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In the presented work, a hybrid optimal simulation model of an assembly shop in the AnyLogic environment has been developed, which allows you to select the parameters of production systems. To build a hybrid model of the investigative approach, discrete-event modeling and aggressive modeling are combined into a single model with an integrating interaction. Within the framework of this work, a mechanism for the development of a production system consisting of several participants-agents is described. An obvious agent corresponds to a class in which a set of agent parameters is specified. In the simulation model, three main groups of operations performed sequentially were taken into account, and the logic for working with rejected sets was determined. The product assembly process is a process that occurs in a multi-phase open-loop system of redundant service with waiting. There are also signs of a closed system — scrap flows for reprocessing. When creating a distribution system in the segment, it is mandatory to use control over the execution of requests in a FIFO queue. For the functional assessment of the production system, the simulation model includes several functional functions that describe the number of finished products, the average time of preparation of products, the number and percentage of rejects, the simulation result for the study, as well as functional variables in which the calculated utilization factors will be used. A series of modeling experiments were carried out in order to study the behavior of the agents of the system in terms of the overall performance indicators of the production system. During the experiment, it was found that the indicator of the average preparation time of the product is greatly influenced by such parameters as: the average speed of the set of products, the average time to complete operations. At a given limitation interval, we managed to select a set of parameters that managed to achieve the largest possible operation of the assembly line. This experiment implements the basic principle of agent-based modeling — decentralized agents make a personal contribution and affect the operation of the entire simulated system as a whole. As a result of the experiments, thanks to the selection of a large set of parameters, it was possible to achieve high performance indicators of the assembly shop, namely: to increase the productivity indicator by 60%; reduce the average assembly time of products by 38%.

Modeling the fight against terrorist, pirate and robbery acts at sea is an urgent scientific task due to the prevalence of force acts and the insufficient number of works on this issue. The actions of pirates and terrorists are diverse. Using a base ship, they can attack ships up to 450–500 miles from the coast. Having chosen the target, they pursue it and use the weapons to board the ship. Actions to free a ship captured by pirates or terrorists include: blocking the ship, predicting where pirates might be on the ship, penetrating (from board to board, by air or from under water) and cleaning up the ship’s premises. An analysis of the special literature on the actions of pirates and terrorists showed that the act of force (and actions to neutralize it) consists of two stages: firstly, blocking the vessel, which consists in forcing it to stop, and secondly, neutralizing the team (terrorist groups, pirates), including penetration of a ship (ship) and its cleaning. The stages of the cycle are matched by indicators — the probability of blocking and the probability of neutralization. The variables of the act of force model are the number of ships (ships, boats) of the attackers and defenders, as well as the strength of the capture group of the attackers and the crew of the ship - the victim of the attack. Model parameters (indicators of naval and combat superiority) were estimated using the maximum likelihood method using an international database of incidents at sea. The values of these parameters are 7.6–8.5. Such high values of superiority parameters reflect the parties' ability to act in force acts. An analytical method for calculating excellence parameters is proposed and statistically substantiated. The following indicators are taken into account in the model: the ability of the parties to detect the enemy, the speed and maneuverability characteristics of the vessels, the height of the vessel and the characteristics of the boarding equipment, the characteristics of weapons and protective equipment, etc. Using the Becker model and the theory of discrete choice, the probability of failure of the force act is estimated. The significance of the obtained models for combating acts of force in the sea space lies in the possibility of quantitative substantiation of measures to protect the ship from pirate and terrorist attacks and deterrence measures aimed at preventing attacks (the presence of armed guards on board the ship, assistance from warships and helicopters).

The study of the mechanism for the development of mass panic in view of its extreme importance and social danger is an important scientific task. Available information about the mechanism of her development is based mainly on the work of psychologists and belongs to the category of inaccurate. Therefore, the theory of fuzzy sets has been chosen as a tool for developing a mathematical model of a person's susceptibility to panic situations. As a result of the study, an fuzzy model was developed, consisting of blocks: “Fuzzyfication”, where the degree of belonging of the values of the input parameters to fuzzy sets is calculated; “Inference” where, based on the degree of belonging of the input parameters, the resulting function of belonging of the output value to an odd model is calculated; “Defuzzyfication”, where using the center of gravity method, the only quantitative value of the output variable characterizing a person's susceptibility to panic situations is determined Since the real quantitative values for linguistic variables mental properties of a person are unknown, then to assess the quality of the developed model, without endangering people, it is not possible. Therefore, the quality of the results of fuzzy modeling was estimated by the calculated value of the determination coefficient R2, which showed that the developed fuzzy model belongs to the category of good quality models $(R^2 = 0.93)$, which confirms the legitimacy of the assumptions made during her development. In accordance with to the results of the simulation, human susceptibility to panic situations for sanguinics and cholerics can be attributed to “increased” (0.88), and for phlegmatics and melancholics — to “moderate” (0.38). This means that cholerics and sanguinics can become epicenters of panic and the initiators of stampede, and phlegmatics and melancholics — obstacles to evacuation routes. What should be taken into account when developing effective evacuation measures, the main task of which is to quickly and safely evacuate people from adverse conditions. In the approved methods, the calculation of normative values of safety parameters is based on simplified analytical models of human flow movement, because a large number of factors have to be taken into account, some of which are quantitatively uncertain. The obtained result in the form of quantitative estimates of a person's susceptibility to panic situations will increase the accuracy of calculations.

Mechanical properties of eukaryotic cells play an important role in life cycle conditions and in the development of pathological processes. In this paper we discuss the problem of parameters identification and verification of viscoelastic constitutive models based on force spectroscopy data of living cells. It is proposed to use one-dimensional continuous wavelet transform to calculate the relaxation function. Analytical calculations and the results of numerical simulation are given, which allow to obtain relaxation functions similar to each other on the basis of experimentally determined force curves and theoretical stress-strain relationships using wavelet differentiation algorithms. Test examples demonstrating correctness of software implementation of the proposed algorithms are analyzed. The cell models are considered, on the example of which the application of the proposed procedure of identification and verification of their parameters is demonstrated. Among them are a structural-mechanical model with parallel connected fractional elements, which is currently the most adequate in terms of compliance with atomic force microscopy data of a wide class of cells, and a new statistical-thermodynamic model, which is not inferior in descriptive capabilities to models with fractional derivatives, but has a clearer physical meaning. For the statistical-thermodynamic model, the procedure of its construction is described in detail, which includes the following. Introduction of a structural variable, the order parameter, to describe the orientation properties of the cell cytoskeleton. Setting and solving the statistical problem for the ensemble of actin filaments of a representative cell volume with respect to this variable. Establishment of the type of free energy depending on the order parameter, temperature and external load. It is also proposed to use an oriented-viscous-elastic body as a model of a representative element of the cell. Following the theory of linear thermodynamics, evolutionary equations describing the mechanical behavior of the representative volume of the cell are obtained, which satisfy the basic thermodynamic laws. The problem of optimizing the parameters of the statisticalthermodynamic model of the cell, which can be compared both with experimental data and with the results of simulations based on other mathematical models, is also posed and solved. The viscoelastic characteristics of cells are determined on the basis of comparison with literature data.

In the development of the previously obtained result on modeling the dynamics of vegetation cover, due to variations in the temperature background, a new scheme for the interval analysis of the dynamics of floristic images of formations is presented in the case when the parameter of the response rate of the model of the dynamics of each counting plant species is set by the interval of scatter of its possible values. The detailed description of the functional parameters of macromodels of biodiversity, desired in fundamental research, taking into account the essential reasons for the observed evolutionary processes, may turn out to be a problematic task. The use of more reliable interval estimates of the variability of functional parameters “bypasses” the problem of uncertainty in the primary assessment of the evolution of the phyto-resource potential of the developed controlled territories. The solutions obtained preserve not only a qualitative picture of the dynamics of species diversity, but also give a rigorous, within the framework of the initial assumptions, a quantitative assessment of the degree of presence of each plant species. The practical significance of two-sided estimation schemes based on the construction of equations for the upper and lower boundaries of the trajectories of the scatter of solutions depends on the conditions and measure of proportional correspondence of the intervals of scatter of the initial parameters with the intervals of scatter of solutions. For dynamic systems, the desired proportionality is not always ensured. The given examples demonstrate the acceptable accuracy of interval estimation of evolutionary processes. It is important to note that the constructions of the estimating equations generate vanishing intervals of scatter of solutions for quasi-constant temperature perturbations of the system. In other words, the trajectories of stationary temperature states of the vegetation cover are not roughened by the proposed interval estimation scheme. The rigor of the result of interval estimation of the species composition of the vegetation cover of formations can become a determining factor when choosing a method in the problems of analyzing the dynamics of species diversity and the plant potential of territorial systems of resource-ecological monitoring. The possibilities of the proposed approach are illustrated by geoinformation images of the computational analysis of the dynamics of the vegetation cover of the Yamal Peninsula and by the graphs of the retro-perspective analysis of the floristic variability of the formations of the landscapelithological group “Upper” based on the data of the summer temperature background of the Salehard weather station from 2010 to 1935. The developed indicators of floristic variability and the given graphs characterize the dynamics of species diversity, both on average and individually in the form of intervals of possible states for each species of plant.

Dynamic scenarios leading to multistability in the form of continuous families of stable solutions are studied for a system of autonomous differential equations. The approach is based on determining the cosymmetries of the problem, calculating stationary solutions, and numerically-analytically studying their stability. The analysis is carried out for equations of the Lotka –Volterra type, describing the interaction of two predators feeding on two related prey species. For a system of ordinary differential equations of the 4th order with 11 real parameters, a numerical-analytical study of possible interaction scenarios was carried out. Relationships are found analytically between the control parameters under which the cosymmetry linear in the variables of the problem is realized and families of stationary solutions (equilibria) arise. The case of multicosymmetry is established and explicit formulas for a two-parameter family of equilibria are presented. The analysis of the stability of these solutions made it possible to reveal the division of the family into regions of stable and unstable equilibria. In a computational experiment, the limit cycles branching off from unstable stationary solutions are determined and their multipliers corresponding to multistability are calculated. Examples of the coexistence of families of stable stationary and non-stationary solutions are presented. The analysis is carried out for the growth functions of logistic and “hyperbolic” types. Depending on the parameters, scenarios can be obtained when only stationary solutions (coexistence of prey without predators and mixed combinations), as well as families of limit cycles, are realized in the phase space. The multistability scenarios considered in the work allow one to analyze the situations that arise in the presence of several related species in the range. These results are the basis for subsequent analysis when the parameters deviate from cosymmetric relationships.

The approach for the analysis of some large-scale biological systems, on the base of quasiequilibrium stages is proposed. The approach allows us to reduce the detailed large-scaled models and obtain the simplified model with an analytical solution. This makes it possible to reproduce the experimental curves with a good accuracy. This approach has been applied to a detailed model of the primary processes of photosynthesis in the reaction center of photosystem II. The resulting simplified model of photosystem II describes the experimental fluorescence induction curves for higher and lower plants, obtained under different light intensities. Derived relationships between variables and parameters of detailed and simplified models, allow us to use parameters of simplified model to describe the dynamics of various states of photosystem II detailed model.