Stability and Monotonicity of Lotka–Volterra Type Operators

Farrukh Mukhamedov; Mansoor Saburov

doi:10.1007/s12346-016-0190-3

Stability and Monotonicity of Lotka–Volterra Type Operators

Farrukh Mukhamedov
, Mansoor Saburov

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

In the present paper, we investigate stability of trajectories of Lotka–Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. It is introduced a new class of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than f-monotone LV type operators.

Original language	English
Pages (from-to)	249-267
Number of pages	19
Journal	Qualitative Theory of Dynamical Systems
Volume	16
Issue number	2
DOIs	https://doi.org/10.1007/s12346-016-0190-3
Publication status	Published - Jul 1 2017
Externally published	Yes

Keywords

Lotka–Volterra type operators
Monotone operator
Simplex
Stability
Surjection

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s12346-016-0190-3

Cite this

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abstract = "In the present paper, we investigate stability of trajectories of Lotka{\textendash}Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. It is introduced a new class of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than f-monotone LV type operators.",

keywords = "Lotka{\textendash}Volterra type operators, Monotone operator, Simplex, Stability, Surjection",

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AU - Saburov, Mansoor

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N2 - In the present paper, we investigate stability of trajectories of Lotka–Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. It is introduced a new class of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than f-monotone LV type operators.

AB - In the present paper, we investigate stability of trajectories of Lotka–Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. It is introduced a new class of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than f-monotone LV type operators.

KW - Lotka–Volterra type operators

KW - Monotone operator

KW - Simplex

KW - Stability

KW - Surjection

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UR - https://www.scopus.com/pages/publications/85024121055#tab=citedBy

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JF - Qualitative Theory of Dynamical Systems

IS - 2

ER -

Stability and Monotonicity of Lotka–Volterra Type Operators

Abstract

Keywords

ASJC Scopus subject areas

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