scholarly journals ON A PLANAR DYNAMICAL SYSTEM ARISING IN THE NETWORK CONTROL THEORY

2016 ◽  
Vol 21 (3) ◽  
pp. 385-398 ◽  
Author(s):  
Svetlana Atslega ◽  
Dmitrijs Finaskins ◽  
Felix Sadyrbaev
Keyword(s):  
Dynamical System ◽  
Control Theory ◽  
Network Control ◽  
Two Dimensional ◽  
Planar Dynamical System ◽  
Attracting Set ◽  
Dimensional Dynamical System

We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

scholarly journals Asymptotic (statistical) periodicity in two-dimensional maps

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fumihiko Nakamura ◽  
Michael C. Mackey
Keyword(s):  
Dynamical System ◽  
Bounded Variation ◽  
High Dimensional ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Function Of Bounded Variation ◽  
Dimensional Dynamical System ◽  
Asymptotic Periodicity ◽  
Parameter Values

<p style='text-indent:20px;'>In this paper we give a new sufficient condition for the existence of asymptotic periodicity of Frobenius–Perron operators corresponding to two–dimensional maps. Asymptotic periodicity for strictly expanding systems, that is, all eigenvalues of the system are greater than one, in a high-dimensional dynamical system was already known. Our new result enables one to deal with systems having an eigenvalue smaller than one. The key idea for the proof is to use a function of bounded variation defined by line integration. Finally, we introduce a new two-dimensional dynamical system numerically exhibiting asymptotic periodicity with different periods depending on parameter values, and discuss the application of our theorem to the example.</p>

scholarly journals STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

2011 ◽  
Vol 11 (04) ◽  
pp. 715-752
Author(s):  
VLADIMIR BELITSKY ◽  
ANTONIO LUIZ PEREIRA ◽  
FERNANDO PIGEARD DE ALMEIDA PRADO
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Asset Price ◽  
Excess Demand ◽  
Market Model ◽  
Asset Market ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Dimensional Dynamical System ◽  
Demand Fluctuations

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system's parameters correspond to: (a) the proportion of speculators in a market; (b) the traders' speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset's fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

scholarly journals Application of Szebehely’s Inverse Problem to Non-Stationary Dynamical Systems

1993 ◽  
Vol 132 ◽  
pp. 373-377
Author(s):  
G.T. Omarova ◽  
T.S. Kozhanov
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Variable Mass ◽  
Linear Partial Differential Equation ◽  
Two Dimensional ◽  
Stationary Potential ◽  
First Order ◽  
Dimensional Dynamical System

AbstractA first-order linear partial differential equation is presented, giving the non-stationary potential functions U=U (x,y,t) which give rise to a given family of evoling planar orbits f(x,y,t) = c in two-dimensional dynamical system. It is shown, that this equation is applied in celestial mechanics of variable mass.

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