the relative risk of dying with CAP in the Hospital decreased during this decade. Graphical

In this work, we investigate attracting periodic orbits for non-autonomous discrete dynamical systems with two maps using a new approach. We study some types of bifurcation in these systems. We show that the pitchfork bifurcation plays an important role in the creation of attracting orbits in families of alternating systems with negative Schwarzian derivative and it is central in the geometry of the bifurcation diagrams.