On the Properties of a Class of Impulsive Competition Beverton–Holt Equations

This paper is devoted to a type of combined impulsive discrete Beverton–Holt equations in ecology when eventual discontinuities at sampling time instants are considered. Such discontinuities could be interpreted as impulses in the corresponding continuous-time logistic equations. The set of equations involve competition-type coupled dynamics among a finite set of species. It is assumed that, in general, the intrinsic growth rates and the carrying capacities are eventually distinct for the various species. The impulsive parts of the equations are parameterized by harvesting quotas and independent consumptions which are also eventually distinct for the various species and which control the populations’ evolution. The performed study includes the existence of extinction and non-extinction equilibrium points, the conditions of non-negativity and boundedness of the solutions for given finite non-negative initial conditions and the conditions of asymptotic stability without or with extinction of the solutions.

Competition of Weeds Dominated by Wild Oat (Avena sterilis) in Wheat (Triticum durum Desf.) in Jordan

Wheat is the main field crop grown in Jordan. Productivity is low due to different factors, including erratic rainfall, poor soil fertility and weed competition. A field experiment was carried out at the University of Jordan Research Station for two growing seasons to determine the effect of weed competition on growth and yield of wheat (Triticum durum Cv. “Hourani”). Treatments consisted of either allowing weeds to infest the crop or maintaining the crop weed-free for increasing durations after emergence. Results showed that, the longer the periods of weed competition, the greater the loss in crop growth and yield. Average reductions in grain and straw yields were 41% and 37%, respectively. The highest grain yield obtained was from weed-free, and the lowest was in weed-infested plots for the entire growing season. Average grain yield was not significantly different at 14 to 49 days of weed-infested periods, while none of the weed-free periods produced a yield similar to that of the weed-free control. However, maintaining a weed-free crop for three weeks after emergence significantly increased grain yield compared with the weed-infested control. High rainfall in the first season almost doubled weed growth and greatly reduced wheat growth and yield compared with the second season. To determine the critical period of weed competition and the influence of weed infestation on wheat grain yield, Gompertz and logistic equations were fitted to data representing increasing duration of weed-free and weed-infested periods, respectively. Based upon an arbitrary 5% level of average grain yield loss in the two years, the critical period of weed competition occurred at 0–49 days after wheat emergence, which corresponded with the rapid increase in weed biomass.

Phenomenological Modeling of Formic Acid Fractionation of Sugarcane Bagasse by Integration of Operation Parameters as an Extended Combined Severity Factor

In order to more conveniently simulate and optimize the solubilization of sugarcane bagasse components during formic acid (FA) fractionation, an extended combined severity factor (CSFext) was defined to integrate various operation parameters as a single factor. Two phenomenological models based on Arrhenius and Logistic equations were further used to describe the phenomenological kinetics. Different data-processing methods were compared to fit the severity parameters and model constants. Both Arrhenius-based and Logistic-based models show satisfying fitting results, though the values of Arrhenius-based CSFext (A-CSFext) and Logistic-based CSFext (L-CSFext) were somewhat different under the same fractionation condition. The solubilization of biomass components increased with CSFext, but two distinct stages could be observed with inflection points at A-CSFext of 42 or L-CSFext of 43, corresponding to bulk and residual solubilization stages, respectively. For the enzymatic hydrolysis of cellulosic solids, the highest initial enzymatic glucan conversion (EGC@6h) was obtained at A-CSFext of 39–40 or A-CSFext of 40–41; however, for a long hydrolysis period (72 h), relatively high glucan conversion (EGC@72h) was observed at A-CSFext of 42–43 or A-CSFext of 43–44. Post-treatment for deformylation with a small amount of lime could help to recover the cellulose digestibility.

Analysis and Simulation of Epidemic COVID-19 Curves with the Verhulst Model Applied to Statistical Inhomogeneous Age Groups

Pandemic curves, such as COVID-19, often show multiple and unpredictable contamination peaks, often called second, third and fourth waves, which are separated by wide plateaus. Here, by considering the statistical inhomogeneity of age groups, we show a quantitative understanding of the different behaviour rules to flatten a pandemic COVID-19 curve and concomitant multi-peak recurrence. The simulations are based on the Verhulst model with analytical generalized logistic equations for the limited growth. From the log–lin plot, we observe an early exponential growth proportional to . The first peak is often τgrow @ 5 d. The exponential growth is followed by a recovery phase with an exponential decay proportional to . For the characteristic time holds: . Even with isolation, outbreaks due to returning travellers can result in a recurrence of multi-peaks visible on log–lin scales. The exponential growth for the first wave is faster than for the succeeding waves, with characteristic times, τ of about 10 d. Our analysis ascertains that isolation is an efficient method in preventing contamination and enables an improved strategy for scientists, governments and the general public to timely balance between medical burdens, mental health, socio-economic and educational interests.