Generalized transport-logistic problem as class of dynamical systems

A. S. Bugaev ; A. P. Buslaev ; V. V. Kozlov ; A. G. Tatashev ; M. V. Yashina

Matematičeskoe modelirovanie, Tome 27 (2015) no. 12, pp. 65-87.

Résumé

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.

Détail

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

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