Most cited papers (RSCI)

311. Frisman Y.Y., Kulakov M.P., Revutskaya O.L., Zhdanova O.L., Neverova G.P.
     The key approaches and review of current researches on dynamics of structured and interacting populations
     Computer Research and Modeling, 2019, v. 11, no. 1, pp. 119-151

     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.

     Keywords: population dynamics, structured population, biological community, “prey–predator” interaction, populations coupled by migration, matapopulation.
     Views (last year): 40. Citations: 2 (RSCI).
312. Yakushevich L.V., Savin A.V., Manevitch L.I.
     Nonlinear waves in the DNA molecules containing a boundary between two homogeneous regions
     Computer Research and Modeling, 2009, v. 1, no. 2, pp. 209-215

     Propagation of nonlinear conformational waves through the boundary dividing the double polynucleotide chain into two different homogeneous regions is investigated. Calculations are made in the frameworks of the DNA model which takes into account the difference in mass of nitrous bases and the difference in distances between sugar-phosphate chain and the centers of mass of bases which are connected with the chain by β-glycoside bond С₁-N. We consider different possible combinations of homogeneous regions placed on the right and on the left from the boundary, and we calculate the changes of the nonlinear wave velocity (v) and size (d) of the nonlinear waves due to overcoming the boundary.

     Keywords: DNA, wave propagation, polynucleotide chain.
     Views (last year): 4. Citations: 1 (RSCI).
313. Kassina N.V., Smirnov L.V.
     Mathematical modelling of branched hydraulic systems
     Computer Research and Modeling, 2009, v. 1, no. 2, pp. 173-179

     Solving the problem of stationary stream distribution for an arbitrary volume-free hydrosystem with a free level can be reduced to determining the extremes of a multi-variable function. Rayleigh function expressed in terms of the hydraulic characteristics of the parts of the system in question is used as such a function. The same function is Lyapunov function when analyzing the stability of the determined stationary operational modes of a hydrosystem using the direct Lyapunov method.

     Keywords: hydraulic systems, Rayleigh function, Lyapunov function.
     Views (last year): 7. Citations: 1 (RSCI).
314. Pogrebnaya A.F.
     Synthesis of ATP by F₁-ATPase in stochastic model
     Computer Research and Modeling, 2009, v. 1, no. 2, pp. 217-223

     The paper continues our series of papers [1-4] devoted to the development of mathematical model on rotation of F₁-AТPase molecular motor. Here it has been considered the synthesis of ATP induced by external force applied to the rotor.

     Keywords: ATP, ATPase, external force.
     Views (last year): 2. Citations: 1 (RSCI).
315. Lavrova A.I., Plusnina T.Yu., Ukrainetz A.V., Riznichenko G.Yu., Rubin A.B.
     Nonlinear dynamic of the transmembrane potential and pH along the cell membrane of Chara alga
     Computer Research and Modeling, 2009, v. 1, no. 2, pp. 233-239

     The model of potential dependent proton transfer trough the cell membrane of Chara alga developed in [1] is considered. In the last version of the model we considered two variables: proton concentration near the surface cell and transmembrane potential. In present version we introduce the new variable — proton concentration in cytoplasm. Oscillative and chaotic dynamic of transmembrane potential was obtained in calculations. The physiological role of these patterns is discussed.

     Keywords: Chara alga, transmembrane potential, pH, oscillations.
     Views (last year): 3. Citations: 1 (RSCI).
316. Stroganov A.V., Aristov V.V.
     Probabilistic aspects of “computer analogy” method for solving differential equations
     Computer Research and Modeling, 2009, v. 1, no. 1, pp. 21-31

     Method which allows to obtain explicit form of the solution as a part of power series of the argument step is developed. Formalization of characteristics of the algorithm analogous to operations of a computer is performed. The operation of transfer from one rank to another leads to a probability scheme of the algorithm that averages unknown intermediate steps in higher ranks of the series. The stochastic characteristics of the method are studied and illustrated. Examples of solving nonlinear equations and systems of nonlinear differential equations are presented.

     Keywords: «computer analogy» method, differential equations solving, Cauchy problem.
     Views (last year): 3. Citations: 1 (RSCI).
317. Trifonov A.Y., Masalova E.A., Shapovalov A.V.
     Semiclassical asymptotics of nonlinear Fokker–Plank equation for distributions of asset returns
     Computer Research and Modeling, 2009, v. 1, no. 1, pp. 41-49

     The semiclassical approximation method is applied for solution construction of the Fokker–Planck equation with quadratic nonlocal nonlinearity and various coefficients in models of asset returns estimation. Analitical expressions determining nonlinear evolution operator are obtained in semiclasical approximation.

     Keywords: Fokker–Plank equation, semiclassical approximation, economics.
     Citations: 1 (RSCI).
318. Fomina E.E., Zhiganov N.K.
     Computer modeling and visualization of discrete-continuous casting of nonferrous metal and alloys
     Computer Research and Modeling, 2009, v. 1, no. 1, pp. 67-75

     This article is devoted to the problem of mathematical modeling of nonferrous metal casting and investigation of the influence of main technological parameters on the cooling process of continuously casted copper under down-draw and up-draw.

     Keywords: metal casting, discrete-continuous casting, nonferrous metal.
     Views (last year): 3. Citations: 1 (RSCI).
319. Lakhno V.D., Fialko N.S.
     Mechanism of soliton stopping in a molecular chain without dispersion
     Computer Research and Modeling, 2009, v. 1, no. 1, pp. 93-99

     It is shown by computer simulation that moving soliton-like solution exists in a molecular chain without dispersion. The speed of the solitary wave decreases with time. This decrease can be explained physically due to excitation of sites by moving wave. Maximum wave track length is estimated.

     Keywords: soliton, oscillations, wave propagation.
     Views (last year): 2. Citations: 1 (RSCI).
320. Gubernov V.V., Kolobov A.V., Polezhaev A.A.
     Pulsating regimes of flames propagation in a model with chain-branching reaction
     Computer Research and Modeling, 2009, v. 1, no. 3, pp. 273-280

     In this paper we investigate propagation of planar combustion waves in an adiabatic model with two-step chain branching reaction mechanism. Pulsating instabilities are found to emerge for fuel Lewis number greater than one due to a Hopf bifurcation. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. Further in-crease of the bifurcation parameter initiates period doubling bifurcation cascade and leads to chaotic regime of combustion wave propagation. The chaotic wave extinguishes when the bifurcation parameter becomes sufficiently large.

     Keywords: chain-branching reaction, wave propagation.
     Citations: 1 (RSCI).

• About Journal
• Open Access Policy
• Publishing Ethics
• Editorial board
• Author index
• For authors
• For Reviewers
• Contacts
• Most viewed papers
• Most cited papers
• Submit publication ONLINE