Spectrum of continuous two-contours system

Tatashev, A. G.; Yashina, M. V.

doi:10.1051/itmconf/20192401014

Cited by 5 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main problems include finding the average velocity of motion of the clusters (particles), finding conditions for the system to enter a state of free-flow traffic (from some time instant on, all clusters move without delays at the current instant and in the future) or a state of traffic breakdown (the motion of the particles ceases completely), and choosing a rule of competition settlement that is best-suited to maximize the average velocity of motion. Analytical results were obtained for two-contour systems with one [12][13][14][15] or two [16][17][18][19] nodes, for systems with several contours and one common node [20] and for contour networks with regular periodic one-dimensional [21][22][23][24] or two-dimensional [25][26][27] contour systems.…”

Section: Introductionmentioning

confidence: 99%

A Two-Contour System with Two Clusters of Different Lengths

Yashina¹,

Tatashev²

2021

Nelin. Dinam.

View full text Add to dashboard Cite

A system belonging to the class of dynamical systems such as Buslaev contour networks is investigated. On each of the two closed contours of the system there is a segment, called a cluster, which moves with constant velocity if there are no delays. The contours have two common points called nodes. Delays in the motion of the clusters are due to the fact that two clusters cannot pass through a node simultaneously. The main characteristic we focus on is the average velocity of the clusters with delays taken into account. The contours have the same length, taken to be unity. The nodes divide each contour into parts one of which has length d, and the other, length 1-d. Previously, this system was investigated under the assumption that the clusters have the same length. It turned out that the behavior of the system depends qualitatively on how the directions of motion of the clusters correlate with each other. In this paper we explore the behavior of the system in the case where the clusters differ in length.

show abstract

Section: Introductionmentioning

confidence: 99%

A Two-Contour System with Two Clusters of Different Lengths

Yashina¹,

Tatashev²

2021

Nelin. Dinam.

View full text Add to dashboard Cite

show abstract

“…The common point of the contours is called the node . A continuous version of two‐cotours system was studied in …”

Section: Introductionmentioning

confidence: 99%

“…A continuous version of two-cotours system was studied in. 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.…”

mentioning

confidence: 99%

See 1 more Smart Citation

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

Yashina

Tatashev

2020

Math Meth Appl Sci

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Spectrum of flows on discrete pair of contours

Tatashev

Yashina

2019

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

We consider a deterministic discrete dynamical system, which is a contour network of Buslaev type. This system contains two contours. The ith contour contains Ni cells, i = 1, 2. There is a cluster of particles on each contour moving in accordance with given rules. The clusters contain 1 ≤ M 1 < N 1 and 1 ≤ M 2 < N 2 particles respectively. There is no more than one particle in each cell at any time. There is a common point (node) of the contours. Particles cannot cross the node simultaneously. A set of repeating system states is called a spectral cycle. Average velocities of clusters correspond to spectral cycles. The set of spectral cycles and values of the average velocities have been found.

show abstract

Spectrum of continuous two-contours system

Cited by 5 publications

References 21 publications

A Two-Contour System with Two Clusters of Different Lengths

A Two-Contour System with Two Clusters of Different Lengths

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

Spectrum of flows on discrete pair of contours

Contact Info

Product

Resources

About