On Flows Spectrum on Closed Trio of Contours with Uniform Load

Buslaev, Alexander P.; Tatashev, A. G.; Yashina, M. V.

doi:10.29020/nybg.ejpam.v11i1.3201

Cited by 19 publications

(20 citation statements)

References 1 publication

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“…The supporter of the system is a closed chain of contours. It has been found in [3] that the dynamical system has a spectrum of velocity and mode periodicity consisted of more than one component.…”

Section: Resultsmentioning

confidence: 99%

“…A closed dynamical chain of contours is considered in [3]. A cluster of the same length moves on each contour.…”

Section: Closed Chain Of Three Contours With Continual Clustersmentioning

confidence: 99%

“…Hypotheses, characterizing the motion on the closed chain of contours, have been formulated in [3]. If the quantity of contours is not less than 6, then the spectrum of velocities can contain more than one value.…”

Section: Closed Chain Of Three Contours With Continual Clustersmentioning

confidence: 99%

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Spectra of Local Cluster Flows on Open Chain of Contours

Buslaev¹,

Tatashev²

2018

Eur. J. Pure Appl. Math.

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A dynamical system is considered. This dynamical system is a flow of clusters with the same length $l$ on contours of unit length connected into open chain. A similar system such that contours of this system are connected into closed chain was considered earlier. It has been found that, in the case of closed chain of contours, the dynamical system has a spectrum of velocity and mode periodicity consisted of more than one component. In this paper, it has been shown that, in the case of open chain, the spectrum of cluster velocity and mode periodicity contains only one component.The conditions of self-organization and the dependence of cluster velocity on load $l$ is developed.

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Section: Resultsmentioning

confidence: 99%

“…A closed dynamical chain of contours is considered in [3]. A cluster of the same length moves on each contour.…”

Section: Closed Chain Of Three Contours With Continual Clustersmentioning

confidence: 99%

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Spectra of Local Cluster Flows on Open Chain of Contours

Buslaev¹,

Tatashev²

2018

Eur. J. Pure Appl. Math.

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“…Under the rule of opposition, the spectrum of average particle velocities over time consists of the values With a fair rule, the system enters a state of free movement over time with a finite mathematical expectation. In [16], a continuous system was studied, similar to the system considered in [14]. Proof.…”

Section: Spectrum 0f Closed Chain In the Case Of Deterministic Competmentioning

confidence: 99%

Analysis of flow dynamics on Buslaev contour networks

Yashina

Tatashev

2019

PEN

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Traffic flow models on networks are relevant because of exponential growth of road transport in megalopolises worldwide. But there are not enough adequate approaches to describe such processes. Buslaev A.P. with co-authors had introduced networks of contours with common nodes, local particles movement on each contour in given direction and competition resolution rules in common nodes. The problem is to study limit system behavior in dependence on initial conditions. In mathematical models of communication systems and computer networks, particles correspond to messages or information blocks (message packages). Behavior of particles on a contour chain with two cells on each contour is similar to behavior of Ising model used in quantum mechanics. In particular, Ising model is used for modeling of behavior of experimental computers based on principles of quantum mechanics. Contour network models can be used for study of spectral quantization. We study a behavior contour networks of Buslaev type for regular cases depending on rules of competition resolutions in common nodes. Exact results were obtained for closed chain with opposite and oddeven resolution rules, and stochastic version of left-priority rule with non-zero probability of indecisive movement.

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“…20,23 Contours networks with regular periodic structures were studied in Buslaev et al 19,21,22 These contours networks are the closed chain of contours 19,21 and the open chain of contours. 22 It was assumed in Buslaev et al 19,21,22 that the nodes divide each contour into parts of the same length. This paper considers a pair of discrete contours with two nodes, which divide each contour into nonequal parts.…”

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confidence: 99%

Spectral cycles and average velocity of clusters in discrete two‐contours system with two nodes

Yashina

Tatashev

2020

Math Meth Appl Sci

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The paper considers a discrete dynamical system containing two contours. There are n cells and m particles in each contour. At any time, the particles of each contour form a cluster. There are two common points of the contours. These common points are called nodes. The nodes divide the contours into two nonequal parts. The system belongs to the class of dynamical systems introduced by A. P. Buslaev. In these systems, the movement of particles (clusters) can be interpreted as the mass transfer on regular networks. A cyclic trajectory in the system state space is called a spectral cycle. The system state space is divided into sets such that any of this set contains the states of the spectral cycle and the nonrecurrent states from which the system results in the set of the spectral cycle states. We have found that, in the general case, what spectral cycle is realized and with what average velocity the clusters move depends on the initial state of the system. We have found the set of spectral cycles and the values of the clusters average velocities taking into account the delays due to that the clusters cannot pass through the same node simultaneously. In one of two considered versions of the system, the clusters move counterclockwise (one‐directional movement). In the other version, one of the clusters moves clockwise and the other cluster moves counterclockwise (codirectional movement). It is turned out that the behavior of system is significantly different in these versions. In particular, in the case of the codirectional movement, the average clusters velocity does not depend on the initial state.

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On Flows Spectrum on Closed Trio of Contours with Uniform Load

Cited by 19 publications

References 1 publication

Spectra of Local Cluster Flows on Open Chain of Contours

Spectra of Local Cluster Flows on Open Chain of Contours

Analysis of flow dynamics on Buslaev contour networks

Spectral cycles and average velocity of clusters in discrete two‐contours system with two nodes

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