[Divergence of Chlorophyll Dynamics in the Naroch Lakes].

We present results of the analysis of long-term chlorophyll a dynamics in the Naroch lakes. It has been shown that an increase in nutrient load in the 1970s resulted in progressive eutrophication of Naroch lakes. Then, starting in the mid-1980s, the increase in water transparency and decreases in concentrations of phosphorus and nitrogen have been occurring due to the environmental improvement program. In the 1980s, the Naroch lakes experienced a strong factor as an invasion by zebra mussel (Dreissena polymorpha Pallas). Our analysis shows that responses of all three lakes to the intensive nutrient load and further decrease in the nutrient concentration as a result of the environmental protection measures have been correlated. At the same time, different degrees of the influence of the zebra mussel invasion on the lakes are shown to lead to divergence in chlorophyll dynamics. This divergence was observed as a drastic decline in correlations between variations in chlorophyll concentrations in every Naroch lakes.

[Long-period endogenous oscillations in fish population size: mathematical modeling].

We present a mathematical model of an aquatic community, where the size-and-age structure of hydrobiont populations is taken into account and the corresponding trophic interactions between zooplankton, peaceful fish and predatory fish are described. We show that the interactions between separate components of the aquatic community can lead to long-period oscillations in fish population size. The period of these oscillations is of the order of dozen years. With the use of the model we show also that an increase in the zooplankton growth rate can be followed by a set of the fish population dynamical bifurcations: stationary states --> regular oscillations --> quasicycles --> the dynamical chaos.

[The analysis of commercial fish population size oscillations in Lake Peipus].

With the use of recurrence plots, we show that the irregular oscillations in time, which commercial fish populations in Lake Peipus undergo, are deterministic.

[The impact of the high dose-refuge strategy on the Bt-crop yield. Mathematical simulations].

A mathematical model is presented, which describes interactions between Bt-plants and pests in terms of the plant growth rate, plant annual reseeding, consumption of plant biomass by pests, the action of Bt toxins, and the emergence of Bt-resistant insects. It has been shown that the migration of Bt-susceptible insects affects the Bt-crop yield dynamics and provides the exclusion of Bt-resistant pests if the migration exceeds the threshold value.

[Mathematical model of invasion of mysids (Mysidacea) into the Naroch Lake system].

We present a mathematical model of the invasion of mysid into the Naroch Lake system. The model is parameterized with the use of field observation data. We show that the mysid invasion can lead to an increase in the time-averaged fish population size, and to a decrease in the time-averaged rotifer population size.

[Mathematical modeling of the spatial distribution of the pollen produced by genetically modified crops].

We represent and analyze the results of mathematical simulation of pollen dispersion from the origin, a field sowed by genetically modified plants. Factors responsible for the genetic isolation of such fields are discussed.

[Research of the Bt crop biomass dynamics upon the invasion of Bt-resistant pests. A mathematical model].

The results of simulations of some consequences of the invasion of Bt-resistant pests into an agricultural ecosystem containing a Bt crop are presented. It is shown that the invasion of Bt-resistant pests leads to changes in the plant biomass dynamics, a decrease in the Bt crop production, and the deterioration of the predictability of the Bt crop production. We show that the parameter values at which the badly predictable Bt crop production takes place, occupy a minor area in the model parameter space. The size of the area depends on the insect reproduction period and the duration of the growing season.

[A conceptual mathematical model of aquatic communities in lakes Naroch and Myastro (Belarus)].

A conceptual mathematical model of fish and zooplankton (rotifer) populations inhabiting the lakes Naroch and Myastro has been developed and studied. The parametrization of the model was carried out having regard to the field observation data. The population dynamics was simulated taking into account that the lakes Naroch and Myastro are coupled with each other by a channel. It was shown that both the population coupling and trophic interactions result in regular and irregular oscillations of the population size.

[Circulation of excitation waves in a model medium containing unexcitable obstacles].

The 3D structure of the heart tissue of Wistar rats from different age groups has been reconstructed by light microscopy of consecutive series of semithin sections. At the histological resolution level, connective tissue segments in the myocardium of aged (18 months) animals were found, while in the myocardium of young (2 months) animals no connective tissue segments were observed. A mathematical model and the results of the 3D reconstruction were used to simulate the formation of excitation wave circulation in the myocardium. The values of conductivity and the excitability threshold, and the pulse frequency rates were found at which the disturbances of the heart rhythm resulting from the excitation wave circulation are predicted by the mathematical modeling.

[Cytoplasmic K/Na balance in heart muscle cells of young and old rats under oxygen and substrate deficiency].

Age-related changes in the content of the major cellular cations of potassium and sodium in heart muscle cells of Wistar rats have been studied. The cytoplasmic concentration of potassium and sodium was determined by the electron probe microanalysis. The results revealed differences in both the concentration of the elements in young and old control animals and the responses of a cardiomyocyte to the state of acute hypoxic deenergization modelled on a perfused heart. The data are consistent with the hypothesis about the presence of genetically-related age changes in the conductance of potassium channels, which in old animals are realized against the background of deficient supply of tissues with oxygen and substrate.

[The rotation of autowaves as a result of their penetration through a system of unexcitable obstacles. A mechanism of arrhythmias associated with aging].

The dependence of the frequency of occurrence of excitation vortices rotating around unexcitable obstacles on the size and the number of the obstacles and also on the medium excitation threshold was studied. It was shown that the vortex formation takes place in a wide range of the model parameter values. The assumption was formulated that the mechanism of formation of excitation vortices under study underlies the increase in the heart arrhythmias associated with aging.

[Unidirectional block of propagation of a single autowave in a narrow gap and emergence of a two-dimensional reentry depends on geometry of the obstacle and on excitability of the media]. / Odnonapravlennyi blok provedeniia odinochnoi avtovolny v uzkom prokhode i vozniknovenie dvumernogo vikhria zavisiat ot geometrii prepitstviia i ot vozbudimosti sredy.

Using mathematical simulation we show that the occurrence of excitation wave circulation (reentry) around an unexcitable obstacle depends on both the geometry of the obstacle and the excitation threshold. The reentry formation is shown to take place in a wide range of model parameters.

[The study of autowave mechanisms of electrocardiogram variability during high frequency arrhythmias: mathematical modeling data]. / Issledovanie avtovolnovykh mekhanizmov variabel'nosti élektrokardiogramm vo vremia vysokochastotnykh aritmii: rezul'tat matematicheskogo modelirovaniia.

High-frequency cardiac arrhythmias are very dangerous, as they quite often lead to sudden death. These high-frequency arrhythmias are frequently produced by rotating autowaves. In the given work, the dynamics of a rotating three-dimensional excitation scroll wave and the influence of this dynamics on the variability of model electrocardiograms (ECGs) were simulated with the use of the Aliev--Panfilov model for both homogeneous and heterogeneous excitable media. Model ECGs were obtained by summing up local membrane potentials, while ECG variability was estimated numerically through the normalized variability analysis. In the homogeneous medium, the stability of the scroll wave to its filament perturbations was shown to be dependent both on the excitability of the medium and tension of the filament, while in the heterogeneous medium, the scroll was shown to be unstable. It was shown that the scroll wave dynamics affects essentially the variability of the model ECGs, and the ECG variability increases as the excitation threshold value grows. It was found that, at some parameters of the excitable medium, the variability of ECGs in the homogeneous medium is higher than in the heterogeneous medium.

[Biological activity in the modern and buried soils of the St.Petersburg's historical center]. / Biologicheskaia aktivnost' sovremennykh i pogrebennykh pochv istoricheskogo tsentra Sankt-Peterburga.

Biological activity in the urban modern and medieval soils of St. Petersburg was determined using soil samples taken from sections located at the historical center of this city nearby the Kazan Cathedral, the Twelve Colleges building (now the main building of St. Petersburg State University), and on the site where the Swedish fortress Nienshants formerly existed. The studied parameters of biological activity included the microbial transformation rate of organic matter under aerobic and anaerobic conditions, the intensity of denitrification and nitrogen fixation, and the amount of microbial biomass. This investigation is the first attempt to comparatively study modern urban anthropogenically impacted soils and buried soils that had formed the soil cover of this region before St. Petersburg was founded. The major microbiological and physicochemical parameters of the soils were subjected to correlation analysis.

[Instability of a three-dimnsional linear vortex in a simple model of a heterogenous excitable medium]. / Neustoichivost' trekhmernogo svitka v prostoi modeli geterogennoi vozbudimoi sredy.

We studied the dynamics of three-dimensional linear vortex in a heterogeneous excitable medium. Using the Aliev-Panfilov model we showed that even a small heterogeneity in excitation threshold can lead to drastic deformations of the vortex filament and an instability in its behavior.

[The mechanism of formation of Liesegang structures around Dictyostelium discoideum]. / Mekhanizm formirovaniia struktur Lizeganga vokrug populiatsii Dictyosteliumdiscoideum.

A theoretical study of the phenomenon of Liesegang structure formation induced by the Dictyostelium discoideum population in a medium containing folic acid was carried out. Using a "reaction-diffusion" model proposed in this work, it was shown that the formation of Liesegang structures around the Dictyostelium discoideum population depends on two competing processes: (a) inactivation of folic acid by vegetative amoebae and (b) the chemical reaction of folic acid with the products of amoeba metabolism, which results in the formation of insoluble sediment. The dependence of the model solutions on the geometric and functional parameters was studied. The results are in good agreement with experimental data.