Stability and Monotonicity of Lotka–Volterra Type Operators

Farrukh Mukhamedov, Mansoor Saburov

Research output: Contribution to journalArticlepeer-review

19 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 languageEnglish
Pages (from-to)249-267
Number of pages19
JournalQualitative Theory of Dynamical Systems
Volume16
Issue number2
DOIs
Publication statusPublished - Jul 1 2017
Externally publishedYes

Keywords

  • Lotka–Volterra type operators
  • Monotone operator
  • Simplex
  • Stability
  • Surjection

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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