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Industrial robots have made it possible for robotics to become a worldwide discipline both in economy and in science. However, their capabilities are limited, especially regarding contact tasks where it is required to regulate or at least limit contact forces. At one point, it was noticed that elasticity in the joint transmission, which was treated as a drawback previously, is actually helpful in this regard. This observation led to the introduction of elastic joint robots that are well-suited to contact tasks and cooperative behavior in particular, so they become more and more widespread nowadays. Many researchers try to implement such devices not with trivial series elastic actuators (SEA) but with more sophisticated variable stiffness actuators (VSA) that can regulate their own mechanical stiffness. All elastic actuators demonstrate shock robustness and safe interaction with external objects to some extent, but when stiffness may be varied, it provides additional benefits, e. g., in terms of energy efficiency and task adaptability. Here, we present a novel variable stiffness actuator with a magnetic coupler as an elastic element. Magnetic transmission is contactless and thus advantageous in terms of robustness to misalignment. In addition, the friction model of the transmission becomes less complex. It also has milder stiffness characteristic than typical mechanical nonlinear springs, moreover, the stiffness curve has a maximum after which it descends. Therefore, when this maximum torque is achieved, the coupler slips, and a new pair of poles defines the equilibrium position. As a result, the risk of damage is smaller for this design solution. The design of the joint is thoroughly described, along with its mathematical model. Finally, the control system is also proposed, and simulation tests confirm the design ideas.

Self-organization of molecules on a solid surface is one of the promising directions for materials generation with unique magnetic, electrical, and optical properties. They can be widely used in fields such as electronics, optoelectronics, catalysis, and biology. However, the structure and physicochemical properties of adsorbed molecules are influenced by many parameters that must be taken into account when studying the self-organization of molecules. Therefore, the experimental study of such materials is expensive, and quite often it is difficult for various reasons. In such situations, it is advisable to use the mathematical modeling. One of the parameters in the considered adsorption systems is the multiparticle interaction, which is often not taken into account in simulations due to the complexity of the calculations. In this paper, we evaluated the influence of multiparticle interactions on the total energy of the system using the transfer-matrix method and the Materials Studio software package. The model of monocentric adsorption with nearest interactions on a triangular lattice was taken as the basis. Phase diagrams in the ground state were constructed and a number of thermodynamic characteristics (coverage $\theta$, entropy $S$, susceptibility $\xi$) were calculated at nonzero temperatures. The formation of all four ordered structures (lattice gas with $\theta=0$, $(\sqrt{3} \times \sqrt{3}) R30^{\circ}$ with $\theta = \frac{1}{3}$, $(\sqrt{3} \times \sqrt{3})R^{*}30^{\circ}$ with $\theta = \frac{2}{3}$ and densest phase with $\theta = 1$) in a system with only pairwise interactions, and the absence of the phase  $(\sqrt{3}\times \sqrt{3}) R30^\circ$ when only three-body interactions are taken into account, were found. Using the example of an atomistic model of the trimesic acid adsorption layer by quantum mechanical methods we determined that in such a system the contribution of multiparticle interactions is 11.44% of the pair interactions energy. There are only quantitative differences at such values. The transition region from the  $(\sqrt{3} \times \sqrt{3}) R^{*}30^\circ$ to the densest phase shifts to the right by 38.25% at $\frac{\varepsilon}{RT} = 4$ and to the left by 23.46% at $\frac{\varepsilon}{RT} = −2$.

We have studied properties of non-linear waves in a mathematical model of a predator – prey system with taxis. We demonstrate that, for systems with negative and positive taxis there typically exists a large region in the parameter space, where the waves demonstrate quasi-soliton interaction; colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries. In this paper, we use numerical simulations to demonstrate also a new wave phenomenon — a half-soliton interaction of waves, when of two colliding waves, one annihilates and the other continues to propagate. We show that this effect depends on the «ages» or, equivalently, «widths» of the colliding waves.

The research is devoted to the problem of the use of social networks as a tool of the illegal activity and as a source of information that could be dangerous to society. The article presents the structure of the multiagent system with which a social network groups could be clustered according to the criteria uniquely defines a group as a destructive. The agents’ of the system clustering algorithm is described.

Heart rate (HR) is the most affordable indicator for measuring. In order to control the individual response to physical exercises of different load types heart rate is measured when the athletes perform different types of muscular work (strength machines, various types of training and competitive exercises). The magnitude of heart rate and its dynamics during muscular work and recovery can be objectively judged on the functional status of the cardiovascular system of an athlete, the level of its individual physical performance, as well as an adaptive response to a particular exercise. However, the heart rate is not an independent determinant of the physical condition of an athlete. HR size is formed by the interaction of the basic physiological mechanisms underlying cardiac hemodynamic ejection mode. Heart rate depends on one hand, on contractility of the heart, the venous return, the volumes of the atria and ventricles of the heart and from vascular heart load, the main components of which are elastic and peripheral resistance of the arterial system on the other hand. The values of arterial system vascular resistances depend on the power of muscular work and its duration. HR sensitivity to changes in heart load and vascular contraction was determined in athletes by pair regression analysis simultaneously recorded heart rate data, and peripheral $(R)$ and elastic $(E_a)$ resistance (heart vascular load), and the power $(W)$ of heartbeats (cardiac contractility). The coefficients of sensitivity and pair correlation between heart rate indicators and vascular load and contractility of left ventricle of the heart were determined in athletes at rest and during the muscular work on the cycle ergometer. It is shown that increase in both ergometer power load and heart rate is accompanied by the increase of correlation coefficients and coefficients of the heart rate sensitivity to $R$, $E_a$ and $W$.

Investigation of the influence of external fields on living systems is one of the most interesting and rapidly developing areas of modern biophysics. However, the mechanisms of such an impact are still not entirely clear. One approach to the study of this issue is associated with modeling the interaction of external fields with internal mobility of biological objects. In this paper, this approach is used to study the effect of external fields on the motion of local conformational distortions — kinks, in the DNA molecule. Realizing and taking into account that on the whole this task is closely connected with the problem of the mechanisms of regulation of vital processes of cells and cellular systems, we set the problem — to investigate the physical mechanisms regulating the motion of kinks and also to answer the question whether permanent and periodic fields can play the role of regulators of this movement. The paper considers the most general case, when constant and periodic fields are switching on and off asynchronously. Three variants of asynchronous switching on/off are studied in detail. In the first variant, the time intervals (or diapasons) of the actions of the constant and periodic fields do not overlap, in the second — overlap, and in the third — the intervals are putting in each other. The calculations were performed for the sequence of plasmid pTTQ18. The kink motion was modeled by the McLaughlin–Scott equation, and the coefficients of the equation were calculated in a quasi-homogeneous approximation. Numerical experiments showed that constant and periodic fields exert a significant influence on the character of the kink motion and regulate it. So the switching on of a constant field leads to a rapid increase of the kink velocity and to the establishment of a stationary velocity of motion, and the switching on of a periodic field leads to the steady oscillations of the kink with the frequency of the external periodic field. It is shown that the behavior of the kink depends on the mutual arrangement of the diapasons of the action of the external fields. As it turned out, events occurring in one of the two diapasons can affect the events in the other diapason, even when the diapasons are sufficiently far apart. It is shown that the overlapping of the diapasons of action of the constant and periodic fields leads to a significant increase in the path traversed by the kink to a complete stop. Maximal growth of the path is observed when one diapason is putting in each other. In conclusion, the question of how the obtained model results could be related to the most important task of biology — the problem of the mechanisms of regulation of the processes of vital activity of cells and cellular systems is discussed.

We consider a one-dimensional three velocity kinetic lattice Boltzmann model, which represents a secondorder difference scheme for hydrodynamic equations. In the framework of kinetic theory this system describes the propagation and interaction of three types of particles. It has been shown previously that the lattice Boltzmann model with external virtual force is equivalent at the hydrodynamic limit to the one-dimensional hemodynamic equations for elastic vessels, this equivalence can be achieved with use of the Chapman – Enskog expansion. The external force in the model is responsible for the ability to adjust the functional dependence between the lumen area of the vessel and the pressure applied to the wall of the vessel under consideration. Thus, the form of the external force allows to model various elastic properties of the vessels. In the present paper the physiological boundary conditions are considered at the inlets and outlets of the arterial network in terms of the lattice Boltzmann variables. We consider the following boundary conditions: for pressure and blood flow at the inlet of the vascular network, boundary conditions for pressure and blood flow for the vessel bifurcations, wave reflection conditions (correspond to complete occlusion of the vessel) and wave absorption at the ends of the vessels (these conditions correspond to the passage of the wave without distortion), as well as RCR-type conditions, which are similar to electrical circuits and consist of two resistors (corresponding to the impedance of the vessel, at the end of which the boundary conditions are set and the friction forces in microcirculatory bed) and one capacitor (describing the elastic properties of arterioles). The numerical simulations were performed: the propagation of blood in a network of three vessels was considered, the boundary conditions for the blood flow were set at the entrance of the network, RCR boundary conditions were stated at the ends of the network. The solutions to lattice Boltzmann model are compared with the benchmark solutions (based on numerical calculations for second-order McCormack difference scheme without viscous terms), it is shown that the both approaches give very similar results.

The paper investigates the dynamics of a finite-dimensional model describing the interaction of three populations: prey $x(t)$, its consuming predator $y(t)$, and a superpredator $z(t)$ that feeds on both species. Mathematically, the problem is formulated as a system of nonlinear first-order differential equations with the following right-hand side: $[x(1-x)-(y+z)g;\,\eta_1^{}yg-d_1^{}f-\mu_1^{}y;\,\eta_2^{}zg+d_2^{}f-\mu_2^{}z]$, where $\eta_j^{}$, $d_j^{}$, $\mu_j^{}$ ($j=1,\,2$) are positive coefficients. The considered model belongs to the class of cosymmetric dynamical systems under the Lotka\,--\,Volterra functional response $g=x$, $f=yz$, and two parameter constraints: $\mu_2^{}=d_2^{}\left(1+\frac{\mu_1^{}}{d_1^{}}\right)$, $\eta_2^{}=d_2^{}\left(1+\frac{\eta_1^{}}{d_1^{}}\right)$. In this case, a family of equilibria is being of a straight line in phase space. We have analyzed the stability of the equilibria from the family and isolated equilibria. Maps of stationary solutions and limit cycles have been constructed. The breakdown of the family is studied by violating the cosymmetry conditions and using the Holling model $g(x)=\frac x{1+b_1^{}x}$ and the Beddington–DeAngelis model $f(y,\,z)=\frac{yz}{1+b_2^{}y+b_3^{}z}$. To achieve this, the apparatus of Yudovich's theory of cosymmetry is applied, including the computation of cosymmetric defects and selective functions. Through numerical experimentation, invasive scenarios have been analyzed, encompassing the introduction of a superpredator into the predator-prey system, the elimination of the predator, or the superpredator.

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%.

The spatiotemporal dynamics of a three-component model for food web is considered. The model describes the interactions among resource, prey and predator that consumes both species. In a previous work, the author analyzed the model without taking into account spatial heterogeneity. This study continues the model study of the community considering the diffusion of individuals, as well as directed movements of the predator. It is assumed that the predator responds to the spatial change in the resource and prey density by occupying areas where species density is higher or avoiding them. Directed predator movement is described by the advection term, where velocity is proportional to the gradient of resource and prey density. The system is considered on a one-dimensional domain with zero-flux conditions as boundary ones. The spatiotemporal dynamics produced by model is determined by the system stability in the vicinity of stationary homogeneous state with respect to small inhomogeneous perturbations. The paper analyzes the possibility of wave instability leading to the emergence of autowaves and Turing instability, as a result of which stationary patterns are formed. Sufficient conditions for the existence of both types of instability are obtained. The influence of local kinetic parameters on the spatial structure formation was analyzed. It was shown that only Turing instability is possible when taxis on the resource is positive, but with a negative taxis, both types of instability are possible. The numerical solution of the system was found by using method of lines (MOL) with the numerical integration of ODE system by means of splitting techniques. The spatiotemporal dynamics of the system is presented in several variants, realizing one of the instability types. In the case of a positive taxis on the prey, both autowave and stationary structures are formed in smaller regions, with an increase in the region size, Turing structures are not formed. For negative taxis on the prey, stationary patterns is observed in both regions, while periodic structures appear only in larger areas.