PubMed Health⌕ Search
Home/Archive/PubMed

PubMed · 2307915

Stability in chemostat equations with delayed nutrient recycling.

E Beretta·G I Bischi·F Solimano
View original source ↗Export metadata ↓

Abstract

The growth of a species feeding on a limiting nutrient supplied at a constant rate is modelled by chemostat-type equations with a general nutrient uptake function and delayed nutrient recycling. Conditions for boundedness of the solutions and the existence of non-negative equilibria are given for the integrodifferential equations with distributed time lags. When the time lags are neglected conditions for the global stability of the positive equilibrium and for the extinction of the species are provided. The positive equilibrium continues to be locally stable when the time lag in recycling is considered and this is proved for a wide class of memory functions. Computer simulations suggest that even in this case the region of stability is very large, but the solutions tend to the equilibrium through oscillations.

Explore related subjects

EukaryotaKineticsMathematicsModels, BiologicalModels, StatisticalPopulation GrowthJournal Article

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

E Beretta, G I Bischi, F Solimano. 1990. Stability in chemostat equations with delayed nutrient recycling.. https://doi.org/10.1007/bf00171521

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2006

Phlorotannins as radical scavengers from the extract of Sargassum ringgoldianum.

To screen algal phlorotannins with antioxidative activities, 50% ethanol extracts of 25 Japanese marine algae were evaluated. Scavenging activity against superoxide anion radicals was frequently found with a high content of total phenolic compounds. Among these, the extract from the brown seaweed, Sargassum ringgoldianum, showed the strongest scavenging activity. The active fraction contained a mixture of high molecular weight polyphenols, phlorotannins that were found to be polymerized bifuhalol, as analyzed by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The scavenging activity of the fraction against superoxide anion radicals was estimated to be 1.0 microg/ml (IC(50)), which were approximately five times stronger than that of catechin.

Eukaryota↗
PubMed2006

Biological weighting functions as a tool for evaluating two ways to measure UVB radiation inhibition on photosynthesis.

To estimate the inhibitory effect of the changing UVB radiation (UVBR, 280-315nm) on earth's ecosystems, an understanding of its wavelength dependency is needed. The tool used for these estimations is the biological weighting function (BWF), whereby the inhibition of different wavelengths is calculated. BWFs were determined for three algae species from different classes, Phaeodactylum tricornutum (Bacillariophyceae), Dunaliella tertiolecta (Chlorophyceae) and Rhodomonas sp. (Cryptophyceae), using polychromatic irradiation, where the UVBR spectra were varied with cut-off filters. For each alga, BWFs were determined for two photosynthetic parameters; the quantum yield measured as fluorescence from Photo System II in a pulse-amplitude-modulation (PAM) fluorometer, and the fixation of (14)C-labelled carbon dioxide. The BWFs were calculated with the Rundel method, using the radiation data between 270 and 360nm with 1nm resolution. The results show that the UVBR damages were generally higher when using the carbon fixation measurements than when measuring with the PAM technique. When using PAM, P. tricornutum in particular had a sensitivity intermediate between the sensitive Rhodomonas sp. and the more tolerant D. tertiolecta, but was as sensitive as, or even more sensitive, than Rhodomonas sp. when using carbon fixation. D. tertiolecta was shown to be less sensitive when using both techniques and the inhibition of its photosynthesis was almost as high when using PAM as when using carbon fixation. We concluded that, although the PAM technique has advantages such as being cleaner and easier to use, it is unable to substitute the carbon fixation measurements. Not only are the algae less sensitive when measured with PAM than they are when measured as carbon fixation, the relationship between the effects on the algae measured with the two techniques also differs. As fixation of carbon dioxide integrates a larger part of the photosynthetic machinery, it should be favoured as a measure of photosynthesis.

Eukaryota↗