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A method for determining bone density based on a single exposure on a serial X-ray machine and subsequent calibration by a stepped aluminum wedge has been developed. The experimental setup is described, the results of measurement on the phantom are presented. During calibration, an effective subtraction of soft tissues was carried out. The results of comparison of experimental data with GEANT-4 simulation are presented. Estimates of the effect of uneven illumination, coordinate resolution and scattered background on the quality of the image are made. The conclusion is made about the competitiveness of the developed technique in comparison with traditional two-beam diagnostics.

—This paper deals with the identification of the type of population dynamics of the green oak tortrix (Tortrix viridana L.) by the available time series with a generalized discrete logistic model. The results of estimates of model parameters obtained by the ordinary least squares (OLS) method and model parameters obtained by the method of extreme points (MEP) are compared. It is assumed that the model adequately describes the population dynamics if and only if the deviations of the theoretical (model) data from the empirical data meet a number of statistical tests. It is shown that the model using OLS estimates does not provide adequate fitting of time series and the type of population dynamics cannot be identified. Analysis of four variants of MEP estimates shows that the observed regime of the population dynamics is not cyclic (if the length of the cycle is less than 15 000 years); in addition, a rapid decrease in the values of the autocorrelation function, followed by their fluctuation in a narrow range, is observed for all regimes.

A wide range of insects affect crop production and cause considerable yield losses. Difficulties reside on the development and adaptation of adequate strategies to predict insect pests for their timely management to ensure enhanced agricultural production. Several conceptual modelling frameworks have been proposed, and the choice of an approach depends largely on the objective of the model and the availability of data. This paper presents a summary of decades of advances in insect population dynamics, phenology models, distribution and risk mapping. Existing challenges on the modelling of insects are listed; followed by innovations in the field. New approaches include artificial neural networks, cellular automata (CA) coupled with fuzzy logic (FL), fractal, multi-fractal, percolation, synchronization and individual/agent-based approaches. A concept for assessing climate change impacts and providing adaptation options for agricultural pest management independently of the United Nations Intergovernmental Panel on Climate Change (IPCC) emission scenarios is suggested. A framework for estimating losses and optimizing yields within crop production system is proposed and a summary on modelling the economic impact of pests control is presented. The assessment shows that the majority of known insect modelling approaches are not holistic; they only concentrate on a single component of the system, i.e. the pest, rather than the whole crop production system. We suggest system thinking as a possible approach for linking crop, pest, and environmental conditions to provide a more comprehensive assessment of agricultural crop production.

Current publication is devoted to the problem in identifying the type of population dynamics (on an example of green oak tortrix (Tortrix viridana L.)). For fitting of time series of tortrix fluctuations (Korzukhin and Semevsky, Sin-ecology of forest. Gidrometeoizdat, Saint-Petersburg, 1992), generalized discrete logistic model was used. Results of model parameter estimations obtained with ordinary least squares (OLS) and method of extreme points (MEP) (Nedorezov. Chaos and Order in Population Dynamics: Modeling, Analysis, Forecast. LAP Lambert Academic Publishing, Saarbrucken. 2012. p. 352; Nedorezov. J. Gen. Biol. 73(2), 114–123, 2012; Nedorezov. Biophysics 61(1), 149–154, 2016) were compared. It was assumed that the model demonstrates good correspondence to time series if and only if deviations between time series and model trajectory satisfy with several statistical tests. It was shown that model with OLS estimations of parameters cannot be used for fitting of time series. Analyses of four various variants of MEP estimations were provided, and it was obtained that observed dynamic regime of population dynamics isn’t cyclic (if length of cycle is less than 1500 years). For the selected dynamic regimes, a rapid decrease in values of auto-correlation functions with further small fluctuations near zero level was observed. It means that forecasting the change in population size for short or long time periods is practically impossible.

The Lotka–Volterra model of predator–prey dynamics was used for approximation of the wellknown empirical time series on the lynx–hare system in Canada that was collected by the Hudson Bay Company in 1845–1935. The model was assumed to demonstrate satisfactory data approximation if the sets of deviations of the model and empirical data for both time series satisfied a number of statistical criteria (for the selected significance level). The frequency distributions of deviations between the theoretical (model) trajectories and empirical datasets were tested for symmetry (with respect to the Y-axis; the Kolmogorov–Smirnov and Lehmann–Rosenblatt tests) and the presence or absence of serial correlation (the Swed–Eisenhart and “jumps up–jumps down” tests). The numerical calculations show that the set of points of the space of model parameters, when the deviations satisfy the statistical criteria, is not empty and, consequently, the model is suitable for describing empirical data.

This paper proposes a design of a predator-prey system with adaptive controller. It assumes simultaneous operation of complex outbreak pressing. Mathematical model for the entire system is represented in the form of a 2-order system. Adaptation mechanism is based on method of Lyapunov function. MATLAB simulation confirms the efficiency of proposed. However, the problem for construction of an adaptive control system with reference model consists in a finding of such parameters with estimations of control at which the complex behavior can be stabilization to the predicted level. The method of Lyapunov's second method the adaptive laws with reference model is also discussed. This should develop the situation throughout the testing and improving new control methods and phases based on population dynamics model.

For fitting of well-known experimental time series on Paramecium aurelia population dynamics ( Gause, 1934 ; Figures 24 and 25) Verhulst and Gompertz models were used. For every model for both considering time series values of parameters were estimated in two different ways: with least squared method (LSM) and with non-traditional method which does not require using of any loss-functions. Properties of deviations between theoretical (model) trajectories and experimental datasets were checked with certain number of non-parametric statistical tests. It was obtained that in some cases properties of deviations corresponding to LSM-estimations, do not satisfy requirements which are producible to “good models”. In some cases small modifications of LSM-estimations can lead to obtaining satisfactory results in approximation of experimental results. It was also obtained that in some cases Gompertz model demonstrates better fitting of time series than Verhulst model.

In current publication, a non­traditional approach to estimation of parameters of ecological models is considered. Within the framework of this approach it is not necessary to construct loss­function or likelihood function. The basic idea of method is as follows: first of all, basic requirements to model and to deviate between theoretical (model) and empirical datasets must be formulated. After that, respective statistical criteria must be selected, and with the help of these statistical criteria, a feasible set in space of model parameters must be determined (where all statistical criterions demonstrate required results). Within the limits of this feasible set must be found elements with strongest properties. These elements can be used as estimations of model parameters. Constructions of feasible sets for Moran – Ricker model with and without time lag and ELP­model were demonstrated on examples of larch bud moth (Zeiraphera diniana Gn.) and pine looper moth (Bupalus piniarius L.) time series. Results of approximation are discussed. For a time series of population dynamics of larch budworm it was found that feasible sets are not empty for the model Moran – Ricker without delay and with delay of one year. At the same time, the analysis of properties of elements of admissible sets showed that among them there are no properties that match the prevailing biological understanding of the dynamics of the Zeiraphera diniana Gn. The resulting estimation allowed taking into account the delay of one year to receive treatment with a cycle length of 18 with two maxima. However, almost all statistical tests gave negative results. These results indicate that the delay in the self­regulation mechanisms of action of more than one year. Given way to simultaneously estimate the parameters of the population dynamics model of pine looper for related time series. The analysis shows that there is every reason for the claim that the observed mode – cyclic short cycle length of two years.

For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a "fine" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.

Modifications of Moran–Ricker model with time lags are applied for fitting of larch bud moth ( Zeiraphera diniana Gn.) time series. Model parameters were estimated, and deviations between model trajectories and empirical time series were analyzed with various statistical tests. It was shown that some of considered models allowed obtaining rather good fitting. For estimated parameters asymptotic stable dynamic regimes were found: it is 9-year cycle (for model with time lag in four years), it is 18-year cycle (with close values of cycle coordinates for model with time lag in one year), or regime with complicated dynamics (for model with time lag in three years). Obtained results correspond to biological imagination about fluctuations of larch bud moth populations.

In paper stochastic model with discrete time of migrations in finite part of plane is considered. It is assumed that migrations can be from every node of integer lattice to nearest nodes only, and these migrations depend on numbers of individuals in the respective nodes. Population size is assumed to be constant for every sequence of population size measurements. It is also assumed that there are two limits D1 and D2, D1, D1 < D2, of local population size in node when respective node is attractable for migrants (Alley effect). If local population size is bigger than D2 node becomes unsuitable for migrants, and all individuals try to leave the respective node. After a certain number of time steps local population size is determined in randomly selected nodes (it looks like method of "throwing of frame" or "cutting of model trees" of entomological data collection but in considering situation it doesn't lead to changing of conditions for population). Dependence of standard deviations of samples of various sizes on fixed values of population density are analyzed. In particular, it is shown that well-known problem of heteroscedasticity cannot be solved in principle for the situation when ecological model parameters must be estimated using empirical or experimental time series. Analysis of dependence of number of interactions of individuals per time step (average in time and space) on total population size allows pointing out new ways in modification of Verhulst model.

In paper continuous-discrete model of parasite-host system dynamics is analyzed. Within the framework of model it is assumed that appearance of individuals of new generations of both populations is realized at fixed time moments tk=hk, t0=0, k=1,2,... , h=const>0; it means that several processes are compressed together: producing of eggs by hosts, attack of eggs by parasites (with respective transformation of host's eggs into parasite's eggs), staying of hosts and parasites in phase "egg", and appearance of new individuals. It is also assumed that death process of individuals has a continuous nature, but developments of both populations are realized independently between fixed time moments. Dynamic regimes of model are analyzed. In particular, it was obtained that with simplest assumptions about birth process in host population and numbers of attacked hosts regime with two non-trivial stable attractors in phase space of system can be realized.

Given the population dynamics model and the fairly long time series of data, the model parameters can be measured in different segments of this series to get respectively different estimates and a model with time-variable parameters. The variations in model parameters can be caused either by variations in the environmental conditions that affect the population size or by mere demographic stochasticity. A possible approach to the issue is considered based on the example of the data on fluctuations in the population density of pine moth (Bupalus piniarius L.) in Germany. To approximate the data, the well-known Moran-Ricker model is used, which has a rich variety of dynamic regimes. The parameter estimation was carried out by the least-squares method (by 12 out of 58 values). The analysis of trends in the two series of model coefficients, i.e., the maximal growth rate and the coefficient of self-regulation, reveals that the changes in both indicators are low for quite a long period of time (60 years), and the hypothesis of no directed trend in the environment changes turns out to be statistically plausible.

In current publication the statistical method of analysis of population time series in considered. This method is based on analysis of dynamics of non-linear ecological model parameter estimations in time, and devoted to investigation of influence of change of weather conditions on population dynamics (on the other words, it is devoted to analysis of climate change from the standpoint of separated population dynamics). Estimations of model parameters were obtained for parts (which contains 12 values each) of initial sample. For the approximation of sub-samples the well-known Kostitzin model of population size changing in time was used. It was used for the approximation of dataset of pine looper moth (Bupalus piniarius L.) dynamics in Germany (total sample size is 58). Estimation of model parameters were obtained with known least squares method. Analyses of tendencies of model parameter estimations showed that there are no reasons for rejecting hypotheses about the equalities of regression line angles to zero. It gives the base for conclusion about the absence of serious change in weather conditions in Germany during analyzing time interval (60 years).

Gause’s experimental data on the population size of Paramecia aurelia and Paramecia caudatum (Gause, 1934) were approximated using the Verhulst, Gompertz, Rosenzweig, and Svirezhev population growth models, in which the effect of self-regulation on the population dynamics is taken into account in a different manner. The parameters of each model were estimated using the least squares method with and without an additional upper bound on the model parameter values (which were assumed to be nonnegative). In the latter (traditional) case, the residuals were tested for normality with zero mean (Kolmogorov-Smirnov, Shapiro-Wilk, and Lilliefors tests) and for serial correlation (Durbin-Watson and Swed-Eisenhart runs tests). The best results were obtained for the Verhulst and Gompertz models. In the former (more realistic) case, the model parameter was interpreted as the carrying capacity and was a priori assumed to be greater than any element of the sample. The best results were obtained for the Gompertz model. Under this constraint, the canonical scheme for residual analysis cannot be applied, since the sequence of residuals always exhibits serial correlation (for sufficiently long samples). The arithmetic mean is not zero (since, starting at some time, all the experimental points are on one side of the theoretical curve) and the residual distribution is not normal. Possible variants for testing residual sequences in these cases are discussed.

Data on the population dynamics of the larch bud moth (Zeiraphera diniana Gn.) in the Swiss Alps are analyzed. The analysis is performed with mathematical models of isolated population dynamics in discrete time (such as the Kostitzin model, Skellam model, discrete logistic model, and others), which include minimum unknown parameters. For all analyzed models, the parameters were estimated using data of the Global Population Dynamics Database (nos. 1407 and 6195) by the method of least squares, and sequences of residuals of empirical data and values predicted by model trajectories were analyzed. It is shown that the best approximations are achieved with the Moran-Ricker model and the discrete logistic model. Statistical tests (Kolmogorov-Smirnov, Shapiro-Wilk) show that normal distribution hypotheses of residuals of empirical data and model trajectories for one of the time series (no. 1407) must be rejected; some models display serial correlations in sequences of residuals (according to the Durbin-Watson test). This leads to the conclusion that periodic changes in the larch bud moth population size (no. 1407) can hardly be explained by intrapopulation regulation mechanisms alone. For the other time series (no. 6195), the modified discrete logistic model is shown to be appropriate for explaining population dynamics.

For the approximation of some of well-known time series of Paramecia aurelia and Paramecia caudatum (under the separated cultivation of both species) population size changing in time, some well-known models were used. For all considering models values of parameters were estimated with least square method (with global fitting) in two different ways: with and without additional limits for parameter values. In the case without additional limits for model parameters deviations between theoretical (model) trajectories and experimental time series were tested for Normality (Kolmogorov-Smirnov' test, and Shapiro-Wilk' test) with zero average, and for existence/absence of serial correlation (Durbin-Watson' criteria). The best results were observed for Gompertz' and Verhulst' models. Under the assumption that parameter K (maximum value of population size) is greater than all elements of initial sample the best results were observed for Gompertz model. In the last case the canonical technique for analysis of set of deviations can be applied in restricted form and needs in further development. In such a situation we cannot test the set of deviations on Normality with zero average (for big samples) because after a certain time moment all experimental points will be at one side of theoretical curve; at this situation we have to have a serial correlation in the sequence of deviations, etc.

The performance of discrete mathematical models to describe the population dynamics of diamondback moth (DBM) ( Plutella xylostella L.) and its parasitoid Diadegma semiclausum was investigated. The parameter values for several well-known models (Nicholson–Bailey, Hassell and Varley, Beddington, Free and Lawton, May, Holling type 2, 3 and Getz and Mills functional responses) were estimated. The models were tested on 20 consecutive sets of time series data collected at 14 days interval for pest and parasitoid populations obtained from a highland cabbage growing area in eastern Kenya. Model parameters were estimated from minimized squared difference between the numerical solution of the model equations and the empirical data using Powell's method. Maximum calculated DBM growth rates varied between 0.02 and 0.07. The carrying capacity determined at 16.5 DBM/plant by the Beddington et al. model was within the range of field data. However, all the estimated parameter values relating to the parasitoid, including the instantaneous searching rate (0.07–0.28), per capita searching efficiency (0.20–0.27), search time (5.20–5.33), handling time (0.77–0.90), and parasitism aggregation index (0.33), were well outside the range encountered empirically. All models evaluated for DBM under Durbin–Watson criteria, except the May model, were not autocorrelated with respect to residuals. In contrast, the criteria applied to the parasitoid residuals showed strong autocorrelations. Thus, these models failed to estimate parasitoid dynamics. We conclude that the interactions of the DBM with its parasitoid cannot be explained by any of the models tested. Two factors may be associated with this failure. First, the parasitoid in this integrated biological control system may not be playing a major role in regulating DBM population. Second, and perhaps more likely, poor correlations reflect gross inadequacies in the theoretical assumptions that underlie the existing models.

The Lotka–Volterra model was applied to the population densities of diamondback moth (DBM), Plutella xylostella (L.) and its exotic larval parasitoid Diadegma semiclausum (Hellen) data that was collected earlier by icipe 's DBM biological control team. The collections were done for 15 months before the release and 36 months after release of the parasitoid in two areas; in Werugha, Coast Province of Kenya and Tharuni, Central Province of Kenya, respectively. For each area in pre- and post-release periods, we estimated Lotka–Volterra model parameters from the minimization of the loss function between the theoretical and experimental time-series datasets following the Nelder-Mead multidimensional method. The model estimated a reduction in the value of the steady state of DBM population from 4.86 to 2.17 in Werugha and from 6.11 to 3.76 and 3.45 (with and without exclusion of the time before D. semiclausum recovery) in Tharuni when transiting from the pre- and post-release periods, respectively. This change was a consequence of the newly introduced parasitoid, in the areas. The study presented a successful and detailed technique for non-linear model parameters restoration which was demonstrated by the correct mimicking of empirical datasets from the classical biological control with D. semiclausum, in different areas of Kenya. The applied model has measured the parasitoids impact on the DBM biological control through a quantitative estimate of the effectiveness of the newly introduced species D. semiclausum . These equations may therefore be used as tool for decision making in the implementation for such pests’ management system strategy.

The applicability of discrete mathematical models for the description of diamondback moth (DBM) ( Plutella xylostella L.) population dynamics was investigated. The parameter values for several well-known discrete time models (Skellam, Moran–Ricker, Hassell, Maynard Smith–Slatkin, and discrete logistic models) were estimated for an experimental time series from a highland cabbage-growing area in eastern Kenya. For all sets of parameters, boundaries of confidence domains were determined. Maximum calculated birth rates varied between 1.086 and 1.359 when empirical values were used for parameter estimation. After fitting of the models to the empirical trajectory, all birth rate values resulted considerably higher (1.742–3.526). The carrying capacity was determined between 13.0 and 39.9 DBM/plant, after fitting of the models these values declined to 6.48–9.3, all values well within the range encountered empirically. The application of the Durbin–Watson criteria for comparison of theoretical and experimental population trajectories produced negative correlations with all models. A test of residual value groupings for randomness showed that their distribution is non-stochastic. In consequence, we conclude that DBM dynamics cannot be explained as a result of intra-population self-regulative mechanisms only (=by any of the models tested) and that more comprehensive models are required for the explanation of DBM population dynamics.

The goal of this work was to perform statistical analysis of experimental trajectories of temperature-myographic BFB training. Approximation of signals was implemented using fractional-linear functions. It was found that the number of approximation functions decreased with increasing number of sessions. Moreover, if the number of approximation functions was large enough, it was possible to find the asymptotic behavior of monitored signal with the help of initial values of the signal. It means that it is possible to reveal the potentialities of patients during 3 or 4 sessions of training. Estimation of the time interval of active work showed that there were two various laws for values of temperature and values of myogram: for the first monitored variable, power law; for the second variable, exponential law. But for both monitored parameters the constants were positive, which meant that there was a minimum of time interval for the active "work" for every patient. Correlation analysis (i.e., analysis of autocorrelation and cross-correlation functions) of temperature and myogram signals showed that there was a correlation between monitored parameters. It means that for both signals we can consider both positive and negative time lag dependence between values of temperature and myogram. Statistical analysis of signal behavior made it possible to construct a phenomenological model of temperature-myogram BFB-training, which comprises the basic parameters of patients. With the help of the model it is possible, in particular, to calculate the sojourn time of system at any part of the phase plane. This characteristic can be used as an integral estimation of the efficiency of BFB-training.

Discrete mathematical model is selected for description of green oak leaf roller (Tortrix viridana L.) population dynamics. Experimental data set from Rubtsov [Rubtsov, V.V., 1992. Models of Oscillation Processes in Forest Ecosystems, Forest Institute, Moscow, Russian Federation, p. 39 (in Russian)] is analyzed from the standpoint of phenomenological theory of forest insect population dynamics [Isaev, A.S., Khlebopros, R.G., Nedorezov, L.V., Kiselev, V.V., Kondakov, Yu. P., 1984. Dynamics of Forest Insects Populations, USSR, Nauka, Novosibirsk, p. 224 (in Russian); Isaev, A.S., Khlebopros, R.G., Nedorezov, L.V., Kiselev, V.V., Kondakov, Yu.P., Soukhovol'sky, V.G., 2001. Population Dynamics of Forest Insects, Russian Federation, Nauka, Moscow, p. 347 (in Russian)]. For checking hypotheses confidence for fitting of experimental time series, Moran–Ricker model, Maynard Smith–Slatkin model, and some others are used. Selection of statistical criteria for estimating parameter's values is discussed. In addition, probabilities of realizations of several dynamical regimes are estimated.

In this paper we describe the development of individual-based simulation model on zoophilic mosquito's behavior that encounters odor plumes from two groups of alternative hosts. Within the framework of the model it is assumed that (i) the hosts are represented by two points located at varying distance from each other and that their odor plumes (“zones of influence”) are represented by fractional–linear functions that depend on the number of individuals in each host group and their relative attractiveness to the mosquito; (ii) a mosquito comes under the attractive influence of the plumes only within a fixed domain with rectangular distribution; (iii) outside the odor zones, the probability of a mosquito locating points that represent human or animal hosts is zero; and (iv) the interval between mosquito's contact with one or the other plume is a stochastic variable with exponential distribution. 10 5 computer experiments were carried out to elucidate the relationship between the number of individual mosquitoes that arrived at the ‘human point’ and its distance from the ‘animal point’. This relationship was found to have a non-linear character with maximum diversion to the alternative hosts occurring at a certain optimum distance. As expected, at any given distance between the host points, the number of mosquitoes that arrived at the ‘human point’ varied with the relative numbers of ‘human and animal individuals’. The implications of the results are discussed.

Analysis of experimental trajectories in temperature-myographic BFB-training is considered. Analysis of point density on the phase plane (first of all, the states of extreme density points with respect to some basic thresholds) makes it possible to determine the main tendencies in the development of the training process. It also provides an opportunity to obtain a qualitative conclusion about the efficacy of BFB-training. There are three different ways for analysis of experimental points. The first way consists in constructing a general (or integral) picture, which can be obtained by reconstructing the point density for all experimental points measured during a single session. The integral picture shows the number of density peaks and their position on the plane, the sojourn time of the system at one or another part of the phase plane, etc. The second way is the analysis of time series of density values during a single session of training. The first density value corresponds to the basic state of the patient. Analysis of the density dynamics makes it possible to determine the character and tendencies of the strategies used by the patient during the session. The third way is the analysis of time series of integral pictures, which can be obtained upon finishing all training sessions. It provides an opportunity to draw a final conclusion about the efficacy of training in general. The analysis made it possible to divide the group of experimental trajectories into several subdomains. The first subgroup contained the trajectories corresponding to BFB-training based on both monitoring parameters (temperature and myogram). The second and third subgroups contained the trajectories corresponding to BFB-training based on one or another monitored parameter. The last group contained the trajectories used without success.

This article is devoted to the development of a program that estimates the energy-force characteristics and other operating parameters for the hot rolling of plates. An explanation is given of aspects of the program’s development and a mathematical model constructed to describe the rolling operation. A comparison is made between calculated and experimental values of the motor current and the temperature of the semifinished product by pass during the rolling of plates of steel 10G2FBYu. The program was successfully tested and introduced on the 2800 plate mill at Ural Steel. Its use has facilitated selection of the appropriate regimes for the controlled rolling of high-strength plates and has eliminated breakage of the mill equipment.

A stochastic model of migrations on a lattice and with discrete time is considered. It is assumed that space is homogenous with respect to its properties and during one time step every individual (independently of local population numbers) can migrate to nearest nodes of lattice with equal probabilities. It is also assumed that population size remains constant during certain time interval of computer experiments. The following variants of estimation of encounter rate between individuals are considered: when for the fixed time moments every individual in every node of lattice interacts with all other individuals in the node; when individuals can stay in nodes independently, or can be involved in groups in two, three or four individuals. For each variant of interactions between individuals, average value (with respect to space and time) is computed for various values of population size. The samples obtained were compared with respective functions of classic models of isolated population dynamics: Verhulst model, Gompertz model, Svirezhev model, and theta-logistic model. Parameters of functions were calculated with least square method. Analyses of deviations were performed using Kolmogorov-Smirnov test, Lilliefors test, Shapiro-Wilk test, and other statistical tests. It is shown that from traditional point of view there are no correspondence between the encounter rate and functions describing effects of self-regulatory mechanisms on population dynamics. Best fitting of samples was obtained with Verhulst and theta-logistic models when using the dataset resulted from the situation when every individual in the node interacts with all other individuals.

Analysis of deviations between trajectories of Lotka-Volterra model of competition between two species and G.F. Gause experimental time series on combined cultivation of Paramecium aurelia and Paramecium caudatum shows that with rather big probability there is no correspondence between model and experimental datasets. Testing of sets of deviations was provided on symmetry with. respect to origin (Kolmogorov-Smirnov, Lehmann-Rosenblatt, Wald-Wolfowitz, and Munn-Whitney criterions) and on existence/absence of serial correlation in sequences of residuals (Swed-Eisenhart and "jumps up-jumps down" tests).

For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a "fine" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.

We consider a parametric model for the dynamics of an isolated population with sex structure which is realized as a system of ordinary differential equations with impulses. The birth rate in the population in this model is assumed to be of a discrete character and the appearance of new generation specimens occurs at fixed moments, while the death rate is of a continuous character. We examine dynamical regimes of the model; in particular, we show that cyclic and chaotic regimes may occur for some values of parameters.

In this paper we consider the system of mathematical models which describes the interaction of population with its various main regulators and the development of population outbreaks. As a result of these models analysis we obtained the set of different phase portraits which corresponds to the various types of population outbreaks. It was possible to select four different types of outbreaks which were determined in a predator-prey system and in a population-food plant system. For some other models we found the conditions of realization of dynamic regimes of population outbreaks and types of these mass propagations.

There exist two main problems in the analysis of correlation between population dynamics models with a discrete and continuous time space, which we consider at present paper. One problem is finding the discrete analog of the well-known Verhulst model. The other is the reason of appearance of chaotic regimes and oscillations with big periods in Moran-Ricker's models. Also we consider the new one-dimensional models with different assumptions about birth and death processes in populations.

Four population dynamics models, namely Verhulst, Gompertz, Rosenzweig, and Svirezhev ones, have been used to approximate two well-known time-series of Paramecia aurelia and P. caudatum population size (Gause, 1934). The parameters are estimated for each of the models by the least-square method (with global fitting) in two different ways: with and without an additional upper bound for a parameter value. In the latter (traditional) case, when the deviations of theoretical (model) trajectories from experimental time-series have been tested for normality (Kolmogorov-Smirnov test, Shapiro-Wilk test) with zero average, and for the presence/absence of serial correlations (Durbin-Watson criteria), the best results are obtained for the Gompertz and Verhulst models. In the former, more realistic, case (when we impose an additional constraint that the parameter meaning the carrying capacity of the environment has to be greater than any element in the sample), the best results are observed for the Gompertz model. Under this constraint, the canonical technique for deviation analysis can be applied in a restricted version only.

Analysed are the data of larch bud moth (Zeiraphera diniana Gn.) fluctuations in Swiss Alps. The analysis applies simplest mathematical models of isolated population dynamics (in particular, Kostitzin model, Skellam model, the discrete logistic model, and some other ones), which include the minimal number of unknown parameters. The parameters have been estimated, for all the models in hand, by the least-squares method, to fit certain data from the Global Population Dynamics Database (N 1407 and N 6195), the sequences of the data deviations from the model trajectories being treated as well. The best approximations are shown to be achieved with Moran-Ricker model and the discrete logistic model. Statistical criteria (Kolmogorov-Smirnov and Shapiro-Wilk tests) reveal that the hypotheses of normal distribution of residuals must be rejected for one of the time series (N 1407); some models demonstrate serial correlations in the sequence of residuals (according to Durbin-Watson test). This leads to the conclusion that periodic fluctuations in the larch bud moth population (N 1407) can hardly be explained by self-regulation mechanisms alone. For another time series (N 6195), the modified discrete logistic model has appeared to be acceptable as a mode of fluctuations.

1 An integrated pest management (IPM) system incorporating the introduction and field release of Diadegma semiclausum (Hellen), a parasitoid of diamondback moth (DBM) Plutella xylostella (L.), comprising the worst insect pest of the cabbage family, has been developed in Kenya to replace the pesticides-only approach. 2 Mathematical modelling using differential equations has been used in theoretical studies of host–parasitoid systems. Although, this method helps in gaining an understanding of the system's dynamics, it is generally less accurate when used for prediction. The artificial neural network (ANN) approach was therefore chosen to aid prediction. 3 The ANN methodology was applied to predict the population density of the DBM and D. semiclausum, its larval parasitoid. Two data sets, each from different release areas in the Kenya highlands, and both collected during a 3-year period after the release of the parasitoid, were used in the present study. Two ANN models were developed using these data. 4 The ANN approach gave satisfactory results for DBM and for D. semiclausum. Sensitivity analysis suggested that pest populations may be naturally controlled by rainfall. 5 The ANN provides a powerful tool for predicting host–parasitoid population densities and made few assumptions on the field data. The approach allowed the use of data collected at any appropriate scale of the system, bypassing the assumptions and uncertainties that could have occurred when parameters are imported from other systems. The methodology can be explored with respect to the development of tools for monitoring and forecasting the population densities of a pest and its natural enemies. In addition, the model can be used to evaluate the relative effectiveness of the natural enemies and to investigate augmentative biological control strategies.

Considered is a mathematical model for dynamics of an isolated population with non-overlapping generations. The individuals' birth process (emergence of new-generation individuals) is assumed to have a discrete nature (there exist some fixed time moments at which the new generations emerge), while the death process is assumed to be continuous. In addition, the birth rate is assumed to be a function of the number of individuals survived till the moment of reproduction, the function being non-monotone: there exists an optimal value of the population size at which the birth rate reaches its maximum (Alley principle). Analysis of the discrete-continuous models has revealed that each of the new models has a rich set of dynamical regimes. New models are compared with a number of well-known discrete ones (like Skellam, Moran-Ricker, Hassell, Maynard Smith-Slatkin models, and others) when approximating an empirical time series on fluctuations of a green oak moth population (Korzukhin, Semevsky, 1992). Neither of the models can provide for a satisfactory description of the green oak moth dynamics. It is also shown that usage of the discrete-continuous models for approximation of real datasets enables one to find several important population parameters, which can hardly (or cannot) be found by means of traditional discrete models.

The goal of this work was to perform statistical analysis of experimental trajectories of temperature-myographic BFB training. Approximation of signals was implemented using fractional-linear functions. It was found that the number of approximation functions decreased with increasing number of sessions. Moreover, if the number of approximation functions was large enough, it was possible to find the asymptotic behavior of monitored signal with the help of initial values of the signal. It means that it is possible to reveal the potentialities of patients during 3 or 4 sessions of training. Estimation of the time interval of active work showed that there were two various laws for values of temperature and values of myogram: for the first monitored variable, power law; for the second variable, exponential law. But for both monitored parameters the constants were positive, which meant that there was a minimum of time interval for the active "work" for every patient. Correlation analysis (i.e., analysis of autocorrelation and cross-correlation functions) of temperature and myogram signals showed that there was a correlation between monitored parameters. It means that for both signals we can consider both positive and negative time lag dependence between values of temperature and myogram. Statistical analysis of signal behavior made it possible to construct a phenomenological model of temperature-myogram BFB-training, which comprises the basic parameters of patients. With the help of the model it is possible, in particular, to calculate the sojourn time of system at any part of the phase plane. This characteristic can be used as an integral estimation of the efficiency of BFB-training.

This chapter is devoted to the analysis of single-species population dynamics models with overlapping and non-overlapping generations. Within the framework of all models it is assumed that there are no activities of individuals during the wintertime (as, for example, is the case for forest insect populations in the boreal zone), and changes in population size at these moments are described with a broken trajectory (“jump down”). Also, it is assumed that the fecundity of individuals is constant and that the quota of individuals surviving winter depends on the within-year population dynamics. The dynamics of the models, which are determined by the influence of winter conditions on the survival of individuals and by the influence of intrapopulation self-regulative mechanisms, are analyzed. For some particular cases the conditions for population extinction and for stabilization at a non-zero level are determined; it is shown numerically that chaotic regimes can also be realized in some models. The conditions for the reduction of the models under consideration to some well-known discrete models are obtained.

The authors propose new type of models with non-overlapping generations. It is assumed that during winter period individuals are not active (as, for example, in insect populations in boreal forests) and some portion of population dyes. However the portion of population, that survives, Q, indirectly depends on feeding conditions in previous growing season. In the formal terms, Q = Q(u) is a decreasing function of the mean population size u (i.e., of the integral) over the growing period, and traditional discrete-time model therefore turns into a discrete-continuous one. Under any constant birth rate Y, the model is reduced to a discrete one in its general form, and a general result consists in global stability of the zero solution for any Y1, e.t., in population extinction from any initial state. In particular cases of dependence of Q(u) and different types of population self-limitation during growing season the general model results in a great variety of discrete models (including well known Moran-Ricker and Skellam models). For logistic growth of population during the growing season and exponential decrease in Q(u), the condition is obtained for a non-trivial steady state to exist, and the outcome is presented for bifurcation analysis with regard to parameter Y: cycles with typical period-doubling and chaotic dynamics.

A polarised and tagged [Formula: see text] ray beam is produced at GRAAL by the Compton scattering of laser light on the high energy electron of the ESRF storage ring. We present results on the beam polarisation asymmetries and cross sections in the photoproduction of mesons on hydrogen and deuterium target in the energy region 500-1500 MeV. These very precise results cover the angular range 30°-150°, providing stringent constraints to theoretical models.