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## Nontrivial stationary points of two-species self-structuring communities

Moscow University Computational Mathematics and Cybernetics. 2017. Vol. 41. No. 3. P. 122-129.

Nikitin A. A., Savost’yanov Anton Sergeevich

The two-species model of self-structured stationary biological communities proposed by U. Dieckmann and R. Law is considered. A way of investigating the system of integro-differential equations describing the model equilibrium is developed, nontrivial stationary points are found, and constraints on the model parameter space resulting in similar stationary points are studied. The results are applied to a number of widely known biological scenarios.

Research target:
Mathematics

Language:
English

Nikitin A.A., Savost’yanov A. S., Moscow University Computational Mathematics and Cybernetics 2017 Vol. 41 No. 3 P. 122-129

The two-species model of self-structured stationary biological communities proposed by U. Dieckmann and R. Law is considered. A way of investigating the system of integro-differential equations describing the model equilibrium is developed, nontrivial stationary points are found, and constraints on the model parameter space resulting in similar stationary points are studied. The results are applied ...

Added: September 3, 2017

Nikitin A. A., Nikolaev M. V., Moscow University Computational Mathematics and Cybernetics 2018 Vol. 42 No. 3 P. 105-113

Integral equations emerging in a model of stationary biological communities such that their kernels have variable coefficients of excess (kurtosian kernels)are investigated. The dependence of the first and second spatial moment on the dimension of the environment is considered. A fastcomputation algorithm for the multi-dimensional nonlinear convolution is considered. The existence of a radial solution ...

Added: October 25, 2018

Галкин Е. Г., Nikitin A. A., Вестник Московского университета. Серия 15: Вычислительная математика и кибернетика 2020 № 2 С. 11-18

The article presents the main approaches to the study of the stochastic process of population dynamics with continuous time and space and with fixed individuals, a countable system of integro-differential equations corresponding to the dynamics of spatial moments of this process is derived, and a method for finding an approximate solution using the method of ...

Added: February 18, 2020

Springer, 2020

This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019.
First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. ...

Added: November 1, 2020

Zakhariev I., Aksenov S. A., Logashina I. V., Металлург 2016

The paper is oriented toward the problem of superplastic materials characterization using free bulging testing. This experimental technique allows one to study the material flow behavior in conditions of biaxial tension which is very close to the ones occurring during hot gas forming. The interpretation of the results is proposed to perform by inverse analysis ...

Added: June 19, 2016

Kalistratova A., Nikitin A. A., Doklady Mathematics 2016 Vol. 94 No. 2 P. 574-577

In this paper, we study the integral equation that has arisen in the spatial model of stationary communities developed by Austrian scientists Ulf Dickman and Richard Low. A special case of this equation is considered with integral kernels, which are the Student’s distribution. The existence of a solution in this case is proved, and the ...

Added: December 8, 2016

Bodrov A.G., Nikitin A. A., Moscow University Computational Mathematics and Cybernetics 2015 Vol. 39 No. 4 P. 157-162

A computational solution to the integral equation in the biological spatial model is found. The numerical techniques that are used (the Nystr{\"o}m and Neumann series methods, the latter being one of successive approximations) yield a reasonably accurate solution. An approach of moving from multidimensional equations to a one-dimensional equation for high-dimensional spaces is proposed. Explicit ...

Added: September 28, 2017

Nikitin A. A., International Journal of Open Information Technologies 2018 Т. 6 № 10 С. 1-8

This article is devoted to the mathematical formulation and numerical study of the spatial model of stationary biological communities by U. Dickman and R. Low. The main idea of this model is to find a "projection" of the simulated biological process on certain characteristics, the dynamics of which can be written analytically. Such "characteristics" in ...

Added: October 25, 2018

Bodrov A.G., Nikitin A. A., Doklady Mathematics 2014 Vol. 89 No. 2 P. 210-213

Added: September 28, 2017

Гаджиев С. Р., Галкин Е. Г., Nikitin A. A., Вестник Московского университета. Серия 15: Вычислительная математика и кибернетика 2021 № 2 С. 11-18

This article explores nonlinear integral equation system that appears in the biological model of spatial stochastic population dynamics by U. Dieckmann and R. Law. We introduce the model and explain the reasoning behind using spatial moments within this model. We show derivation of nonlinear integral equation for equilibrium state after performing third degree closure on ...

Added: December 15, 2020

Chumachenko E. N., Logashina I. V., Zakhariev I., Металлург 2016 № 4 С. 102-105

The paper is devoted to simulation, analysis and optimization of a forging technology for manufacturing of titanium sections of high-pressure apparatuses. Computer simulation of material forming during the forging was performed using finite element method. The punching force evolution was study as well as deformation uniformity of the product walls, fillability of the dies and ...

Added: May 17, 2016

D. V. Gribanov, D.S. Malyshev, P. M. Pardalos et al., Journal of Combinatorial Optimization 2018 Vol. 35 No. 4 P. 1128-1146

In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems’ formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms ...

Added: February 19, 2018

Revenko A., Kuznetsov S., Fundamenta Informaticae 2012 Vol. 4 No. 115 P. 377-394

An approach for studying relations between properties of functions on sets is proposed. The approach is based on Attribute Exploration. 16 properties of functions are considered, among them monotonicity, idempotency, path independence, exchange properties, convexity, etc. Example functions are partially computer generated on the powersets of sets with 2, 3 and 4 elements. Attribute Exploration ...

Added: December 31, 2012

Belomestny D., Iosipoi L., Mathematics and Computers in Simulation 2021 No. 181 P. 351-363

Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use ...

Added: October 31, 2020

Yasnitsky L., Пермь : Пермский государственный национальный исследовательский университет. – Электронные данные. , 2020

The collection contains materials from the international conference "Intelligent systems in science and technology" and the Sixth all-Russian scientific and practical conference "Artificial intelligence in solving urgent social and economic problems of the XXI century", which was held on October 12-18, 2020 in Perm as part of the Perm natural science forum "Mathematics and global ...

Added: December 4, 2020

Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...

Added: March 13, 2016

Malyshev D., Вестник Нижегородского университета им. Н.И. Лобачевского 2008 № 6 С. 141-146

Рассматривается понятие граничного класса, которое является полезным инструментом для анализа вычислительной сложности задач на графах. Исследуются два конкретных класса графов, и приводятся задачи, для которых эти классы являются граничными. ...

Added: August 31, 2012

Popkov Y., Popkov A., Dubnov Y. A., Автоматика и телемеханика 2020 № 7 С. 148-172

A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...

Added: October 31, 2020

Barcelona : IEEE, 2017

International Conference on Control, Decision and Information Technologies. ...

Added: January 17, 2018

Babash A. V., М. : ИНФРА-М, РИОР, 2013

Пособие предназначено для студентов высших учебных заведений, обучающихся по специальности «Прикладная информатика (в экономике)». Оно также содержит методический материал для ряда инновационных курсов лекций по профилю «Информационная безопасность» и может быть использовано и для блока дисциплин этого профиля. Ряд представленных результатов полезен специалистам и аспирантам, специализирующихся в указанной области. ...

Added: January 14, 2014

Lanham : University Press of America, 2012

The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...

Added: February 13, 2013

Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 3 P. 573-607

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal ...

Added: October 9, 2012

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014

Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021