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Том 243, № 2 (2019)
- Год: 2019
- Статей: 10
- URL: https://journals.rcsi.science/1072-3374/issue/view/15036
Article
Construction of Lyapunov Functions in the Form of Pencils of Quadratic Forms
Аннотация
By using the method of alternating Lyapunov functions, we investigate the problem of regularity of linear extensions of dynamical systems on manifolds. The structures of Lyapunov functions are constructed in the form of pencils of quadratic forms.
183-191
Approximation of Solutions to the Optimal Control Problems for Systems with Maximum
Аннотация
We consider optimal control problems for nonlinear systems whose dynamics depends on the maximum of the control function and the maximum of the state over a certain time interval of prehistory. We are interested in the approximation of solutions for this kind of problems. An averaging method is developed for this purpose.
192-203
Asymptotic Behavior of Solutions of Ordinary Differential Equations of the nth Order with Regularly Varying Nonlinearities
Аннотация
We establish conditions for the existence of some classes of solutions of nonautonomous differential equations of the nth order with regularly varying nonlinearities and asymptotic representations of these solutions and their derivatives up to order n – 1; inclusively, as t ↑ ω ( ω ≤ + ∞ ).
204-229
Fundamental Solution of the Cauchy Problem for \( \left\{\overrightarrow{p},\overrightarrow{h}\right\} \)-Parabolic Systems with Variable Coefficients
Аннотация
We define a class of parabolic systems of partial differential equations and substantiate their \( \left\{\overrightarrow{p},\overrightarrow{h}\right\} \) -parabolicity. We study the properties of the spatial behavior of fundamental solutions of the Cauchy problem for \( \left\{\overrightarrow{p},\overrightarrow{h}\right\} \) -parabolic systems with time-dependent coefficients and present examples of these systems.
230-239
240-278
Optimal Morse–Smale Flows with Singularities on the Boundary of a Surface
Аннотация
We consider the optimal flows on noncompact surfaces with boundary, which have a minimum number of fixed points and all these points lie on the boundary of the surface. It is proved that the flow is optimal if it has a single sink and a single source. We describe the structures of the optimal flows on a simply connected region, on a Möbius strip, on a torus with hole, and on a Klein bottle with hole.
279-286
287-312
313-325
Periodic Matrix Boundary-Value Problems with Concentrated Delay
Аннотация
We establish necessary and sufficient conditions for the existence of solutions of a linear periodic matrix boundary-value problem for a system of differential equations with concentrated delay in the critical case. We deduce conditions for the existence of the best solution (in a sense of the least-squares method) of the linear periodic matrix boundary-value problem for a system of differential equations with concentrated delay and find this solution.
326-337
Scenarios of Transitions to Hyperchaos in Nonideal Oscillating Systems
Аннотация
We consider a class of nonideal oscillating (by Sommerfeld and Kononenko) dynamical systems and establish the existence of two types of hyperchaotic attractors in these systems. The scenarios of transitions from regular to chaotic ones attractors and the scenarios of transitions between chaotic attractors of different types are described.
338-346