Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Lyapunov functions for stable cascades and applications to global stabilization

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems, one of which is stable rather than asymptotically stable. A new cross-term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition. This method is instrumental in the global stabilization of feedforward systems, and new stabilization results are derived from the generalized construction.

Seasonal variations in stable isotope ratios of two biomanipulation fishes and seston in a large pen culture in hypereutrophic Meiliang Bay, Lake Taihu

This paper reports on seasonal changes in stable carbon and nitrogen isotope ratios of seston and muscle tissue of silver carp and bighead carp during 2004 and 2005, focusing primarily on the carbon sources and trophic relationships among phytoplankton, zooplankton and silver carp and bighead carp in a large fish pen of Meiliang Bay (Lake Taihu, China). delta C-13 showed a minimal value in March 2005 and a maximal value in August 2005 in seston both inside and outside the pen, whereas delta N-15 of seston showed the minimum in winter and the maximum during algal blooms. A positive correlation between delta C-13 of silver carp and that of seston suggested that temporal variation Of delta C-13 in seston was preserved in fish via the food chain. The differences of delta C-13 among seston, zooplankton and muscle tissue of silver carp and bighead carp ranged only 0.2-1.7%, indicating that plankton production was the primary food source of filter-feeding fishes. According to a mass balance model, we estimated that the contributions of zooplankton to the diets of silver carp and bighead carp were 45.7% and 54.3%, respectively, based on the delta N-15 values of zooplankton and planktivorous fishes. (C) 2007 Elsevier B.V. All rights reserved

Diatom community succession in the recent history of a eutrophic Yunnan Plateau lake, Lake Dianchi, in subtropical China

Fish introduction, eutrophication and disappearance of aquatic vegetation are important disturbances of aquatic ecosystems, especially in plateau lakes, which are generally considered to be very vulnerable. Fish were introduced to Lake Dianchi, a eutrophic plateau lake in southwest China, in the late 1950s and 1970s. After the introduction, invasive fish became the dominant species, and the total fish yield increased. Meanwhile, the trophic level of Lake Dianchi had a tendency to increase in the past decades because of the increases in human activities in the watershed area. In addition, the area of aquatic vegetation decreased from more than 90 to 1.8% of the lake area from the 1950s to 2000. This study investigated the effects of fish introduction, eutrophication and aquatic vegetation on the diatom community of Lake Dianchi by examining the changes of microfossil diatom assemblage and abundance. Results showed that the absolute abundance and diatom assemblages changed after fish were introduced. The endemic species, Cyclotella rohomboideo-elliptica, disappeared with the introduction of fish and increasing trophic levels after 1958. Fragilaria crotonensis entered into the lake with the introduction of fish and gradually thrived in the lake after 1958. Diatom species numbers also decreased gradually from 21 to 9 from the past to present. Epiphytic diatoms disappeared with the decrease of aquatic vegetation after 1985. Our study indicated that eutrophication was the most important process determining diatom abundance, and fish introduction was a secondary process determining diatom abundance, while aquatic vegetation had a more important role in structuring the diatom community in this eutrophic plateau lake.

The effect of organic matter accumulation on phosphorus release in sediment of Chinese shallow lakes

The effects of organic matter in sediment on phosphorus release were studied by field investigations in eight Chinese shallow freshwater lakes with different trophic status and a laboratory experiment. The sediment organic matter content paralleled the trophic status, ranging from 6.1 to 173.0 g kg(-1) (dry weight), with the mean value of 63.1 g kg(-1) (dry weight). It was positively proportional to Soluble reactive phosphorus concentration in the interstitial water in a form of exponential function, but inversely related to the sediment Fe/P ratio. The sediment alkaline phosphatase activity was significantly related not only to the organic matter content (r = 0.829, P < 0.01, n = 120), but also to the soluble reactive phosphorus concentration in interstitial water (r = 0.454, P < 0.01, n = 42). In the laboratory experiment, the addition of organic matter (dry materials of an aquatic macrophyte) into the sediment significantly enhanced alkaline phosphatase activity and soluble reactive phosphorus release. However, in the treatment with organic matter added and aeration, this release was generally prevented in spite of an increase in APA. Hence, sediment organic matter can effectively accelerate phosphorus release by enzymatic hydrolysis and anaerobic desorption. The latter mechanism seems to be more important.

Growth and food availability of silver and bighead carps: evidence from stable isotope and gut content analysis

A 2-year investigation of growth and food availability of silver carp and bighead was carried out using stable isotope and gut content analysis in a large pen in Meiliang Bay of Lake Taihu, China. Both silver carp and bighead exhibited significantly higher delta 13C in 2005 than in 2004, which can probably be attributed to two factors: (i) the difference between isotopic compositions at the base of the pelagic food web and (ii) the difference between the compositions of prey items and stable isotopes. The significantly positive correlations between body length, body weight and stable isotope ratios indicated that isotopic changes in silver carp and bighead resulted from the accumulation of biomass concomitant with rapid growth. Because of the drastic decrease in zooplankton in the diet in 2005, silver carp and bighead grew faster in 2004 than in 2005. Bighead carp showed a lower trophic level than silver carp in 2005 as indicated by stable nitrogen isotope ratios, which was possibly explained by the interspecific difference between the prey species and the food quality of silver carp and bighead.

Relationships between Testate Amoebae Assemblages (Protozoa) and Geographic Factors in Yunnan Plateau Lakes, China

Knowledge of the effect of geographic factors on the assemblages of protozoan testate amoebae is still limited, despite there having been a number of studies on this fauna. We applied statistical analyses to data on the distribution of testate amoebae from nine major lakes in the Yunnan Plateau, southwest China. Cluster analysis, based on community structure, separated the lakes into two groups - the oligotrophic/mesotrophic lakes and the hypercutrophic lakes - confirming the idea that the testate amoebae assemblages in lakes are closely related to the trophic status. Additionally, within the oligotrophic/mesotrophic lakes, there was distinct geographic clustering. Linear regression analysis and the Mantel test both revealed that similarity of species composition decreased with increasing geographic distance among the oligotrophic/mesotrophic lakes.

Phosphorus in suspended matter and sediments of a hypertrophic lake. A case study: Lake Dianchi, China

From June 2004 to December 2004, Lake Dianchi, which had large scale of cyanobacterial blooms was investigated in order to study P-fractionation in the suspended matter and the sediment. The investigation improves our understanding of phosphorus in Lake Dianchi and the relationship between phosphorus and cyanobacterial blooms. It contributes to the available literature on the behavior of P in hypertrophic lakes. The distribution of P-fractions in Lake Dianchi was not uniform from northwest to south, but was closely related to the trophic status of the whole lake. The concentrations of total phosphorus, labile P (NH4Cl-P), Organic P (NaOH-NRP) and loss on ignition in suspended matter were positively correlated with the strength of cyanobacterial blooms. Total phosphorus in suspended matter was relatively stable for almost half an year and closely related to Chl. a concentration. The main content of organic phosphorus is in the cyanobacterial blooms. The concentrations of phosphorus bound to metal oxides and carbonates (NaOH-SRP and HCl-P) in sediment were similar to NaOH-SRP and HCl-P in the corresponding suspended matter. The latter two forms of P in suspended matter were not affected by cyanobacterial blooms, indicating that the inorganic phosphorus is derived from the sediment after resuspension from the sediment due to wind and wave action. The contribution of the different P-fractions to TP in sediment and in suspended matter indicates that NH4Cl-P in the suspended matter is an important buffer for maintaining dissolved phosphorus in water.

Extracellular phosphatases produced by phytoplankton and other sources in shallow eutrophic lakes (Wuhan, China): taxon-specific versus bulk activity

Extracellular phosphatases are an important part of the phosphorus cycle in aquatic environments. Phosphatase activity (PA) in plankton was studied in seven subtropical shallow lakes of different exploitation management and trophic status in the urban area of Wuhan City. Bulk PA was rather high (range 1.1-11 mu mol l(-1) h(-1)), although concentrations of soluble reactive phosphorus (SRP) were also high (range 27 mu g P l(-1) to similar to 1.5 mg P l(-1)) in all lakes. Cell-associated extracellular PA in phytoplankton was detected using the fluorescence-labelled enzyme activity technique. Phytoplankton species partly contributed to the bulk PA. We found explicit differences in the presence of cell-associated phosphatase within the main phytoplankton groups; species belonging to Chlorophyta and Dinophyta were regularly phosphatase-positive, while Cyanophyta and Bacillariophyceae were phosphatase-negative in all but one case. Furthermore, there is a certain potential of extracellular phosphatases produced by heterotrophic nanoflagellates in most of the lakes. This new finding compromises the 'traditional' interpretation of bulk phosphatase data as being due to overall phytoplankton or bacterial P regeneration.

Diversity and abundance of ammonia-oxidizing bacteria in eutrophic and oligotrophic basins of a shallow Chinese lake (Lake Donghu)

Classical cultivation and molecular methods based on the ammonia monooxygenase gene (amoA) were used to study the abundance and diversity of beta-proteobacterial ammonia-oxidizing bacteria (AOB) in lake sediments. The eutrophic and oligotrophic basins of a Chinese shallow lake (Lake Donghu), in terms of ammonium (NH4+) concentrations, were sampled. The AOB number was significantly lower in the oligotrophic basin, but significantly higher in the eutrophic basin. In addition, using restriction fragment length polymorphism targeting the amoA, ten restriction patterns including six unique ones were found in the eutrophic basin, while five patterns were observed in the oligotrophic basin with only one unique restriction group. Phylogenetic analysis for AOB revealed that Nitrosomonas oligotropha- and Nitrosomonas ureae-related AOB and Nitrosospira-affiliated AOB were ubiquitous; the former dominated in the eutrophic basin (87.2%), while the latter dominated in the oligotrophic basin (65.5%). Furthermore, Nitrosomonas communis-related AOB was only detected in the eutrophic basin, at a small proportion (3.2%). These results indicate significant selection and adaptation of sediment AOB in lakes with differing trophic status. (C) 2009 Elsevier Masson SAS. All rights reserved.

Transfer, distribution and bioaccumulation of microcystins in the aquatic food web in Lake Taihu, China, with potential risks to human health

In this paper, accumulation and distribution of microcystins (MCs) was examined monthly in six species of fish with different trophic levels in Meiliang Bay, Lake Taihu, China, from June to November 2005, Microcystins were analyzed by liquid chromatography electrospray ionization mass spectrometry (LC-ESI-MS). Average recoveries of spiked fish samples were 67.7% for MC-RR, 85.3% for MC-YR, and 88.6% for MC-LR. The MCs (MC-RR+MC-YR+MC-LR) concentration in liver and gut content was highest in phytoplanktivorous fish, followed by omnivorous fish, and was lowest in carnivorous fish; while MCs concentration in muscle was highest in omnivorous fish, followed by phytoplanktivorous fish, and was lowest in carnivorous fish. This is the first study reporting MCs accumulation in the gonad of fish in field. The main uptake of MC-YR in fish seems to be through the gills from the dissolved MCs. The WHO limit for tolerable daily intake was exceeded only in common carp muscle. (C) 2008 Elsevier B.V. All rights reserved.

Diel isotopic fluctuation in surface seston and its physiological and ecological implications

We reported diet fluctuation in isotopic composition of surface seston from two connected lakes in China, oligotrophic Lake Fuxian and eutrophic Lake Xingyun. The decrease in nighttime and the increase in daytime of isotope signatures of seston might be attributed to the light-dependent balance between the photosynthesis and the respiration of phytoplankton and to the changes in the species composition and the relative abundance of phytoplankton functional groups at the water's surface in diel growth. The relatively high isotopic signatures and the large-extent diel fluctuation of phytoplankton in the eutrophic lake could be due to utilization of heavy-isotope-enriched inorganic sources and the high primary productivity. Extent of diel fluctuation in delta C-13 and delta N-15 of phytoplankton were relatively small compared with the isotopic enrichment per trophic transfer and thus might have negligible effect on the source identification and the trophic evaluation of consumers.

RNAi suppression of zebrafish peptidoglycan recognition protein 6 (zfPGRP6) mediated differentially expressed genes involved in Toll-like receptor signaling pathway and caused increased susceptibility to Flavobacterium columnare

In Drosophila, Toll signaling cascade, which resembles the mammalian Toll-like receptor (TLR)/IL-1R signaling pathways and regulates the expression of anti-microbial peptide genes, mainly relies on peptidoglycan recognition proteins (PGRPs) for the detection of bacterial pathogens. To explore the effect of zebrafish peptidoglycan recognition protein 6 (zfPGRP6) on Toll-like receptor signaling pathway, RNA interference (siRNA) and real time quantitative PCR (RQ-PCR) methods were used to identify differentially expressed genes regulated by zfPGRP6. The target genes included TLR2, TLR3, TLR5, TLR7, TLR8, IL1R, Sterile-alpha and Armadillo motif containing protein (SARM), myeloid differentiation factor 88 (MyD88) and nuclear factor (NF)-kappa B2 (p100/p52). The results of RQ-PCR showed that RNAi-mediated Suppression of zfPGRP6 significantly down-regulated the expression of TLR2, TLR5, IL1R, SARM, MyD88 and p100/p52. The expression of beta-defensin-1 was also down-regulated in those embryos silenced by zfPGRP6. In challenge experiments to determine the anti-bacterial response to Gram-negative bacteria, RNAi knock-down of zfPGRP6 markedly increased susceptibility to Flavobacterium columnare. (C) 2008 Elsevier B.V. All rights reserved.

Food web of benthic macro invertebrates in a large Yangtze River-connected lake: the role of flood disturbance

This Study was conducted in Lake Dongtinghu, a large river-connected lake on the Yangtze River flood-plain, China. Our goal was to determine trophic relationships among benthic macroinvertebrates, as well as the effects of flood disturbance on the benthic food web of a river-connected lake. Macroinvertebrates in the lake fed mainly on detritus and plankton (both zooplankton and phytoplankton). Food web Structure in Lake Dongtinghu was characterized by molluscs as the dominant group, low connectance, high level of omnivory. based oil detritus and primary production, and most ingestion concentrating on a few links. Our analyses showed that flood disturbance is an important factor affecting the benthic food web in Lake Dongtinghu. The numbers of species and functional feeding groups (FFGs), and the density and biomass of macroinvertebrates decreased significantly during flooding. Connectance was higher during the flood season than in other seasons, indicating that floods have a strong effect on connectance in this Yangtze River-connected lake. Flood effects on the benthic web were also evident in the decrease of niche overlaps within and anion, FFGs. Our results provide useful information regarding biodiversity conservation on the Yangtze floodplain. Reconstructing and maintaining natural and regular flow regimes between Yangtze lakes and the river is essential for restoration of macroinvertebrates on the floodplain.

In situ study on effect of food competition on diet shifts and growth of silver and bighead carps in large biomanipulation fish pens in Meiliang Bay, Lake Taihu

Silver and bighead carps were cultured in large fish pens to reduce the risks of cyanobacterial bloom outbreaks in Meiliang Bay, Lake Tauhu in 2004 and 2005. Diet compositions and growth rates of the carps were studied from April to November each year. Both carp species fed mainly on zooplankton (> 50% in diet) in 2004 when competition was low, but selected more phytoplankton in 2005 when competition was high. Silver carp had a broader diet breadth than did bighead carp. Higher densities and fewer food resources increased diet breadths but decreased the diet overlap in both types of carps. It can be predicted that silver and bighead carps would be released from diet competition and shift to feed mainly on zooplankton at low densities, decreasing the efficiency of controlling cyanobacterial blooms. Conclusively, when silver and bighead carps are used to control cyanobacterial blooms, a sufficiently high stocking density is very important for a successful practice.