Численное моделирование репликаторных систем специального вида
Background Replicator systems often arise when evolution is concerned. Mathematical models of population dynamics, game theory, economics and biological and molecular evolution lead to the systems of partial differential equations. Due to the absence of analytical solutions for the vast majority of such problems, approximate solutions obtained via numerical simulation are required. Hence, construction of efficient algorithms for the solution of spatial and time-dependent replicator systems is crucial for understanding the dynamics and properties of evolution. Results We give an overview of existing approaches to numerical simulation of replicator systems arising in various fields. We describe a mathematical model of population dynamics with explicit space in game theory setting with asymmetric conflict and a model of biological evolution in presence of a mutator-gene. Both models lead to nonlinear systems of partial differential equations that we cast to the same general form. Then we describe the numerical method based on finite volume framework to solve the system, and provide some numerical examples that demonstrate the method’s validity. Conclusions We conclude that constructed numerical method is suitable for simulation of replicator systems of general form.
The collection of materials of the International Conference
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. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.
In discrete time, asymptotic dynamics in the neighborhood of mixed equilibrium excludes coordination. However, this result is possible given specific payoff matrices. This paper considers characteristics of payoff matrices under which iterative process never converges to a mixed equilibrium, even if it starts from this. This suggests that asymptotically stability can be inherent to only pure equilibria. If sum of equilibrium mixed strategies is not equal to unity there is not convergence to a mixed equilibrium. From the standpoint of total payoff this means that a small change of the payoff matrix should result in that given any initial strategy distribution players acheive coordination and the related payoffs.
The paper presents a framework for numerical simulation that allows you to ensure saving of resources due to the numerical selection of the optimal size and temperatures in the preparation of bimetallic castings. Modeling obtained boundary and initial conditions at which the metal parts submelting first layer in the contact area with the second layer and is saved in the unmelted state of the first layer with a thickness of 1.5-2 mm, which is in contact with the mold.
In the present study, issues related to the hydrogeology of the basin of the Volga River from Rybinsk to Cheboksary Reservoir are reviewed and analyzed, evaluation of the current state of hydrogeology reservoirs on various parameters is performed. It is revealed that the erosion processes in the basin of the Gorky Reservoir has an average intensity in comparison with similar processes in the basins of the Rybinsk and Cheboksary reservoirs, but the activity is presented. Particular attention to the processes of erosion and shoreline erosion of the Gorky Reservoir is given. The mathematical and numerical model of the slope stability coefficient is presented.
A new mathematical model of heat transfer in silicon field emission pointed cathode of small dimensions is constructed which permits taking its partial melting into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type problems. The approach used by the authors is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the obtained mathematical model including its parallel implementation. The results of numerical simulation conclude the book.
The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.
In the present work the results of different scenario of the cliff of Cape Canaille hypothetic collapse (South of France) are presented. Three scenarios were considered: falling of one block, falling of several blocks in one time and debris flow avalanche. The analysis of the entire scenario was done.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l 2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l 2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.