On dynamics of quadratic stochastic operators: a survey

We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m-1)-dimensional simplex, where l∈{0,1,...,m}. The l-Volterra operator is a Volterra operator if and only if l=m. We study the structure of the set of all Volterra and l-Volterra operators and desc...
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Autor*in:	Akbar Zada [verfasserIn] Syed Omar Shah [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch ; Französisch

Erschienen:	2017

Schlagwörter:	Quadratic stochastic operator fixed point trajectory Volterra and non-Volterra operators

Übergeordnetes Werk:	In: Surveys in Mathematics and its Applications - University Constantin Brancusi of Targu-Jiu, 2008, 12 (2017)(2017), Seite 117-164
Übergeordnetes Werk:	volume:12 (2017) ; year:2017 ; pages:117-164

Links:	Link aufrufen Link aufrufen Journal toc Journal toc

Katalog-ID:	DOAJ024354228

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520			\|a We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m-1)-dimensional simplex, where l∈{0,1,...,m}. The l-Volterra operator is a Volterra operator if and only if l=m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m=2 and m=3 we describe behavior of trajectories of (m-1)-Volterra operators. We also mention many remarks with comparisons of l-Volterra operators and Volterra ones. Also we discuss the dynamics of separable quadratic stochastic operators.
650		4	\|a Quadratic stochastic operator
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650		4	\|a Volterra and non-Volterra operators
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language	English French
source	In Surveys in Mathematics and its Applications 12 (2017)(2017), Seite 117-164 volume:12 (2017) year:2017 pages:117-164
sourceStr	In Surveys in Mathematics and its Applications 12 (2017)(2017), Seite 117-164 volume:12 (2017) year:2017 pages:117-164
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topic_facet	Quadratic stochastic operator fixed point trajectory Volterra and non-Volterra operators Mathematics
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container_title	Surveys in Mathematics and its Applications
authorswithroles_txt_mv	Akbar Zada @@aut@@ Syed Omar Shah @@aut@@
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callnumber-first	Q - Science
author	Akbar Zada
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topic_title	QA1-939 On dynamics of quadratic stochastic operators: a survey Quadratic stochastic operator fixed point trajectory Volterra and non-Volterra operators
topic	misc QA1-939 misc Quadratic stochastic operator misc fixed point misc trajectory misc Volterra and non-Volterra operators misc Mathematics
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title	On dynamics of quadratic stochastic operators: a survey
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title_sort	on dynamics of quadratic stochastic operators: a survey
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title_auth	On dynamics of quadratic stochastic operators: a survey
abstract	We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m-1)-dimensional simplex, where l∈{0,1,...,m}. The l-Volterra operator is a Volterra operator if and only if l=m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m=2 and m=3 we describe behavior of trajectories of (m-1)-Volterra operators. We also mention many remarks with comparisons of l-Volterra operators and Volterra ones. Also we discuss the dynamics of separable quadratic stochastic operators.
abstractGer	We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m-1)-dimensional simplex, where l∈{0,1,...,m}. The l-Volterra operator is a Volterra operator if and only if l=m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m=2 and m=3 we describe behavior of trajectories of (m-1)-Volterra operators. We also mention many remarks with comparisons of l-Volterra operators and Volterra ones. Also we discuss the dynamics of separable quadratic stochastic operators.
abstract_unstemmed	We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m-1)-dimensional simplex, where l∈{0,1,...,m}. The l-Volterra operator is a Volterra operator if and only if l=m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m=2 and m=3 we describe behavior of trajectories of (m-1)-Volterra operators. We also mention many remarks with comparisons of l-Volterra operators and Volterra ones. Also we discuss the dynamics of separable quadratic stochastic operators.
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title_short	On dynamics of quadratic stochastic operators: a survey
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