Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d...

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Autores principales:	Abdulla Azamov, Gafurjan Ibragimov, Tolanbay Ibaydullaev, Idham Arif Alias
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	graph of a polyhedron differential game pursuit game evasion game game in normal form <i>π</i>-strategy Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/c13f1825f308430bbcbf73eb71f9e83f
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spelling	oai:doaj.org-article:c13f1825f308430bbcbf73eb71f9e83f2021-11-25T19:07:18ZOptimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex10.3390/sym131121702073-8994https://doaj.org/article/c13f1825f308430bbcbf73eb71f9e83f2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2170https://doaj.org/toc/2073-8994We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies.Abdulla AzamovGafurjan IbragimovTolanbay IbaydullaevIdham Arif AliasMDPI AGarticlegraph of a polyhedrondifferential gamepursuit gameevasion gamegame in normal form<i>π</i>-strategyMathematicsQA1-939ENSymmetry, Vol 13, Iss 2170, p 2170 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	graph of a polyhedron differential game pursuit game evasion game game in normal form <i>π</i>-strategy Mathematics QA1-939
spellingShingle	graph of a polyhedron differential game pursuit game evasion game game in normal form <i>π</i>-strategy Mathematics QA1-939 Abdulla Azamov Gafurjan Ibragimov Tolanbay Ibaydullaev Idham Arif Alias Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
description	We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies.
format	article
author	Abdulla Azamov Gafurjan Ibragimov Tolanbay Ibaydullaev Idham Arif Alias
author_facet	Abdulla Azamov Gafurjan Ibragimov Tolanbay Ibaydullaev Idham Arif Alias
author_sort	Abdulla Azamov
title	Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
title_short	Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
title_full	Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
title_fullStr	Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
title_full_unstemmed	Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
title_sort	optimal number of pursuers in differential games on the 1-skeleton of an orthoplex
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c13f1825f308430bbcbf73eb71f9e83f
work_keys_str_mv	AT abdullaazamov optimalnumberofpursuersindifferentialgamesonthe1skeletonofanorthoplex AT gafurjanibragimov optimalnumberofpursuersindifferentialgamesonthe1skeletonofanorthoplex AT tolanbayibaydullaev optimalnumberofpursuersindifferentialgamesonthe1skeletonofanorthoplex AT idhamarifalias optimalnumberofpursuersindifferentialgamesonthe1skeletonofanorthoplex
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Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

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