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Methods for establishing standards of environmental quality by data of ecological monitoring are proposed. These are: methods of bioindication by indices of species diversity and size structure of communities, by indices of fish productivity; method for searching for reasons of environmental trouble and ranking them by their contribution into the trouble; methods for standardization of factors which are important as causes of environmental trouble.

The three-dimensional model of biomass dynamics of a tree growing on a limited territory presented. The tree consists of structural sections periodically arising on its top. Each section generates a virtual "tree". Adjacent virtual trees are nested each other and their difference is the section. Sections have biomass dynamics which differs from the dynamics of the tree and gradually die off (including in course of the free growth of the tree), giving effect denudation of trunk from bottom. This is observed in nature. The 3D-model of biomass dynamics of a tree, growing in a limited area, for describing the biomass dynamics of sections and their constituent sectors uses equations similar to those proposed earlier for the 2D-tree model. Examples of biomass dynamics of sectors, sections and tree obtained using the developed model are presented. The dynamics of the hodographs of the azimuthal biomass distribution of sections demonstrates that the lower sections of a tree growing in a limited area, are in oppression and die (more quickly compared with the model of freely growing tree), and new sections on top of the tree appear and grow freely. As a result, "wave" of tree biomass runs up the trunk.

The paper is devoted to the secondary use of spectrum in telecommunication networks. It is emphasized that one of the solutions to this problem is the use of cognitive radio technologies and dynamic spectrum access for the successful functioning of which a large amount of information is required, including the parameters of base stations and network subscribers. Storage and processing of information should be carried out using a radio environment map, which is a spatio-temporal database of all activity in the network and allows you to determine the frequencies available for use at a given time. The paper presents a two-level model for forming a map of the radio environment of a cellular communication system LTE, in which the local and global levels are highlighted, which is described by the following parameters: a set of frequencies, signal attenuation, signal propagation map, grid step, current time count. The key objects of the model are the base station and the subscriber unit. The main parameters of the base station include: name, identifier, cell coordinates, range number, radiation power, numbers of connected subscriber devices, dedicated resource blocks. For subscriber devices, the following parameters are used: name, identifier, location, current coordinates of the device cell, base station identifier, frequency range, numbers of resource blocks for communication with the station, radiation power, data transmission status, list of numbers of the nearest stations, schedules movement and communication sessions of devices. An algorithm for the implementation of the model is presented, taking into account the scenarios of movement and communication sessions of subscriber devices. A method for calculating a map of the radio environment at a point on a coordinate grid, taking into account losses during the propagation of radio signals from emitting devices, is presented. The software implementation of the model is performed using the MatLab package. The approaches are described that allow to increase the speed of its work. In the simulation, the choice of parameters was carried out taking into account the data of the existing communication systems and the economy of computing resources. The experimental results of the algorithm for the formation of a radio environment map are demonstrated, confirming the correctness of the developed model.

At the middle of the 2000-th, scientists studying the functioning of insect communities identified four basic patterns of the organizational structure of such communities. (i) Cooperation is more developed in groups with strong kinship. (ii) Cooperation in species with large colony sizes is often more developed than in species with small colony sizes. And small-sized colonies often exhibit greater internal reproductive conflict and less morphological and behavioral specialization. (iii) Within a single species, brood size (i. e., in a sense, efficiency) per capita usually decreases as colony size increases. (iv) Advanced cooperation tends to occur when resources are limited and intergroup competition is fierce. Thinking of the functioning of a group of organisms as a two-level competitive market in which individuals face the problem of allocating their energy between investment in intergroup competition and investment in intragroup competition, i. e., an internal struggle for the share of resources obtained through intergroup competition, we can compare such a biological situation with the economic phenomenon of “coopetition” — the cooperation of competing agents with the goal of later competitively dividing the resources won in consequence In the framework of economic researches the effects similar to (ii) — in the framework of large and small group competition the optimal strategy of large group would be complete squeezing out of the second group and monopolization of the market (i. e. large groups tend to act cooperatively) and (iii) — there are conditions, in which the size of the group has a negative impact on productivity of each of its individuals (this effect is called the paradox of group size or Ringelman effect). The general idea of modeling such effects is the idea of proportionality — each individual (an individual/rational agent) decides what share of his forces to invest in intergroup competition and what share to invest in intragroup competition. The group’s gain must be proportional to its total investment in competition, while the individual’s gain is proportional to its contribution to intra-group competition. Despite the prevalence of empirical observations, no gametheoretic model has yet been introduced in which the empirically observed effects can be confirmed. This paper proposes a model that eliminates the problems of previously existing ones and the simulation of Nash equilibrium states within the proposed model allows the above effects to be observed in numerical experiments.

The coconut tree is often mentioned as the “tree of life” due to its immense benefits to the human community ranging from edible products to building materials. Rugose spiraling whitefly (RSW), a natural enemy seems to be a major threat to farmers in bringing up these coconut trees. A mathematical model to study the dynamics of pest population in the presence of predator and parasite is developed. The biologically feasible equilibrium points are derived. Local asymptotic stability as well as global asymptotic stability is analyzed at the points. Furthermore, in order to educate farmers on pest control, we have added the impact of awareness programs in the model. The conditions of existence and stability properties of all feasible steady states of this model are analyzed. The result reveals that predator and parasite play a major role in reducing the immature pest. It also shows that pest control activities through awareness programs further reduce the mature pest population which decreases the egg laying rate which in turn reduces the immature population.

A vertically distributed three-component model of marine ecosystem is considered. State of the plankton community with nutrients is analyzed under the active movement of zooplankton in a vertical column of water. The necessary conditions of the Turing instability in the vicinity of the spatially homogeneous equilibrium are obtained. Stability of the spatially homogeneous equilibrium, the Turing instability and the oscillatory instability are examined depending on the biological characteristics of zooplankton and spatial movement of plankton. It is shown that at low values of zooplankton grazing rate and intratrophic interaction rate the system is Turing instable when the taxis rate is low. Stabilization occurs either through increased decline of zooplankton either by increasing the phytoplankton diffusion. With the increasing rate of consumption of phytoplankton range of parameters that determine the stability is reduced. A type of instability depends on the phytoplankton diffusion. For large values of diffusion oscillatory instability is observed, with a decrease in the phytoplankton diffusion zone of Turing instability is increases. In general, if zooplankton grazing rate is faster than phytoplankton growth rate the spatially homogeneous equilibrium is Turing instable or oscillatory instable. Stability is observed only at high speeds of zooplankton departure or its active movements. With the increase in zooplankton search activity spatial distribution of populations becomes more uniform, increasing the rate of diffusion leads to non-uniform spatial distribution. However, under diffusion the total number of the population is stabilized when the zooplankton grazing rate above the rate of phytoplankton growth. In general, at low rate of phytoplankton consumption the spatial structures formation is possible at low rates of zooplankton decline and diffusion of all the plankton community. With the increase in phytoplankton predation rate the phytoplankton diffusion and zooplankton spatial movement has essential effect on the spatial instability.

This paper proposes the implementation of a coherent transceiver with a constant delay and the ability to select any clock frequency grid used for clocking peripheral DACs and ADCs, tasks of device synchronization and data transmission. The choice of the required clock frequency grid directly affects the data transfer rate in the network, however, it allows one to flexibly configure the network for the tasks of transmitting clock signals and subnanosecond generation of sync signals on all devices in the network. A method for increasing the synchronization accuracy to tenths of nanoseconds by using digital phase detectors and a Phase Locked Loop (PLL) system on the slave device is proposed. The use of high-speed fiber-optic communication lines (FOCL) for synchronization tasks allows simultaneously exchanging control commands and signaling data. To simplify and reduce the cost of devices of a synchronous network of transceivers, it is proposed to use a clock signal restored from a data transmission line to filter phase noise and form a frequency grid in the PLL system for heterodyne signals and clock peripheral devices, including DAC and ADC. The results of multiple synchronization tests in the proposed synchronous network are presented.

It is known that the sound speed in medium that contain highly compressible inclusions, e.g. air pores in an elastic medium or gas bubbles in the liquid may be significantly reduced compared to a homogeneous medium. Effective nonlinear parameter of medium, describing the manifestation of nonlinear effects, increases hundreds and thousands of times because of the large differences in the compressibility of the inclusions and the medium. Spatial change in the concentration of such inclusions leads to the variable local sound speed, which in turn calls the spatial-temporal redistribution of acoustic energy in the wave and the distortion of its temporal profiles and cross-section structure of bounded beams. In particular, focal areas can form. Under certain conditions, the sound channel is formed that provides waveguide propagation of acoustic signals in the medium with similar inclusions. Thus, it is possible to control spatial-temporal structure of acoustic waves with the introduction of highly compressible inclusions with a given spatial distribution and concentration. The aim of this work is to study the propagation of acoustic waves in a rubberlike material with non-uniform spatial air cavities. The main objective is the development of an adequate theory of such structurally inhomogeneous media, theory of propagation of nonlinear acoustic waves and beams in these media, the calculation of the acoustic fields and identify the communication parameters of the medium and inclusions with characteristics of propagating waves. In the work the evolutionary self-consistent equation with integro-differential term is obtained describing in the low-frequency approximation propagation of intense acoustic beams in a medium with highly compressible cavities. In this equation the secondary acoustic field is taken into account caused by the dynamics of the cavities oscillations. The method is developed to obtain exact analytical solutions for nonlinear acoustic field of the beam on its axis and to calculate the field in the focal areas. The obtained results are applied to theoretical modeling of a material with non-uniform distribution of strongly compressible inclusions.

Execution or violation of the principle of competitive exclusion in communities is the subject of many studies. The principle of competitive exclusion means that coexistence of species in community is impossible if the number of species exceeds the number of controlling mutually independent factors. At that time there are many examples displaying the violations of this principle in the natural systems. The explanations for this paradox vary from inexact identification of the set of factors to various types of spatial and temporal heterogeneities. One of the factors breaking the principle of competitive exclusion is intraspecific competition. This study holds the model of community with two species and one influencing factor with density-dependent mortality and spatial heterogeneity. For such models possibility of the existence of stable equilibrium is proved in case of spatial homogeneity and negative effect of the species on the factor. Our purpose is analysis of possible variants of dynamics of the system with spatial heterogeneity under the various directions of the species effect on the influencing factor. Numerical analysis showed that there is stable coexistence of the species agreed with homogenous spatial distributions of the species if the species effects on the influencing factor are negative. Density-dependent mortality and spatial heterogeneity lead to violation of the principle of competitive exclusion when equilibriums are Turing unstable. In this case stable spatial heterogeneous patterns can arise. It is shown that Turing instability is possible if at least one of the species effects is positive. Model nonlinearity and spatial heterogeneity cause violation of the principle of competitive exclusion in terms of both stable spatial homogenous states and quasistable spatial heterogeneous patterns.

The paper uses methods of mathematical modeling to estimate a zooplankton influence on the dynamics of phytoplankton abundance. We propose a three-component model of the “phytoplankton–zooplankton” community with discrete time, considering a heterogeneity of zooplankton according to the developmental stage and type of feeding; the model takes into account cannibalism in zooplankton community, during which mature individuals of some of its species consume juvenile ones. Survival rates at the early stages of zooplankton life cycle depend explicitly on the interaction between zooplankton and phytoplankton. Loss of phytoplankton biomass because of zooplankton consumption is explicitly considered. We use the Holling functional response of type II to describe saturation during biomass consumption. The dynamics of the phytoplankton community is represented by the Ricker model, which allows to take into account the restriction of phytoplankton biomass growth by the availability of external resources (mineral nutrition, oxygen, light, etc.) implicitly.

The study analyzed scenarios of the transition from stationary dynamics to fluctuations in the size of phytoand zooplankton for various values of intrapopulation parameters determining the nature of the dynamics of the species constituting the community, and the parameters of their interaction. The focus is on exploring the complex modes of community dynamics. In the framework of the model used for describing dynamics of phytoplankton in the absence of interspecific interaction, phytoplankton dynamics undergoes a series of perioddoubling bifurcations. At the same time, with zooplankton appearance, the cascade of period-doubling bifurcations in phytoplankton and the community as a whole is realized earlier (at lower reproduction rates of phytoplankton cells) than in the case when phytoplankton develops in isolation. Furthermore, the variation in the cannibalism level in zooplankton can significantly change both the existing dynamics in the community and its bifurcation; e.g., with a certain structure of zooplankton food relationships the realization of Neimark–Sacker bifurcation scenario in the community is possible. Considering the cannibalism level in zooplankton can change due to the natural maturation processes and achievement of the carnivorous stage by some individuals, one can expect pronounced changes in the dynamic mode of the community, i.e. abrupt transitions from regular to quasiperiodic dynamics (according to Neimark–Sacker scenario) and further cycles with a short period (the implementation of period halving bifurcation).