Most cited papers (RSCI)

91. Topaj A.G., Abramova A.V., Tolstopyatov S.E.
    Discrete Models in Population Dynamics: Advantages, Problems, and Justification
    Computer Research and Modeling, 2016, v. 8, no. 2, pp. 267-284

    This article is dedicated to applicability justification as well as advantages and disadvantages analysis of discrete models in population dynamics. Discretization is the process of transferring continuous functions, models, and equations into discrete counterparts. We consider how temporal, spatial and structural discretization can be applied for solving typical issues in mathematical ecology, and try to estimate corresponding models adequacy and applicability limitations.

    Keywords: discrete models, discretization, Verhulst equation, replication dynamics, mathematical ecology, agent-based approach.
    Views (last year): 6. Citations: 6 (RSCI).
92. Zubkova E.V., Zhukova L.A., Frolov P.V., Shanin V.N.
    A.S. Komarov’s publications about cellular automata modelling of the population-ontogenetic development in plants: a review
    Computer Research and Modeling, 2016, v. 8, no. 2, pp. 285-295

    The possibilities of cellular automata simulation applied to herbs and dwarf shrubs are described. Basicprinciples of discrete description of the ontogenesis of plants on which the mathematical modeling based are presents. The review discusses the main research results obtained with the use of models that revealing the patterns of functioning of populations and communities. The CAMPUS model and the results of computer experiment to study the growth of two clones of lingonberry with different geometry of the shoots are described. The paper is dedicated to the works of the founder of the direction of prof. A. S. Komarov. A list of his major publications on this subject is given.

    Keywords: computer models, individual-based approach.
    Views (last year): 2. Citations: 6 (RSCI).
93. Madera A.G., Kandalov P.I.
    Mathematical modeling of the interval stochastic thermal processes in technical systems at the interval indeterminacy of the determinative parameters
    Computer Research and Modeling, 2016, v. 8, no. 3, pp. 501-520

    The currently performed mathematical and computer modeling of thermal processes in technical systems is based on an assumption that all the parameters determining thermal processes are fully and unambiguously known and identified (i.e., determined). Meanwhile, experience has shown that parameters determining the thermal processes are of undefined interval-stochastic character, which in turn is responsible for the intervalstochastic nature of thermal processes in the electronic system. This means that the actual temperature values of each element in an technical system will be randomly distributed within their variation intervals. Therefore, the determinative approach to modeling of thermal processes that yields specific values of element temperatures does not allow one to adequately calculate temperature distribution in electronic systems. The interval-stochastic nature of the parameters determining the thermal processes depends on three groups of factors: (a) statistical technological variation of parameters of the elements when manufacturing and assembling the system; (b) the random nature of the factors caused by functioning of an technical system (fluctuations in current and voltage; power, temperatures, and flow rates of the cooling fluid and the medium inside the system); and (c) the randomness of ambient parameters (temperature, pressure, and flow rate). The interval-stochastic indeterminacy of the determinative factors in technical systems is irremediable; neglecting it causes errors when designing electronic systems. A method that allows modeling of unsteady interval-stochastic thermal processes in technical systems (including those upon interval indeterminacy of the determinative parameters) is developed in this paper. The method is based on obtaining and further solving equations for the unsteady statistical measures (mathematical expectations, variances and covariances) of the temperature distribution in an technical system at given variation intervals and the statistical measures of the determinative parameters. Application of the elaborated method to modeling of the interval-stochastic thermal process in a particular electronic system is considered.

    Keywords: mathematical modelling, thermal process, technical system, interval, stochastic, non-linear, unsteady, statistical measures, mathematical expectation, variance, covariance.
    Views (last year): 15. Citations: 6 (RSCI).
94. Bashashin M.V., Zemlyanay E.V., Rahmonov I.R., Shukrinov J.M., Atanasova P.C., Volokhova A.V.
    Numerical approach and parallel implementation for computer simulation of stacked long Josephson Junctions
    Computer Research and Modeling, 2016, v. 8, no. 4, pp. 593-604

    We consider a model of stacked long Josephson junctions (LJJ), which consists of alternating superconducting and dielectric layers. The model takes into account the inductive and capacitive coupling between the neighbor junctions. The model is described by a system of nonlinear partial differential equations with respect to the phase differences and the voltage of LJJ, with appropriate initial and boundary conditions. The numerical solution of this system of equations is based on the use of standard three-point finite-difference formulae for discrete approximations in the space coordinate, and the applying the four-step Runge-Kutta method for solving the Cauchy problem obtained. Designed parallel algorithm is implemented by means of the MPI technology (Message Passing Interface). In the paper, the mathematical formulation of the problem is given, numerical scheme and a method of calculation of the current-voltage characteristics of the LJJ system are described. Two variants of parallel implementation are presented. The influence of inductive and capacitive coupling between junctions on the structure of the current-voltage characteristics is demonstrated. The results of methodical calculations with various parameters of length and number of Josephson junctions in the LJJ stack depending on the number of parallel computing nodes, are presented. The calculations have been performed on multiprocessor clusters HybriLIT and CICC of Multi-Functional Information and Computing Complex (Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna). The numerical results are discussed from the viewpoint of the effectiveness of presented approaches of the LJJ system numerical simulation in parallel. It has been shown that one of parallel algorithms provides the 9 times speedup of calculations.

    Keywords: Josephson junctions, finite difference approximation, parallel computing.
    Views (last year): 7. Citations: 6 (RSCI).
95. Ostrovskaya N.V., Skidanov V.A., Iusipova I.A.
    Classification of dynamical switching regimes in a three-layered ferromagnetic nanopillar governed by spin-polarized injection current and external magnetic field. I. Longitudinal anisotropy
    Computer Research and Modeling, 2016, v. 8, no. 4, pp. 605-620

    The mathematical model of the magnetic memory cell MRAM with the in-plane anisotropy axis parallel to the edge of a free ferromagnetic layer (longitudinal anisotropy) has been constructed using approximation of uniform magnetization. The model is based on the Landau–Lifshits–Gilbert equation with the injection-current term in the Sloncžewski–Berger form. The set of ordinary differential equations for magnetization dynamics in a three-layered Co/Cu/Cu valve under the control of external magnetic field and spin-polarized current has been derived in the normal coordinate form. It was shown that the set of equations has two main stationary points on the anisotropy axis at any values of field and current. The stationary analysis of them has been performed. The algebraic equations for determination of additional stationary points have been derived. It has been shown that, depending on the field and current magnitude, the set of equations can have altogether two, four, or six stationary points symmetric in pairs relatively the anisotropy axis. The bifurcation diagrams for all the points have been constructed. The classification of the corresponding phase portraits has been performed. The typical trajectories were calculated numerically using Runge–Kutta method. The regions, where stable and unstable limit cycles exist, have been determined. It was found that the unstable limit cycles exist around the main stable equilibrium point on the axis that coincides with the anisotropy one, whereas the stable cycles surround the unstable additional points of equilibrium. The area of their existence was determined numerically. The new types of dynamics, such as accidental switching and non-complete switching, have been found. The threshold values of switching current and field have been obtained analytically. The estimations of switching times have been performed numerically.

    Keywords: MRAM, uniaxial anisotropy, magnetization, free layer, fixed layer, the Landau–Lifshits–Gilbert equation, magnetization reversal.
    Views (last year): 2. Citations: 6 (RSCI).
96. Ougolnitsky G.A., Usov A.B.
    Game-theoretic model of coordinations of interests at innovative development of corporations
    Computer Research and Modeling, 2016, v. 8, no. 4, pp. 673-684

    Dynamic game theoretic models of the corporative innovative development are investigated. The proposed models are based on concordance of private and public interests of agents. It is supposed that the structure of interests of each agent includes both private (personal interests) and public (interests of the whole company connected with its innovative development first) components. The agents allocate their personal resources between these two directions. The system dynamics is described by a difference (not differential) equation. The proposed model of innovative development is studied by simulation and the method of enumeration of the domains of feasible controls with a constant step. The main contribution of the paper consists in comparative analysis of efficiency of the methods of hierarchical control (compulsion or impulsion) for information structures of Stackelberg or Germeier (four structures) by means of the indices of system compatibility. The proposed model is a universal one and can be used for a scientifically grounded support of the programs of innovative development of any economic firm. The features of a specific company are considered in the process of model identification (a determination of the specific classes of model functions and numerical values of its parameters) which forms a separate complex problem and requires an analysis of the statistical data and expert estimations. The following assumptions about information rules of the hierarchical game are accepted: all players use open-loop strategies; the leader chooses and reports to the followers some values of administrative (compulsion) or economic (impulsion) control variables which can be only functions of time (Stackelberg games) or depend also on the followers’ controls (Germeier games); given the leader’s strategies all followers simultaneously and independently choose their strategies that gives a Nash equilibrium in the followers’ game. For a finite number of iterations the proposed algorithm of simulation modeling allows to build an approximate solution of the model or to conclude that it doesn’t exist. A reliability and efficiency of the proposed algorithm follow from the properties of the scenario method and the method of a direct ordered enumeration with a constant step. Some comprehensive conclusions about the comparative efficiency of methods of hierarchical control of innovations are received.

    Keywords: Germeyer’s game, Shtakelberg’s game, hierarchy, simulation modeling, innovative development, compulsion, impulsion.
    Views (last year): 9. Citations: 6 (RSCI).
97. Aponin Yu.M., Aponina E.A.
    Mathematical model of predator – prey system with lower critical prey density
    Computer Research and Modeling, 2009, v. 1, no. 1, pp. 51-56

    A mathematical model of predator – prey microecosystem with lower critical population number of prey is considered. The predator – prey system is assumed to be under harvesting. Harvesting intensity variations generate changes in two model parameters which are considered as controllable. Bifurcation diagram in control-lable parameters plane is constructed and corresponding phase portraits are represented.

    Keywords: predator – prey system, ecosystems dynamics, bifurcation theory.
    Views (last year): 23. Citations: 5 (RSCI).
98. Brazhe A.R., Brazhe N.A., Sosnovtseva O.V., Pavlov A.N., Mosekilde E., Maksimov G.V.
    Wavelet-based analysis of cell dynamics measured by interference microscopy
    Computer Research and Modeling, 2009, v. 1, no. 1, pp. 77-83

    Laser interference microscopy was used to study morphology and intracellular dynamics of erythrocytes, neurons and mast cells. We have found that changes of the local refractive index (RI) of cells have regular components that relate to the cooperative processes in the cellular submembrane and centre regions. We have shown that characteristic frequencies of RI dynamics differ for various cell types and can be used as markers of specific cellular processes.

    Keywords: laser interference microscopy, wavelet-based analysis.
    Views (last year): 1. Citations: 5 (RSCI).
99. Trukhan E.M.
    Impact of weak electro-magnetic fields on biological activity of water phase
    Computer Research and Modeling, 2009, v. 1, no. 1, pp. 101-108

    It was found that water preliminary activated by a vector potential changes mobility of infusoria, rate of sugar fermentation in yeast cells and is more attractive for drinking for mice. Modifications of certain physical characteristics of water (UV absorbtions spectrum and state of a silica admixture) was also discovered. It was supposed that water is the primary target for weak electro-magnetic fields impact on biological objects.

    Keywords: electro-magnetic field, water phase.
    Views (last year): 3. Citations: 5 (RSCI).
100. Terekhin A.T., Budilova E.V., Karpenko M.P., Kachalova L.M., Chmyhova E.V.
     Lyapunov function as a tool for the study of cognitive and regulatory processes in organism
     Computer Research and Modeling, 2009, v. 1, no. 4, pp. 449-456

     Cognitive and regulatory processes in organism are ensured by the functioning of several different network systems — neural, endocrine, immune, and gene ones. These systems are, however, closely related and form a single integrated neurogenohumoral cognitive-regulatory dynamic system of organism. A review of publications is given which shows that it is possible to associate with this dynamic system a corresponding Lyapunov function (energy function, potential function) and that analyzing this function allows, due to its geometrical insight, to easily discover a set of general properties of cognitive and regulatory functioning of organism.

     Keywords: Lyapunov function, cognitive functioning, regulatory mechanisms.
     Views (last year): 4. Citations: 5 (RSCI).

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