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Tkhai V.N.,RAS Trapeznikov Institute of Control Sciences
Automation and Remote Control | Year: 2013

Consideration was given to the model with coupled subsystems. In the absence of relations between the subsystems, the MIS falls down into independent systems of autonomous ordinary differential equations. In the structure of the entire system, the subsystems make up hierarchical levels. Sun-planets- satellites, interacting moving objects, and so on exemplify the models with coupled subsystems. The problem of studying dynamics of such models was posed. The following natural approach to their analysis was proposed: classification of the subsystems by types (dynamic properties), specification of various bundles of subsystems, and subsequent analysis of these bundles. Realization of the approach to oscillations, stability, stabilization, bifurcation, and resonance was given. These problems were solved for the model with coupled subsystems having two second-kind subsystems in the basic combination of the oscillation modes in the subsystem. © 2013 Pleiades Publishing, Ltd. Source


Tkhai V.N.,RAS Trapeznikov Institute of Control Sciences
Automation and Remote Control | Year: 2015

Consideration was given to the model containing coupled subsystems (MCCS). In the absence of coupling, MCCS falls down into independent subsystems represented by autonomous ordinary differential equations (ODE). In the structure of the entire system its subsystems make up hierarchical levels. The autonomous MCCS was studied. The “cycle or family of periodic motions” alternative was shown to be always realized by an individual system in a nondegenerate situation. For the main mode of oscillations, a scenario was given for bifurcation of the family of all families of periodic solutions arising with generation of the MCCS cycles. Consideration was given to stability of cycles, and the problem of their stabilization was solved. © 2015, Pleiades Publishing, Ltd. Source


Tkhai V.N.,RAS Trapeznikov Institute of Control Sciences
Automation and Remote Control | Year: 2011

Consideration was given to the single-frequency oscillations of a periodic system allied to the nonlinear autonomous system. The publications of the present author demonstrated that the period on the family of oscillations of the autonomous system usually depends only on a single parameter. At that, the points of the family are divided into the ordinary (the derivative with respect to the period in parameter is other than zero) and critical (this derivative vanishes) points. Origination of oscillations at the critical point was studied. It was established that at least two resonance oscillations are generated. The first part of the paper considered the ordinary point. © Pleiades Publishing, Ltd., 2011. Source


Breer V.V.,RAS Trapeznikov Institute of Control Sciences
Automation and Remote Control | Year: 2012

We consider a certain game-theoretic model of non-anonymous threshold conformity behavior over binary action sets of the players. For a given player, non-anonymity implies different level of confidence in the neighbors. The notions of conformity and autonomy are briefly analyzed; the corresponding game-theoretic threshold model is built to describe counteraction of these phenomena. Nash equilibria characterizing the conformity behavior are derived. Finally, characteristic conditions of the Nash equilibria are studied, and structure of the equilibria is described. © Pleiades Publishing, Ltd., 2012. Source


Zhilyakova L.Yu.,RAS Trapeznikov Institute of Control Sciences
Automation and Remote Control | Year: 2012

We study stabilization processes in resource networks with arbitrary topology for large values of the resource, when certain vertices accumulate the resource, and resource in these vertices exceeds output bandwidth. We introduce the notion of flow in a network and study monotone and nonmonotone flows. We prove existence and uniqueness for the limit flow and, as a corollary, of the limit state. We introduce the notion of a potential attractor and study networks with one and several attractors. We show that in networks with several potential attractors, in case of large resources the limit state depends on the initial state. © Pleiades Publishing, Ltd., 2012. Source

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