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Matem. Mod., 2015, Volume 27, Number 12, Pages 65–87 (Mi mm3679)  

Generalized transport-logistic problem as class of dynamical systems

A. S. Bugaeva, A. P. Buslaevb, V. V. Kozlovc, A. G. Tatashevd, M. V. Yashinad

a Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences
b Moscow Automobile and Road State Technical University (MADI)
c Steklov Mathematical Institute of Russian Academy of Sciences
d Moscow Technical University of Communications and Informatics (MTUCI)

Abstract: Dynamical systems on network with discrete set of states and discrete time are considered. Sites, channels and particles are forming an abstract model of mass transport, information and so on, on the one hand, and another, they are forming dynamical system of deterministic or stochastic type. State of the system in the following discrete instant of time $S(T+1)$ is defined by transformation of the state at the moment $S(T)$ with given rules $L$, $S(T+1)=L(S(T))$. In this case, $S(T+1)$ does not necessarily belong to the admissible states set $A$. Then "judicial system" is activated, i.e. operator $P$ such that projects $S(T+1)$ to $A$. Thus, $S(T+1)=\{L(S(T))$, if $L(S(T))$ belongs $A$; $PL(S(T))$, if $L(S(T))$ does not belong $A\}$. Properties of these systems are researched, and applications for transport problems are discussed.

Keywords: discrete dynamical systems, transport-logistic problem, Markov chains.

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Document Type: Article
UDC: 517
Received: 09.02.2015

Citation: A. S. Bugaev, A. P. Buslaev, V. V. Kozlov, A. G. Tatashev, M. V. Yashina, “Generalized transport-logistic problem as class of dynamical systems”, Matem. Mod., 27:12 (2015), 65–87

Citation in format AMSBIB
\Bibitem{BugBusKoz15}
\by A.~S.~Bugaev, A.~P.~Buslaev, V.~V.~Kozlov, A.~G.~Tatashev, M.~V.~Yashina
\paper Generalized transport-logistic problem as class of dynamical systems
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 12
\pages 65--87
\mathnet{http://mi.mathnet.ru/mm3679}
\elib{http://elibrary.ru/item.asp?id=25707588}


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