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The review and systematization of current papers on the mathematical modeling of population dynamics allow us to conclude the key interests of authors are two or three main research lines related to the description and analysis of the dynamics of both local structured populations and systems of interacting homogeneous populations as ecological community in physical space. The paper reviews and systematizes scientific studies and results obtained within the framework of dynamics of structured and interacting populations to date. The paper describes the scientific idea progress in the direction of complicating models from the classical Malthus model to the modern models with various factors affecting population dynamics in the issues dealing with modeling the local population size dynamics. In particular, they consider the dynamic effects that arise as a result of taking into account the environmental capacity, density-dependent regulation, the Allee effect, complexity of an age and a stage structures. Particular attention is paid to the multistability of population dynamics. In addition, studies analyzing harvest effect on structured population dynamics and an appearance of the hydra effect are presented. The studies dealing with an appearance and development of spatial dissipative structures in both spatially separated populations and communities with migrations are discussed. Here, special attention is also paid to the frequency and phase multistability of population dynamics, as well as to an appearance of spatial clusters. During the systematization and review of articles on modeling the interacting population dynamics, the focus is on the “prey–predator” community. The key idea and approaches used in current mathematical biology to model a “prey–predator” system with community structure and harvesting are presented. The problems of an appearance and stability of the mosaic structure in communities distributed spatially and coupled by migration are also briefly discussed.

The paper constructs and studies a generalized model describing two-component systems of reaction – diffusion type with power nonlinearity, considering the influence of external noise. A methodology has been developed for analyzing the generalized model, which includes linear stability analysis, nonlinear stability analysis, and numerical simulation of the system’s evolution. The linear analysis technique uses basic approaches, in which the characteristic equation is obtained using a linearization matrix. Nonlinear stability analysis realized up to third-order moments inclusively. For this, the functions describing the dynamics of the components are expanded in Taylor series up to third-order terms. Then, using the Novikov theorem, the averaging procedure is carried out. As a result, the obtained equations form an infinite hierarchically subordinate structure, which must be truncated at some point. To achieve this, contributions from terms higher than the third order are neglected in both the equations themselves and during the construction of the moment equations. The resulting equations form a set of linear equations, from which the stability matrix is constructed. This matrix has a rather complex structure, making it solvable only numerically. For the numerical study of the system’s evolution, the method of variable directions was chosen. Due to the presence of a stochastic component in the analyzed system, the method was modified such that random fields with a specified distribution and correlation function, responsible for the noise contribution to the overall nonlinearity, are generated across entire layers. The developed methodology was tested on the reaction – diffusion model proposed by Barrio et al., according to the results of the study, they showed the similarity of the obtained structures with the pigmentation of fish. This paper focuses on the system behavior analysis in the neighborhood of a non-zero stationary point. The dependence of the real part of the eigenvalues on the wavenumber has been examined. In the linear analysis, a range of wavenumber values is identified in which Turing instability occurs. Nonlinear analysis and numerical simulation of the system’s evolution are conducted for model parameters that, in contrast, lie outside the Turing instability region. Nonlinear analysis found noise intensities of additive noise for which, despite the absence of conditions for the emergence of diffusion instability, the system transitions to an unstable state. The results of the numerical simulation of the evolution of the tested model demonstrate the process of forming spatial structures of Turing type under the influence of additive noise.

The article describes the migration process of a certain population, taking into account the spatial heterogeneity of the local capacity of the ecological niche. It is assumed that this spatial heterogeneity is caused by various natural or artificial factors. The mathematical model of the migration process under consideration is a Cauchy problem on a straight line for some quasi-linear partial differential equation of the first order, which is satisfied by the linear population density under consideration. In this paper, a general solution to this Cauchy problem is found for an arbitrary dependence of the local capacity of an ecological niche on the spatial coordinate. This general solution was applied to describe the migration of the population in question in two different cases: in the case of a dependence of the local capacity of the ecological niche on the spatial coordinate in the form of a smooth step and in the case of a hill-like dependence of the local capacity of the ecological niche on the spatial coordinate. In both cases, the solution to the Cauchy problem is expressed in terms of higher transcendental functions. By applying special relations to the model parameters, these higher transcendental functions are reduced to elementary functions, which makes it possible to obtain exact model solutions explicitly expressed in terms of elementary functions. With the help of these precise solutions, an extensive program of computational experiments has been implemented, showing how the initial population density of the Gaussian form is dispersed by the considered two types of spatial heterogeneity of the local capacity of the ecological niche. These computational experiments have shown that when passing through both step-like and hill-like spatial inhomogeneities of the local capacity of an ecological niche with a narrow Gaussian width of its initial density compared to the characteristic spatial scale of these inhomogeneities, the system forgets its initial state. In particular, if we interpret the system under study as a population living in an extended calm rectilinear river along its bed, then it can be argued that under this initial condition, after the current of this river carries the population under consideration through the area of spatial heterogeneity of the local capacity of the ecological niche, the population density becomes a quasi-rectangular function.

This paper considers the inverse problem of seismic exploration — determining the structure of the media based on the recorded wave response from it. Large cracks are considered as target objects, whose size and position are to be determined.

he direct problem is solved using the grid-characteristic method. The method allows using physically based algorithms for calculating outer boundaries of the region and contact boundaries inside the region. The crack is assumed to be thin, a special condition on the crack borders is used to describe the crack.

The inverse problem is solved using convolutional neural networks. The input data of the neural network are seismograms interpreted as images. The output data are masks describing the medium on a structured grid. Each element of such a grid belongs to one of two classes — either an element of a continuous geological massif, or an element through which a crack passes. This approach allows us to consider a medium with an unknown number of cracks.

The neural network is trained using only samples with one crack. The final testing of the trained network is performed using additional samples with several cracks. These samples are not involved in the training process. The purpose of testing under such conditions is to verify that the trained network has sufficient generality, recognizes signs of a crack in the signal, and does not suffer from overtraining on samples with a single crack in the media.

The paper shows that a convolutional network trained on samples with a single crack can be used to process data with multiple cracks. The networks detects fairly small cracks at great depths if they are sufficiently spatially separated from each other. In this case their wave responses are clearly distinguishable on the seismogram and can be interpreted by the neural network. If the cracks are close to each other, artifacts and interpretation errors may occur. This is due to the fact that on the seismogram the wave responses of close cracks merge. This cause the network to interpret several cracks located nearby as one. It should be noted that a similar error would most likely be made by a human during manual interpretation of the data. The paper provides examples of some such artifacts, distortions and recognition errors.

This paper examines the impact of the spatial resolution of a discretized (lattice) representation of the environment on the efficiency and correctness of optimal pathfinding in complex environments. Scenarios are considered that may include bottlenecks, non-uniform obstacle distributions, and areas of increased safety requirements in the immediate vicinity of obstacles. Despite the widespread use of lattice representations of the environment in robotics due to their compatibility with sensor data and support for classical trajectory planning algorithms, the resolution of these lattices has a significant impact on both goal reachability and optimal path performance. An algorithm is proposed that combines environmental connectivity analysis, trajectory optimization, and geometric safety refinement. In the first stage, the Leath algorithm is used to estimate the reachability of the target point by identifying a connected component containing the starting position. Upon confirmation of the target point’s reachability, the A* algorithm is applied to the nodes of this component in the second stage to construct a path that simultaneously minimizes both the path length and the risk of collision. In the third stage, a refined obstacle distance estimate is performed for nodes located in safety zones using a combination of the Gilbert – Johnson –Keerthi (GJK) and expanding polyhedron (EPA) algorithms. Experimental analysis revealed a nonlinear relationship between the probability of the existence and effectiveness of an optimal path and the lattice parameters. Specifically, reducing the spatial resolution of the lattice increases the likelihood of connectivity loss and target unreachability, while increasing its spatial resolution increases computational complexity without a proportional improvement in the optimal path’s performance.

On the basis of the MGD equations we consider 2D- and 3D- nonstationary problems about the evolution of perturbations in the lower atmosphere and the Earth’s ionosphere which are caused by the movement of large meteoroids along gently sloping paths of the entry with the simulation of their destruction by the momentary increase of the midship at the point of the pressure head maximum. According to the results of our numerical investigation we obtain and analyze the detailed spatial-temporal distributions of the main parameters of the plasma flows from which in particular a number of phenomena that are similar to those seen in the Chelyabinsk phenomenon follow.

A molecular model of phicobilisome complex with a quenching protein OCP which regulates the energy transfer from phicobilisome to photosystem in photosynthetic apparatus of cyanobacteria has been developed. In the model obtained a well known spatial structure of interacting proteins remains intact and also the energy transfer from phycobilisome to OCP with reasonable rates is possible. Free energy of complex formation was calculated using MM–PBSA approach. By the order of magnitude this energy is about tens of kJ/mole. This value correlates well with experimental observed low stability of this complex. The specific surface energy of interaction between hydrophylic phicobilisome and OCP is twice larger than specific surface energy of their interaction with water. This reflects a high molecular complementary of interacting protein surfaces and is a strong pro argument for proposed model.

Work is devoted to modeling instrumental errors of a laser beam diameter measurement using a method based on a lambertian transmissive screen. Super-Lorenz distribution was used as a model of the beam. To determine the effect of each parameter on the measurement error were performed computational experiments, results of which were approximated by analytic functions. There were obtained the errors depending on relative beam size, spatial non-uniformity of the transmission screen, lens distortion, physical vignetting, beam tilt, CCD spatial resolution, ADC resolution of a camera. There was shown that the error can be less then 1 %.

New numerical simulation technique to calculate electrical properties of rocks with two-phase “oil– water” saturation is proposed. This technique takes into account surface conductivity of electrical double layers at the contact between solid rock and aqueous solution inside pore space. The numerical simulation technique is based on acquiring of electrical potential distribution in high-resolution three-dimensional digital model of porous medium. The digital model incorporates the spatial geometry of pore channels and contains bulk and surface grid cells. Numerical simulation results demonstrate the importance of surface conductivity effects.

The course and outcome of the battle is largely dependent on the morale of the troops, characterized by the percentage of loss in killed and wounded, in which the troops still continue to fight. Every fight is a psychological act of ending his rejection of one of the parties. Typically, models of battle psychological factor taken into account in the decision of Lanchester equations (the condition of equality of forces, when the number of one of the parties becomes zero). It is emphasized that the model Lanchester type satisfactorily describe the dynamics of the battle only in the initial stages. To resolve this contradiction is proposed to use a modification of Lanchester's equations, taking into account the fact that at any moment of the battle on the enemy firing not affected and did not abandon the battle fighters. The obtained differential equations are solved by numerical method and allow the dynamics to take into account the influence of psychological factor and evaluate the completion time of the conflict. Computational experiments confirm the known military theory is the fact that the fight usually ends in refusal of soldiers of one of the parties from its continuation (avoidance of combat in various forms). Along with models of temporal and spatial dynamics proposed to use a modification of the technology features of the conflict of S. Skaperdas, based on the principles of combat. To estimate the probability of victory of one side in the battle takes into account the interest of the maturing sides of the bloody casualties and increased military superiority.