A model of information warfare in a society when one of the parties periodically destabilizes the system by a short-term jump-wise increase in the intensity of the propaganda in the media is analyzed. The model has the form of two nonlinear ordinary differential equations with a periodic discontinuous right-hand side. The asymptotical solution to the periodic solutions are constructed for the case of low-intensity dissemination of information through interpersonal communication. The transient regime is investigated numerically
Abstract. Associative Yang-Baxter equation arises in different areas of algebra, e.g., when studying double quadratic Poisson brackets, non-abelian quadratic Poisson brack- ets, or associative algebras with cyclic 2-cocycle (anti-Frobenius algebras). Precisely, faithful representations of anti-Frobenius algebras (up to isomorphism) are in one-to-one correspondence with skew-symmetric solutions of associative Yang-Baxter equation (up to equivalence). Following the work of Odesskii, Rubtsov and Sokolov and using comput- er algebra system Sage, we found some constant skew-symmetric solutions of associative Yang-Baxter equation and construct corresponded non-abelian quadratic Poisson brack- ets.
In this article we propose the description and the rationale of the heuristic approach, which can be used in applied dynamic economic models containing agents' optimization problems. Solution of these problems leads to a system containing differential and algebraic equations, inequalities and complementary slackness conditions. These conditions significantly complicate the analysis of such models even on the calibration stage. In this article we show how the natural assumption of the alternation of regimes, which are defined by a way of complementary slackness conditions resolution, leads to relations which are more regular and convenient from the point of model calibration.
This paper is devoted to developing a system of models of information dissemination in society. As a superstructure for the base model, four new mechanisms that have an effect on information disseminating are proposed. For the model with these four echanisms, sufficient conditions of the stability of the nonadherent state are obtained
Based on the well-known model of monopolistic competition by Melitz with a finite number of firms, we built a number of dynamic models, designed to clarify the dynamic behavior of the original construction. Two variants of the formal Melitz dynamic model are presented, with the quasi-steady state found in one of them. Also, the models with the creation of new firms at the cost of labor and product are presented. We found that in the latter, under certain conditions on the parameters of the economy there is superexponential growth. We calculate the equilibrium states of the models and compare them.
In this paper, a mathematical model is developed for information warfare in society whereby an individual chooses between two suggested viewpoints. The model is based on the traditional Rashevsky framework of imitative behavior. A primary analysis of the model is conducted. The model has the form of a nonlinear integro-differential equation in which the unknown function is under the sign of the derivative and within the integration limit and acts as an argument of an exogenously given function.
A linear infinite-dimensional mathematical model of a hierarchical system is considered in which there is a sequential excitation transfer from the upper to the lower levels and where the phenomenon of filling levels in finite time is possible, which is typical of explosive processes. A substantiated model of simulation modeling is suggested and test calculations are performed
The paper is devoted to the problem of stabilizing a linear stochastic control system. Thequadratic cost functional measures the total loss caused by deviation from the fixed (target) levels and control trajectories, as well as a decision-maker’s time preferences expressed in the discount function. The long-term impacts of the use of decision-making, optimal on average, over an infinite-time horizon are taken as estimates of the deviation of the optimal trajectory from its target in the mean square sense and with the probability of 1.
The work is devoted to fundamental aspects of the classical molecular dynamics method, which was developed half a century ago as a means of solving computational problems in statistical physics and has now become one of the most important numerical methods in the theory of condensed state. At the same time, the molecular dynamics method based on solving the equations of motion for a multiparticle system proved to be directly related to the basic concepts of classical statistical physics, in particular, to the problem of the occurrence of irreversibility. This paper analyzes the dynamic and stochastic properties of molecular dynamics systems connected with the local instability of trajectories and the errors of the numerical integration. The probabilistic nature of classical statistics is discussed. We propose a concept explaining the finite dynamic memory time and the emergence of irreversibility in real systems.
We propose a description and explanation of a heuristic approach that can be used in applied dynamic economic models containing agent optimization problems. Solving such problems, we can obtain a system containing differential and algebraic equations, inequalities, and complementary slackness conditions. These conditions significantly complicate the analysis of such models even at the calibration stage. We show that the natural assumption about the alternation of regimes defined by the method of the resolution of the complementary slackness conditions allows us to pass to relations that are more regular and convenient from the point of view of the model’s calibration.
In this article model of intertemporal equilibrium of two agents (a firm-producer and a proprietor-consumer) is presented. Its distinguishing feature is the description of the firm as a joint stock company, the purpose of which is to maximize the present value of dividends paid. A complete solution for all initial conditions is obtained. It is shown that the equilibrium in the model is effective.