Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Том 223, № 3 (2017)
- Жылы: 2017
- Мақалалар: 12
- URL: https://journals.rcsi.science/1072-3374/issue/view/14829
Article
199-209
210-222
223-231
Periodic Solutions and Their Properties for Systems of Functional-Differential Equations with Parameter
Аннотация
We establish sufficient conditions for the existence of periodic solutions for systems of nonlinear functional-differential equations with deviations of the argument and a small parameter ε. We also study the properties of these solutions as ε → 0.
232-256
On the Unique Solvability of a Nonlinear Nonlocal Boundary-Value Problem for Systems of Second-Order Functional Differential Equations
Аннотация
We establish some optimal, in a certain sense, general conditions sufficient for the unique solvability of the boundary-value problem for a system of nonlinear second-order functional differential equations. The considered class of equations covers, in particular, equations of the neutral type. Specific example is presented to illustrate the general theory.
257-272
Existence of an Invariant Torus for a Degenerate Linear Extension of Dynamical Systems
Аннотация
Under the assumptions that a degenerate system defined on the direct product of a torus and a Euclidean space can be reduced to a central canonical form and that the corresponding homogeneous nondegenerate system is exponentially dichotomous on the semiaxes, we establish a necessary and sufficient condition for the existence of a unique invariant torus of the degenerate linear system. We also establish conditions for the preservation of an asymptotically stable invariant toroidal manifold for a degenerate linear extension of the dynamical system on a torus under small perturbations in the set of nonwandering points.
273-284
One Numerical Realization of a Generalized Model of World Dynamics and Sustainable Development
Аннотация
We present a modification of the Forrester model of world dynamics. A new characteristic that describes the discontent with the development is introduced in each level of the model. It is shown that the proposed model may have a limit cycle.
285-292
Specific Features of the Dynamic Behavior of a Straight Pipeline for Supercritical Velocities of the Flow of Liquid
Аннотация
We study specific features of the behavior of a straight pipeline in the case where the velocity of flowing liquid varies within the subcritical or supercritical range. On the basis of a model that takes into account four modes of vibration and the Coriolis force, we study the ranges of stability of vibrations of the straight pipeline. We discover new dynamical modes of the behavior of pipeline in the supercritical case. The numerical simulation performed within the framework of the 12-mode model confirms the obtained qualitative results. We also reveal the specific character of the action of the Coriolis force for supercritical modes of the flow of liquid in the pipeline.
293-297
Boundary-Value Problems for the Lyapunov Equation in Banach Spaces
Аннотация
We propose an approach to the construction of solutions and quasisolutions of a boundary-value problem for the Lyapunov equation in a Banach space. If the necessary and sufficient conditions for the solvability of this boundary-value problem are satisfied, then the corresponding solutions of the problem are constructed by using the generalized inverse operator. As an example, we consider the problem in the space of bounded sequences with countably dimensional matrices.
298-304
305-310
Asymptotic Expansions of Eigenfunctions and Eigenvalues of the Steklov Spectral Problem in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions
Аннотация
We consider a Steklov spectral problem for an elliptic differential equation with rapidly oscillating coefficients for thin perforated domains with rapidly varying thickness. We describe asymptotic algorithms for the solution of problems of this kind for thin perforated domains with different limit dimensions. We also establish asymptotic estimates for eigenvalues of the Steklov spectral problem for thin perforated domains with different limit dimensions. For certain symmetry conditions imposed on the structure of thin perforated domain and on the coefficients of differential operators, we construct and substantiate asymptotic expansions for eigenfunctions and eigenvalues.
311-336
Weakly Nonlinear Matrix Boundary-Value Problem in the Case of Parametric Resonance
Аннотация
We establish necessary and sufficient conditions for the existence of solutions of a nonlinear matrix boundary-value problem for a system of ordinary differential equations in the case of parametric resonance. We construct a convergent iterative scheme for finding approximate solutions of the problem. As an example of application of the proposed iterative scheme, we obtain approximations to the solutions of a periodic boundary-value problem for the Riccati-type equation with parametric perturbation. To check the accuracy of the obtained approximations, we introduce residuals in the original equation.
337-350